03-Gaussians.ipynb

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   "source": [
    "[Table of Contents](./table_of_contents.ipynb)"
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   "source": [
    "# Probabilities, Gaussians, and Bayes' Theorem"
   ]
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   "source": [
    "%matplotlib inline"
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   "source": [
    "#format the book\n",
    "import book_format\n",
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    "## Introduction\n",
    "\n",
    "The last chapter ended by discussing some of the drawbacks of the Discrete Bayesian filter. For many tracking and filtering problems our desire is to have a filter that is *unimodal* and *continuous*. That is, we want to model our system using floating point math (continuous) and to have only one belief represented (unimodal). For example, we want to say an aircraft is at (12.34, -95.54, 2389.5) where that is latitude, longitude, and altitude. We do not want our filter to tell us \"it might be at (1.65, -78.01, 2100.45) or it might be at (34.36, -98.23, 2543.79).\" That doesn't match our physical intuition of how the world works, and as we discussed, it can be prohibitively expensive to compute the multimodal case. And, of course, multiple position estimates makes navigating impossible.\n",
    "\n",
    "We desire a unimodal, continuous way to represent probabilities that models how the real world works, and that is computationally efficient to calculate. Gaussian distributions provide all of these features."
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    "## Mean, Variance, and Standard Deviations\n",
    "\n",
    "Most of you will have had exposure to statistics, but allow me to cover this material anyway. I ask that you read the material even if you are sure you know it well. I ask for two reasons. First, I want to be sure that we are using terms in the same way. Second, I strive to form an intuitive understanding of statistics that will serve you well in later chapters. It's easy to go through a stats course and only remember the formulas and calculations, and perhaps be fuzzy on the implications of what you have learned.\n",
    "\n",
    "### Random Variables\n",
    "\n",
    "Each time you roll a die the *outcome* will be between 1 and 6. If we rolled a fair die a million times we'd expect to get a one 1/6 of the time. Thus we say the *probability*, or *odds* of the outcome 1 is 1/6. Likewise, if I asked you the chance of 1 being the result of the next roll you'd reply 1/6.  \n",
    "\n",
    "This combination of values and associated probabilities is called a [*random variable*](https://en.wikipedia.org/wiki/Random_variable). Here *random* does not mean the process is nondeterministic, only that we lack information about the outcome. The result of a die toss is deterministic, but we lack enough information to compute the result. We don't know what will happen, except probabilistically.\n",
    "\n",
    "While we are defining terms, the range of values is called the [*sample space*](https://en.wikipedia.org/wiki/Sample_space). For a die the sample space is {1, 2, 3, 4, 5, 6}. For a coin the sample space is {H, T}. *Space* is a mathematical term which means a set with structure. The sample space for the die is a subset of the natural numbers in the range of 1 to 6.\n",
    "\n",
    "Another example of a random variable is the heights of students in a university. Here the sample space is a range of values in the real numbers between two limits defined by biology.\n",
    "\n",
    "Random variables such as coin tosses and die rolls are *discrete random variables*. This means their sample space is represented by either a finite number of values or a countably infinite number of values such as the natural numbers. Heights of humans are called *continuous random variables* since they can take on any real value between two limits.\n",
    "\n",
    "Do not confuse the *measurement* of the random variable with the actual value. If we can only measure the height of a person to 0.1 meters we would only record values from 0.1, 0.2, 0.3...2.7, yielding 27 discrete choices. Nonetheless a person's height can vary between any arbitrary real value between those ranges, and so height is a continuous random variable. \n",
    "\n",
    "In statistics capital letters are used for random variables, usually from the latter half of the alphabet. So, we might say that $X$ is the random variable representing the die toss, or $Y$ are the heights of the students in the freshmen poetry class. Later chapters use linear algebra to solve these problems, and so there we will follow the convention of using  lower case for vectors, and upper case for matrices. Unfortunately these conventions clash, and you will have to determine which an author is using from context. I always use bold symbols for vectors and matrices, which helps distinguish between the two."
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    "## Probability Distribution\n",
    "\n",
    "\n",
    "The [*probability distribution*](https://en.wikipedia.org/wiki/Probability_distribution) gives the probability for the random variable to take any value in a sample space. For example, for a fair six sided die we might say:\n",
    "\n",
    "|Value|Probability|\n",
    "|-----|-----------|\n",
    "|1|1/6|\n",
    "|2|1/6|\n",
    "|3|1/6|\n",
    "|4|1/6|\n",
    "|5|1/6|\n",
    "|6|1/6|\n",
    "\n",
    "We denote this distribution with a lower case p: $p(x)$. Using ordinary function notation, we would write:\n",
    "\n",
    "$$P(X{=}4) = p(4) = \\frac{1}{6}$$\n",
    "\n",
    "This states that the probability of the die landing on 4 is $\\frac{1}{6}$. $P(X{=}x_k)$ is notation for \"the probability of $X$ being $x_k$\". Note the subtle notational difference. The capital $P$ denotes the probability of a single event, and the lower case $p$ is the probability distribution function. This can lead you astray if you are not observent. Some texts use $Pr$ instead of $P$ to ameliorate this. \n",
    "\n",
    "Another example is a fair coin. It has the sample space {H, T}. The coin is fair, so the probability for heads (H) is 50%, and the probability for tails (T) is 50%. We write this as\n",
    "\n",
    "$$\\begin{gathered}P(X{=}H) = 0.5\\\\P(X{=}T)=0.5\\end{gathered}$$\n",
    "\n",
    "Sample spaces are not unique. One sample space for a die is {1, 2, 3, 4, 5, 6}. Another valid sample space would be {even, odd}. Another might be {dots in all corners, not dots in all corners}. A sample space is valid so long as it covers all possibilities, and any single event is described by only one element.  {even, 1, 3, 4, 5} is not a valid sample space for a die since a value of 4 is matched both by 'even' and '4'.\n",
    "\n",
    "The probabilities for all values of a *discrete random value* is known as the *discrete probability distribution* and the probabilities for all values of a *continuous random value* is known as the *continuous probability distribution*.\n",
    "\n",
    "To be a probability distribution the probability of each value $x_i$ must be $x_i \\ge 0$, since no probability can be less than zero. Secondly, the sum of the probabilities for all values must equal one. This should be intuitively clear for a coin toss: if the odds of getting heads is 70%, then the odds of getting tails must be 30%. We formulize this requirement as\n",
    "\n",
    "$$\\sum\\limits_u P(X{=}u)= 1$$\n",
    "\n",
    "for discrete distributions, and as \n",
    "\n",
    "$$\\int\\limits_u P(X{=}u) \\,du= 1$$\n",
    "\n",
    "for continuous distributions.\n",
    "\n",
    "In the previous chapter we used probability distributions to estimate the position of a dog in a hallway. For example:"
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      "sum =  1.0\n"
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\n",
      "text/plain": [
       "<Figure size 800x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import kf_book.book_plots as book_plots\n",
    "\n",
    "belief = np.array([1, 4, 2, 0, 8, 2, 2, 35, 4, 3, 2])\n",
    "belief = belief / np.sum(belief)\n",
    "with book_plots.figsize(y=2):\n",
    "    book_plots.bar_plot(belief)\n",
    "print('sum = ', np.sum(belief))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each position has a probability between 0 and 1, and the sum of all equals one, so this makes it a probability distribution. Each probability is discrete, so we can more precisely call this a discrete probability distribution. In practice we leave out the terms discrete and continuous unless we have a particular reason to make that distinction."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Mean, Median, and Mode of a Random Variable\n",
    "\n",
    "Given a set of data we often want to know a representative or average value for that set. There are many measures for this, and the concept is called a [*measure of central tendency*](https://en.wikipedia.org/wiki/Central_tendency). For example we might want to know the *average* height of the students in a class. We all know how to find the average of a set of data, but let me belabor the point so I can introduce more formal notation and terminology. Another word for average is the *mean*. We compute the mean by summing the values and dividing by the number of values. If the heights of the students in meters is \n",
    "\n",
    "$$X = \\{1.8, 2.0, 1.7, 1.9, 1.6\\}$$\n",
    "\n",
    "we compute the mean as\n",
    "\n",
    "$$\\mu = \\frac{1.8 + 2.0 + 1.7 + 1.9 + 1.6}{5} = 1.8$$\n",
    "\n",
    "It is traditional to use the symbol $\\mu$ (mu) to denote the mean.\n",
    "\n",
    "We can formalize this computation with the equation\n",
    "\n",
    "$$ \\mu = \\frac{1}{n}\\sum^n_{i=1} x_i$$\n",
    "\n",
    "NumPy provides `numpy.mean()` for computing the mean."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.8"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = [1.8, 2.0, 1.7, 1.9, 1.6]\n",
    "np.mean(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a convenience NumPy arrays provide the method `mean()`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.8"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([1.8, 2.0, 1.7, 1.9, 1.6])\n",
    "x.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The *mode* of a set of numbers is the number that occurs most often. If only one number occurs most often we say it is a *unimodal* set, and if two or more numbers occur the most with equal frequency than the set is *multimodal*. For example the set {1, 2, 2, 2, 3, 4, 4, 4} has modes 2 and 4, which is multimodal, and the set {5, 7, 7, 13} has the mode 7, and so it is unimodal. We will not be computing the mode in this manner in this book, but we do use the concepts of unimodal and multimodal in a more general sense. For example, in the **Discrete Bayes** chapter we talked about our belief in the dog's position as a *multimodal distribution* because we assigned different probabilities to different positions.\n",
    "\n",
    "Finally, the *median* of a set of numbers is the middle point of the set so that half the values are below the median and half are above the median. Here, above and below is in relation to the set being sorted.  If the set contains an even number of values then the two middle numbers are averaged together.\n",
    "\n",
    "Numpy provides `numpy.median()` to compute the median. As you can see the median of {1.8, 2.0, 1.7, 1.9, 1.6} is 1.8, because 1.8 is the third element of this set after being sorted. In this case the median equals the mean, but that is not generally true."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.8"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.median(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Expected Value of a Random Variable\n",
    "\n",
    "The [*expected value*](https://en.wikipedia.org/wiki/Expected_value) of a random variable is the average value it would have if we took an infinite number of samples of it and then averaged those samples together. Let's say we have $x=[1,3,5]$ and each value is equally probable. What value would we *expect* $x$ to have, on average?\n",
    "\n",
    "It would be the average of 1, 3, and 5, of course, which is 3. That should make sense; we would expect equal numbers of 1, 3, and 5 to occur, so $(1+3+5)/3=3$ is clearly the average of that infinite series of samples. In other words, here the expected value is the *mean* of the sample space.\n",
    "\n",
    "Now suppose that each value has a different probability of happening. Say 1 has an 80% chance of occurring, 3 has an 15% chance, and 5 has only a 5% chance. In this case we compute the expected value by multiplying each value of $x$ by the percent chance of it occurring, and summing the result. For this case we could compute\n",
    "\n",
    "$$\\mathbb E[X] = (1)(0.8) + (3)(0.15) + (5)(0.05) = 1.5$$\n",
    "\n",
    "Here I have introduced the notation $\\mathbb E[X]$ for the expected value of $x$. Some texts use $E(x)$. The value 1.5 for $x$ makes intuitive sense because $x$ is far more likely to be 1 than 3 or 5, and 3 is more likely than 5 as well.\n",
    "\n",
    "We can formalize this by letting $x_i$ be the $i^{th}$ value of $X$, and $p_i$ be the probability of its occurrence. This gives us\n",
    "\n",
    "$$\\mathbb E[X] = \\sum_{i=1}^n p_ix_i$$\n",
    "\n",
    "A trivial bit of algebra shows that if the probabilities are all equal, the expected value is the same as the mean:\n",
    "\n",
    "$$\\mathbb E[X] = \\sum_{i=1}^n p_ix_i = \\frac{1}{n}\\sum_{i=1}^n x_i = \\mu_x$$\n",
    "\n",
    "If $x$ is continuous we substitute the sum for an integral, like so\n",
    "\n",
    "$$\\mathbb E[X] = \\int_{a}^b\\, xf(x) \\,dx$$\n",
    "\n",
    "where $f(x)$ is the probability distribution function of $x$. We won't be using this equation yet, but we will be using it in the next chapter.\n",
    "\n",
    "We can write a bit of Python to simulate this. Here I take 1,000,000 samples and compute the expected value of the distribution we just computed analytically."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.499952"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "total = 0\n",
    "N = 1000000\n",
    "for r in np.random.rand(N):\n",
    "    if r <= .80: total += 1\n",
    "    elif r < .95: total += 3\n",
    "    else: total += 5\n",
    "\n",
    "total / N"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can see that the computed value is close to the analytically derived value. It is not exact because getting an exact values requires an infinite sample size."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "\n",
    "What is the expected value of a die roll?\n",
    "\n",
    "### Solution\n",
    "\n",
    "Each side is equally likely, so each has a probability of 1/6. Hence\n",
    "$$\\begin{aligned}\n",
    "\\mathbb E[X] &= 1/6\\times1 + 1/6\\times 2 + 1/6\\times 3 + 1/6\\times 4 + 1/6\\times 5 + 1/6\\times6 \\\\\n",
    "&= 1/6(1+2+3+4+5+6)\\\\&= 3.5\\end{aligned}$$\n",
    "\n",
    "### Exercise\n",
    "\n",
    "Given the uniform continuous distribution\n",
    "\n",
    "$$f(x) = \\frac{1}{b - a}$$\n",
    "\n",
    "compute the expected value for $a=0$ and $b=20$.\n",
    "\n",
    "### Solution\n",
    "$$\\begin{aligned}\n",
    "\\mathbb E[X] &= \\int_0^{20}\\, x\\frac{1}{20} \\,dx \\\\\n",
    "&= \\bigg[\\frac{x^2}{40}\\bigg]_0^{20} \\\\\n",
    "&= 10 - 0 \\\\\n",
    "&= 10\n",
    "\\end{aligned}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Variance of a Random Variable\n",
    "\n",
    "The computation above tells us the average height of the students, but it doesn't tell us everything we might want to know. For example, suppose we have three classes of students, which we label $X$, $Y$, and $Z$, with these heights:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = [1.8, 2.0, 1.7, 1.9, 1.6]\n",
    "Y = [2.2, 1.5, 2.3, 1.7, 1.3]\n",
    "Z = [1.8, 1.8, 1.8, 1.8, 1.8]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using NumPy we see that the mean height of each class is the same. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.8 1.8 1.8\n"
     ]
    }
   ],
   "source": [
    "print(np.mean(X), np.mean(Y), np.mean(Z))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The mean of each class is 1.8 meters, but notice that there is a much greater amount of variation in the heights in the second class than in the first class, and that there is no variation at all in the third class.\n",
    "\n",
    "The mean tells us something about the data, but not the whole story. We want to be able to specify how much *variation* there is between the heights of the students. You can imagine a number of reasons for this. Perhaps a school district needs to order 5,000 desks, and they want to be sure they buy sizes that accommodate the range of heights of the students. \n",
    "\n",
    "Statistics has formalized this concept of measuring variation into the notion of [*standard deviation*](https://en.wikipedia.org/wiki/Standard_deviation) and [*variance*](https://en.wikipedia.org/wiki/Variance). The equation for computing the variance is\n",
    "\n",
    "$$\\mathit{VAR}(X) = \\mathbb  E[(X - \\mu)^2]$$\n",
    "\n",
    "Ignoring the square for a moment, you can see that the variance is the *expected value* for how much the sample space $X$ varies from the mean $\\mu:$ ($X-\\mu)$. I will explain the purpose of the squared term later. The formula for the expected value is $\\mathbb E[X] = \\sum\\limits_{i=1}^n p_ix_i$ so we can substitute that into the equation above to get\n",
    "\n",
    "$$\\mathit{VAR}(X) = \\frac{1}{n}\\sum_{i=1}^n (x_i - \\mu)^2$$\n",
    " \n",
    "Let's compute the variance of the three classes to see what values we get and to become familiar with this concept.\n",
    "\n",
    "The mean of $X$ is 1.8 ($\\mu_x = 1.8$) so we compute\n",
    "\n",
    "$$ \n",
    "\\begin{aligned}\n",
    "\\mathit{VAR}(X) &=\\frac{(1.8-1.8)^2 + (2-1.8)^2 + (1.7-1.8)^2 + (1.9-1.8)^2 + (1.6-1.8)^2} {5} \\\\\n",
    "&= \\frac{0 + 0.04 + 0.01 + 0.01 + 0.04}{5} \\\\\n",
    "\\mathit{VAR}(X)&= 0.02 \\, m^2\n",
    "\\end{aligned}$$\n",
    "\n",
    "NumPy provides the function `var()` to compute the variance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.02 meters squared\n"
     ]
    }
   ],
   "source": [
    "print(f\"{np.var(X):.2f} meters squared\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is perhaps a bit hard to interpret. Heights are in meters, yet the variance is meters squared. Thus we have a more commonly used measure, the *standard deviation*, which is defined as the square root of the variance:\n",
    "\n",
    "$$\\sigma = \\sqrt{\\mathit{VAR}(X)}=\\sqrt{\\frac{1}{n}\\sum_{i=1}^n(x_i - \\mu)^2}$$\n",
    "\n",
    "It is typical to use $\\sigma$ for the *standard deviation* and $\\sigma^2$ for the *variance*. In most of this book I will be using $\\sigma^2$ instead of $\\mathit{VAR}(X)$ for the variance; they symbolize the same thing.\n",
    "\n",
    "For the first class we compute the standard deviation with\n",
    "\n",
    "$$ \n",
    "\\begin{aligned}\n",
    "\\sigma_x &=\\sqrt{\\frac{(1.8-1.8)^2 + (2-1.8)^2 + (1.7-1.8)^2 + (1.9-1.8)^2 + (1.6-1.8)^2} {5}} \\\\\n",
    "&= \\sqrt{\\frac{0 + 0.04 + 0.01 + 0.01 + 0.04}{5}} \\\\\n",
    "\\sigma_x&= 0.1414\n",
    "\\end{aligned}$$\n",
    "\n",
    "We can verify this computation with the NumPy method `numpy.std()` which computes the standard deviation. 'std' is a common abbreviation for standard deviation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "std 0.1414\n",
      "var 0.0200\n"
     ]
    }
   ],
   "source": [
    "print(f\"std {np.std(X):.4f}\")\n",
    "print(f\"var {np.std(X)**2:.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And, of course, $0.1414^2 = 0.02$, which agrees with our earlier computation of the variance.\n",
    "\n",
    "What does the standard deviation signify? It tells us how much the heights vary amongst themselves. \"How much\" is not a mathematical term. We will be able to define it much more precisely once we introduce the concept of a Gaussian in the next section. For now I'll say that for many things 68% of all values lie within one standard deviation of the mean. In other words we can conclude that for a random class 68% of the students will have heights between 1.66 (1.8-0.1414) meters and 1.94 (1.8+0.1414) meters. \n",
    "\n",
    "We can view this in a plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from kf_book.gaussian_internal import plot_height_std\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plot_height_std(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For only 5 students we obviously will not get exactly 68% within one standard deviation. We do see that 3 out of 5 students are within $\\pm1\\sigma$, or 60%, which is as close as you can get to 68% with only 5 samples. Let's look at the results for a class with 100 students.\n",
    "\n",
    ">  We write one standard deviation as  $1\\sigma$, which is pronounced \"one standard deviation\", not \"one sigma\". Two standard deviations is $2\\sigma$, and so on."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean = 1.811\n",
      "std  = 0.130\n"
     ]
    }
   ],
   "source": [
    "from numpy.random import randn\n",
    "data = 1.8 + randn(100)*.1414\n",
    "mean, std = data.mean(), data.std()\n",
    "\n",
    "plot_height_std(data, lw=2)\n",
    "print(f'mean = {mean:.3f}')\n",
    "print(f'std  = {std:.3f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By eye roughly 68% of the heights lie within $\\pm1\\sigma$ of the mean 1.8, but we can verify this with code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "69.0"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum((data > mean-std) & (data < mean+std)) / len(data) * 100."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll discuss this in greater depth soon. For now let's compute the standard deviation for \n",
    "\n",
    "$$Y = [2.2, 1.5, 2.3, 1.7, 1.3]$$\n",
    "\n",
    "The mean of $Y$ is $\\mu=1.8$ m, so \n",
    "\n",
    "$$ \n",
    "\\begin{aligned}\n",
    "\\sigma_y &=\\sqrt{\\frac{(2.2-1.8)^2 + (1.5-1.8)^2 + (2.3-1.8)^2 + (1.7-1.8)^2 + (1.3-1.8)^2} {5}} \\\\\n",
    "&= \\sqrt{0.152} = 0.39 \\ m\n",
    "\\end{aligned}$$\n",
    "\n",
    "We will verify that with NumPy with"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "std of Y is 0.39 m\n"
     ]
    }
   ],
   "source": [
    "print(f'std of Y is {np.std(Y):.2f} m')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This corresponds with what we would expect. There is more variation in the heights for $Y$, and the standard deviation is larger.\n",
    "\n",
    "Finally, let's compute the standard deviation for $Z$. There is no variation in the values, so we would expect the standard deviation to be zero.\n",
    "\n",
    "$$ \n",
    "\\begin{aligned}\n",
    "\\sigma_z &=\\sqrt{\\frac{(1.8-1.8)^2 + (1.8-1.8)^2 + (1.8-1.8)^2 + (1.8-1.8)^2 + (1.8-1.8)^2} {5}} \\\\\n",
    "&= \\sqrt{\\frac{0+0+0+0+0}{5}} \\\\\n",
    "\\sigma_z&= 0.0 \\ m\n",
    "\\end{aligned}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0\n"
     ]
    }
   ],
   "source": [
    "print(np.std(Z))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before we continue I need to point out that I'm ignoring that on average  men are taller than women. In general the height variance of a class that contains only men or women will be smaller than a class with both sexes. This is true for other factors as well. Well nourished children are taller than malnourished children. Scandinavians are taller than Italians. When designing experiments statisticians need to take these factors into account. \n",
    "\n",
    "I suggested we might be performing this analysis to order desks for a school district.  For each age group there are likely to be two different means - one clustered around the mean height of the females, and a second mean clustered around the mean heights of the males. The mean of the entire class will be somewhere between the two. If we bought desks for the mean of all students we are likely to end up with desks that fit neither the males or females in the school! \n",
    "\n",
    "We will not to consider these issues in this book.  Consult any standard probability text if you need to learn techniques to deal with these issues."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Why the Square of the Differences\n",
    "\n",
    "Why are we taking the *square* of the differences for the variance? I could go into a lot of math, but let's look at this in a simple way. Here is a chart of the values of $X$ plotted against the mean for $X=[3,-3,3,-3]$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = [3, -3, 3, -3]\n",
    "mean = np.average(X)\n",
    "for i in range(len(X)):\n",
    "    plt.plot([i ,i], [mean, X[i]], color='k')\n",
    "plt.axhline(mean)\n",
    "plt.xlim(-1, len(X))\n",
    "plt.tick_params(axis='x', labelbottom=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we didn't take the square of the differences the signs would cancel everything out:\n",
    "\n",
    "$$\\frac{(3-0) + (-3-0) + (3-0) + (-3-0)}{4} = 0$$\n",
    "\n",
    "This is clearly incorrect, as there is more than 0 variance in the data. \n",
    "\n",
    "Maybe we can use the absolute value? We can see by inspection that the result is $12/4=3$ which is certainly correct — each value varies by 3 from the mean. But what if we have $Y=[6, -2, -3, 1]$? In this case we get $12/4=3$. $Y$ is clearly more spread out than $X$, but the computation yields the same variance. If we use the formula using squares we get a variance of 3.5 for $Y$, which reflects its larger variation.\n",
    "\n",
    "This is not a proof of correctness. Indeed, Carl Friedrich Gauss, the inventor of the technique, recognized that it is somewhat arbitrary. If there are outliers then squaring the difference gives disproportionate weight to that term. For example, let's see what happens if we have:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Variance of X with outlier    = 621.45\n",
      "Variance of X without outlier =   2.03\n"
     ]
    }
   ],
   "source": [
    "X = [1, -1, 1, -2, -1, 2, 1, 2, -1, 1, -1, 2, 1, -2, 100]\n",
    "print(f'Variance of X with outlier    = {np.var(X):6.2f}')\n",
    "print(f'Variance of X without outlier = {np.var(X[:-1]):6.2f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Is this \"correct\"? You tell me. Without the outlier of 100 we get $\\sigma^2=2.03$, which accurately reflects how $X$ is varying absent the outlier. The one outlier swamps the variance computation. Do we want to swamp the computation so we know there is an outlier, or robustly incorporate the outlier and still provide an estimate close to the value absent the outlier? Again, you tell me. Obviously it depends on your problem.\n",
    "\n",
    "I will not continue down this path; if you are interested you might want to look at the work that James Berger has done on this problem, in a field called *Bayesian robustness*, or the excellent publications on *robust statistics* by Peter J. Huber [4]. In this book we will always use variance and standard deviation as defined by Gauss.\n",
    "\n",
    "The point to gather from this is that these *summary* statistics always tell an incomplete story about our data. In this example variance as defined by Gauss does not tell us we have a single large outlier. However, it is a powerful tool, as we can concisely describe a large data set with a few numbers. If we had 1 billion data points we would not want to inspect plots by eye or look at lists of numbers; summary statistics give us a way to describe the shape of the data in a useful way."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gaussians\n",
    "\n",
    "We are now ready to learn about [Gaussians](https://en.wikipedia.org/wiki/Gaussian_function). Let's remind ourselves of the motivation for this chapter.\n",
    "\n",
    "> We desire a unimodal, continuous way to represent probabilities that models how the real world works, and that is computationally efficient to calculate.\n",
    "\n",
    "Let's look at a graph of a Gaussian distribution to get a sense of what we are talking about."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from filterpy.stats import plot_gaussian_pdf\n",
    "plot_gaussian_pdf(mean=1.8, variance=0.1414**2, \n",
    "                  xlabel='Student Height', ylabel='pdf');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This curve is a [*probability density function*](https://en.wikipedia.org/wiki/Probability_density_function) or *pdf* for short. It shows the relative likelihood  for the random variable to take on a value. We can tell from the chart student is somewhat more likely to have a height near 1.8 m than 1.7 m, and far more likely to have a height of 1.9 m vs 1.4 m. Put another way, many students will have a height near 1.8 m, and very few students will have a height of 1.4 m or 2.2 meters. Finally, notice that the curve is centered over the mean of 1.8 m.\n",
    "\n",
    "> I explain how to plot Gaussians, and much more, in the Notebook *Computing_and_Plotting_PDFs* in the \n",
    "Supporting_Notebooks folder. You can read it online [here](https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/Supporting_Notebooks/Computing_and_plotting_PDFs.ipynb) [1].\n",
    "\n",
    "This may be recognizable to you as a 'bell curve'. This curve is ubiquitous because under real world conditions many observations are distributed in such a manner. I will not use the term 'bell curve' to refer to a Gaussian because many probability distributions have a similar bell curve shape. Non-mathematical sources might not be as precise, so be judicious in what you conclude when you see the term used without definition.\n",
    "\n",
    "This curve is not unique to heights — a vast amount of natural phenomena exhibits this sort of distribution, including the sensors that we use in filtering problems. As we will see, it also has all the attributes that we are looking for — it represents a unimodal belief or value as a probability, it is continuous, and it is computationally efficient. We will soon discover that it also has other desirable qualities which we may not realize we desire.\n",
    "\n",
    "To further motivate you, recall the shapes of the probability distributions in the *Discrete Bayes* chapter:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import kf_book.book_plots as book_plots\n",
    "belief = [0., 0., 0., 0.1, 0.15, 0.5, 0.2, .15, 0, 0]\n",
    "book_plots.bar_plot(belief)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "They were not perfect Gaussian curves, but they were similar. We will be using Gaussians to replace the discrete probabilities used in that chapter!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Nomenclature\n",
    "\n",
    "A bit of nomenclature before we continue - this chart depicts the *probability density* of a *random variable* having any value between ($-\\infty..\\infty)$. What does that mean? Imagine we take an infinite number of infinitely precise measurements of the speed of automobiles on a section of highway. We could then plot the results by showing the relative number of cars going past at any given speed. If the average was 120 kph, it might look like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_gaussian_pdf(mean=120, variance=17**2, xlabel='speed(kph)');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The y-axis depicts the *probability density* — the relative amount of cars that are going the speed at the corresponding x-axis. I will explain this further in the next section.\n",
    "\n",
    "The Gaussian model is imperfect. Though these charts do not show it, the *tails* of the distribution extend out to infinity. *Tails* are the far ends of the curve where the values are the lowest. Of course human heights or automobile speeds cannot be less than zero, let alone $-\\infty$ or $\\infty$. “The map is not the territory” is a common expression, and it is true for Bayesian filtering and statistics. The Gaussian distribution above models the distribution of the measured automobile speeds, but being a model it is necessarily imperfect. The difference between model and reality will come up again and again in these filters. Gaussians are used in many branches of mathematics, not because they perfectly model reality, but because they are easier to use than any other relatively accurate choice. However, even in this book Gaussians will fail to model reality, forcing us to use computationally expensive alternatives. \n",
    "\n",
    "You will hear these distributions called *Gaussian distributions* or *normal distributions*.  *Gaussian* and *normal* both mean the same thing in this context, and are used interchangeably. I will use both throughout this book as different sources will use either term, and I want you to be used to seeing both. Finally, as in this paragraph, it is typical to shorten the name and talk about a *Gaussian* or *normal* — these are both typical shortcut names for the *Gaussian distribution*. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gaussian Distributions\n",
    "\n",
    "Let's explore how Gaussians work. A Gaussian is a *continuous probability distribution* that is completely described with two parameters, the mean ($\\mu$) and the variance ($\\sigma^2$). It is defined as:\n",
    "\n",
    "$$ \n",
    "f(x, \\mu, \\sigma) = \\frac{1}{\\sigma\\sqrt{2\\pi}} \\exp\\big [{-\\frac{(x-\\mu)^2}{2\\sigma^2} }\\big ]\n",
    "$$\n",
    "\n",
    "$\\exp[x]$ is notation for $e^x$.\n",
    "\n",
    "<p> Don't be dissuaded by the equation if you haven't seen it before; you will not need to memorize or manipulate it. The computation of this function is stored in `stats.py` with the function `gaussian(x, mean, var, normed=True)`. \n",
    "    \n",
    "Shorn of the constants, you can see it is a simple exponential:\n",
    "    \n",
    "$$f(x)\\propto e^{-x^2}$$\n",
    "\n",
    "which has the familiar bell curve shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(-3, 3, .01)\n",
    "plt.plot(x, np.exp(-x**2));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's remind ourselves how to look at the code for a function. In a cell, type the function name followed by two question marks and press CTRL+ENTER. This will open a popup window displaying the source. Uncomment the next cell and try it now."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "from filterpy.stats import gaussian\n",
    "#gaussian??"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot a Gaussian with a mean of 22 $(\\mu=22)$, with a variance of 4 $(\\sigma^2=4)$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_gaussian_pdf(22, 4, mean_line=True, xlabel='$^{\\circ}C$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What does this curve *mean*? Assume we have a thermometer which reads 22°C. No thermometer is perfectly accurate, and so we expect that each reading will be slightly off the actual value. However, a theorem called  [*Central Limit Theorem*](https://en.wikipedia.org/wiki/Central_limit_theorem) states that if we make many measurements that the measurements will be normally distributed. When we look at this chart we can see it is proportional to the probability of the thermometer reading a particular value given the actual temperature of 22°C. \n",
    "\n",
    "Recall that a Gaussian distribution is *continuous*. Think of an infinitely long straight line - what is the probability that a point you pick randomly is at 2. Clearly 0%, as there is an infinite number of choices to choose from. The same is true for normal distributions; in the graph above the probability of being *exactly* 2°C is 0% because there are an infinite number of values the reading can take.\n",
    "\n",
    "What is this curve? It is something we call the *probability density function.* The area under the curve at any region gives you the probability of those values. So, for example, if you compute the area under the curve between 20 and 22 the resulting area will be the probability of the temperature reading being between those two temperatures. \n",
    "\n",
    "Here is another way to understand it. What is the *density* of a rock, or a sponge? It is a measure of how much mass is compacted into a given space. Rocks are dense, sponges less so. So, if you wanted to know how much a rock weighed but didn't have a scale, you could take its volume and multiply by its density. This would give you its mass. In practice density varies in most objects, so you would integrate the local density across the rock's volume.\n",
    "\n",
    "$$M = \\iiint_R p(x,y,z)\\, dV$$\n",
    "\n",
    "We do the same with *probability density*. If you want to know the temperature being between 20°C and 21°C you would integrate the curve above from 20 to 21. As you know the integral of a curve gives you the area under the curve. Since this is a curve of the probability density, the integral of the density is the probability. \n",
    "\n",
    "What is the probability of the temperature being exactly 22°C? Intuitively, 0. These are real numbers, and the odds of 22°C vs, say, 22.00000000000017°C is infinitesimal. Mathematically, what would we get if we integrate from 22 to 22? Zero. \n",
    "\n",
    "Thinking back to the rock, what is the weight of an single point on the rock? An infinitesimal point must have no weight. It makes no sense to ask the weight of a single point, and it makes no sense to ask about the probability of a continuous distribution having a single value. The answer for both is obviously zero.\n",
    "\n",
    "In practice our sensors do not have infinite precision, so a reading of 22°C implies a range, such as 22 $\\pm$ 0.1°C, and we can compute the probability of that range by integrating from 21.9 to 22.1.\n",
    "\n",
    "We can think of this in Bayesian terms or frequentist terms. As a Bayesian, if the thermometer reads exactly 22°C, then our belief is described by the curve - our belief that the actual (system) temperature is near 22°C is very high, and our belief that the actual temperature is near 18 is very low. As a frequentist we would say that if we took 1 billion temperature measurements of a system at exactly 22°C, then a histogram of the measurements would look like this curve. \n",
    "\n",
    "How do you compute the probability, or area under the curve? You integrate the equation for the Gaussian \n",
    "\n",
    "$$ \\int^{x_1}_{x_0}  \\frac{1}{\\sigma\\sqrt{2\\pi}} e^{-\\frac{1}{2}{(x-\\mu)^2}/\\sigma^2 } dx$$\n",
    "\n",
    "This is called the *cumulative probability distribution*, commonly abbreviated *cdf*.\n",
    "\n",
    "I wrote `filterpy.stats.norm_cdf` which computes the integral for you. For example, we can compute"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cumulative probability of range 21.5 to 22.5 is 19.74%\n",
      "Cumulative probability of range 23.5 to 24.5 is 12.10%\n"
     ]
    }
   ],
   "source": [
    "from filterpy.stats import norm_cdf\n",
    "print('Cumulative probability of range 21.5 to 22.5 is {:.2f}%'.format(\n",
    "      norm_cdf((21.5, 22.5), 22,4)*100))\n",
    "print('Cumulative probability of range 23.5 to 24.5 is {:.2f}%'.format(\n",
    "      norm_cdf((23.5, 24.5), 22,4)*100))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The mean ($\\mu$) is what it sounds like — the average of all possible probabilities. Because of the symmetric shape of the curve it is also the tallest part of the curve. The thermometer reads 22°C, so that is what we used for the mean.  \n",
    "\n",
    "The notation for a normal distribution for a random variable $X$ is $X \\sim\\ \\mathcal{N}(\\mu,\\sigma^2)$ where $\\sim$ means *distributed according to*. This means I can express the temperature reading of our thermometer as\n",
    "\n",
    "$$\\text{temp} \\sim \\mathcal{N}(22,4)$$\n",
    "\n",
    "This is an extremely important result. Gaussians allow me to capture an infinite number of possible values with only two numbers! With the values $\\mu=22$ and $\\sigma^2=4$ I can compute the distribution of measurements over any range.\n",
    "\n",
    "Some sources use $\\mathcal N (\\mu, \\sigma)$ instead of $\\mathcal N (\\mu, \\sigma^2)$. Either is fine, they are both conventions. You need to keep in mind which form is being used if you see a term such as $\\mathcal{N}(22,4)$. In this book I always use $\\mathcal N (\\mu, \\sigma^2)$, so $\\sigma=2$, $\\sigma^2=4$ for this example."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Variance and Belief\n",
    "\n",
    "Since this is a probability density distribution it is required that the area under the curve always equals one. This should be intuitively clear — the area under the curve represents all possible outcomes, *something* happened, and the probability of *something happening* is one, so the density must sum to one. We can prove this ourselves with a bit of code. (If you are mathematically inclined, integrate the Gaussian equation from $-\\infty$ to $\\infty$)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n"
     ]
    }
   ],
   "source": [
    "print(norm_cdf((-1e8, 1e8), mu=0, var=4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This leads to an important insight. If the variance is small the curve will be narrow. this is because the variance is a measure of *how much* the samples vary from the mean. To keep the area equal to 1, the curve must also be tall. On the other hand if the variance is large the curve will be wide, and thus it will also have to be short to make the area equal to 1.\n",
    "\n",
    "Let's look at that graphically. We will use the aforementioned `filterpy.stats.gaussian` which can take either a single value or array of values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.24197072451914337\n",
      "[0.378 0.622]\n"
     ]
    }
   ],
   "source": [
    "from filterpy.stats import gaussian\n",
    "\n",
    "print(gaussian(x=3.0, mean=2.0, var=1))\n",
    "print(gaussian(x=[3.0, 2.0], mean=2.0, var=1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By default `gaussian` normalizes the output, which turns the output back into a probability distribution. Use the argument`normed` to control this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.242 0.399]\n"
     ]
    }
   ],
   "source": [
    "print(gaussian(x=[3.0, 2.0], mean=2.0, var=1, normed=False))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If the Gaussian is not normalized it is called a *Gaussian function* instead of *Gaussian distribution*.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = np.arange(15, 30, 0.05)\n",
    "plt.plot(xs, gaussian(xs, 23, 0.2**2), label='$\\sigma^2=0.2^2$')\n",
    "plt.plot(xs, gaussian(xs, 23, .5**2), label='$\\sigma^2=0.5^2$', ls=':')\n",
    "plt.plot(xs, gaussian(xs, 23, 1**2), label='$\\sigma^2=1^2$', ls='--')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What is this telling us? The Gaussian with $\\sigma^2=0.2^2$ is very narrow. It is saying that we believe $x=23$, and that we are very sure about that: within $\\pm 0.2$ std. In contrast, the Gaussian with $\\sigma^2=1^2$ also believes that $x=23$, but we are much less sure about that. Our belief that $x=23$ is lower, and so our belief about the likely possible values for $x$ is spread out — we think it is quite likely that $x=20$ or $x=26$, for example. $\\sigma^2=0.2^2$ has almost completely eliminated $22$ or $24$ as possible values, whereas $\\sigma^2=1^2$ considers them nearly as likely as $23$.\n",
    "\n",
    "If we think back to the thermometer, we can consider these three curves as representing the readings from three different thermometers. The curve for $\\sigma^2=0.2^2$ represents a very accurate thermometer, and curve for $\\sigma^2=1^2$ represents a fairly inaccurate one. Note the very powerful property the Gaussian distribution affords us — we can entirely represent both the reading and the error of a thermometer with only two numbers — the mean and the variance.\n",
    "\n",
    "An equivalent formation for a Gaussian is $\\mathcal{N}(\\mu,1/\\tau)$ where $\\mu$ is the *mean* and $\\tau$ the *precision*. $1/\\tau = \\sigma^2$; it is the reciprocal of the variance. While we do not use this formulation in this book, it underscores that the variance is a measure of how precise our data is. A small variance yields large precision — our measurement is very precise. Conversely, a large variance yields low precision — our belief is spread out across a large area. You should become comfortable with thinking about Gaussians in these equivalent forms. In Bayesian terms Gaussians reflect our *belief* about a measurement, they express the *precision* of the measurement, and they express how much *variance* there is in the measurements. These are all different ways of stating the same fact.\n",
    "\n",
    "I'm getting ahead of myself, but in the next chapters we will use Gaussians to express our belief in things like the estimated position of the object we are tracking, or the accuracy of the sensors we are using."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The  68-95-99.7 Rule\n",
    "\n",
    "It is worth spending a few words on standard deviation now. The standard deviation is a measure of how much the data deviates from the mean. For Gaussian distributions, 68% of all the data falls within one standard deviation ($\\pm1\\sigma$) of the mean, 95% falls within two standard deviations ($\\pm2\\sigma$), and 99.7% within three ($\\pm3\\sigma$). This is often called the [68-95-99.7 rule](https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule). If you were told that the average test score in a class was 71 with a standard deviation of 9.4, you could conclude that 95% of the students received a score between 52.2 and 89.8 if the distribution is normal (that is calculated with $71 \\pm (2 * 9.4)$). \n",
    "\n",
    "Finally, these are not arbitrary numbers. If the Gaussian for our position is $\\mu=22$ meters, then the standard deviation also has units meters. Thus $\\sigma=0.2$ implies that 68% of the measurements range from 21.8 to 22.2 meters. Variance is the standard deviation squared, thus $\\sigma^2 = .04$ meters$^2$. As you saw in the last section, writing $\\sigma^2 = 0.2^2$ can make this somewhat more meaningful, since the 0.2 is in the same units as the data.\n",
    "\n",
    "The following graph depicts the relationship between the standard deviation and the normal distribution. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from kf_book.gaussian_internal import display_stddev_plot\n",
    "display_stddev_plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interactive Gaussians\n",
    "\n",
    "For those that are reading this in a Jupyter Notebook, here is an interactive version of the Gaussian plots. Use the sliders to modify $\\mu$ and $\\sigma^2$. Adjusting $\\mu$ will move the graph to the left and right because you are adjusting the mean, and adjusting $\\sigma^2$ will make the bell curve thicker and thinner."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a07afca115cb406abe449c6fdd78d44f",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=5.0, description='mu', max=7.0, min=3.0), FloatSlider(value=0.03, desc…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import math\n",
    "from ipywidgets import interact, FloatSlider\n",
    "\n",
    "def plt_g(mu,variance):\n",
    "    plt.figure()\n",
    "    xs = np.arange(2, 8, 0.01)\n",
    "    ys = gaussian(xs, mu, variance)\n",
    "    plt.plot(xs, ys)\n",
    "    plt.ylim(0, 0.04)\n",
    "\n",
    "interact(plt_g, mu=FloatSlider(value=5, min=3, max=7),\n",
    "         variance=FloatSlider(value = .03, min=.01, max=1.));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, if you are reading this online, here is an animation of a Gaussian. First, the mean is shifted to the right. Then the mean is centered at $\\mu=5$ and the variance is modified.\n",
    "\n",
    "<img src='animations/04_gaussian_animate.gif'>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computational Properties of Gaussians\n",
    "\n",
    "The discrete Bayes filter works by multiplying and adding arbitrary probability distributions. The Kalman filter uses Gaussians instead of arbitrary distributions, but the rest of the algorithm remains the same. This means we will need to multiply and add Gaussians. \n",
    "\n",
    "A remarkable property of Gaussians is that the sum of two independent independent normal variables (https://en.wikipedia.org/wiki/Sum_of_normally_distributed_random_variables) is also normally distributed! The product is not Gaussian, but proportional to a Gaussian. There we can say that the result of multipying two Gaussian distributions is a Gaussian function (recall function in this context means that the property that the values sum to one is not guaranteed).\n",
    "\n",
    "Before we do the math, let's test this visually. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(-1, 3, 0.01)\n",
    "g1 = gaussian(x, mean=0.8, var=.1)\n",
    "g2 = gaussian(x, mean=1.3, var=.2)\n",
    "plt.plot(x, g1, x, g2)\n",
    "\n",
    "g = g1 * g2  # element-wise multiplication\n",
    "g = g / sum(g)  # normalize\n",
    "plt.plot(x, g, ls='-.');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here I created two Gaussians, g1=$\\mathcal N(0.8, 0.1)$ and g2=$\\mathcal N(1.3, 0.2)$ and plotted them. Then I multiplied them together and normalized the result. As you can see the result *looks* like a Gaussian distribution.\n",
    "\n",
    "Gaussians are nonlinear functions. Typically, if you multiply a nonlinear equations you end up with a different type of function. For example, the shape of multiplying two sins is very different from `sin(x)`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(0, 4*np.pi, 0.01)\n",
    "plt.plot(np.sin(1.2*x))\n",
    "plt.plot(np.sin(1.2*x) * np.sin(2*x));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But the result of multiplying two Gaussians distributions is a Gaussian function. This is a key reason why Kalman filters are computationally feasible. Said another way, Kalman filters use Gaussians *because* they are computationally nice. \n",
    "\n",
    "The product of two independent Gaussians is given by:\n",
    "\n",
    "$$\\begin{aligned}\\mu &=\\frac{\\sigma_1^2\\mu_2 + \\sigma_2^2\\mu_1}{\\sigma_1^2+\\sigma_2^2}\\\\\n",
    "\\sigma^2 &=\\frac{\\sigma_1^2\\sigma_2^2}{\\sigma_1^2+\\sigma_2^2} \n",
    "\\end{aligned}$$\n",
    "\n",
    "The sum of two Gaussians is given by\n",
    "\n",
    "$$\\begin{gathered}\\mu = \\mu_1 + \\mu_2 \\\\\n",
    "\\sigma^2 = \\sigma^2_1 + \\sigma^2_2\n",
    "\\end{gathered}$$\n",
    "\n",
    "At the end of the chapter I derive these equations. However, understanding the deriviation is not very important."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Putting it all Together\n",
    "\n",
    "Now we are ready to talk about how Gaussians can be used in filtering. In the next chapter we will implement a filter using Gaussins. Here I will explain why we would want to use Gaussians.\n",
    "\n",
    "In the previous chapter we represented probability distributions with an array. We performed the update computation by computing the element-wise product of that distribution with another distribution representing the likelihood of the measurement at each point, like so:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def normalize(p):\n",
    "    return p / sum(p)\n",
    "\n",
    "def update(likelihood, prior):\n",
    "    return normalize(likelihood * prior)\n",
    "\n",
    "prior =      normalize(np.array([4, 2, 0, 7, 2, 12, 35, 20, 3, 2]))\n",
    "likelihood = normalize(np.array([3, 4, 1, 4, 2, 38, 20, 18, 1, 16]))\n",
    "posterior = update(likelihood, prior)\n",
    "book_plots.bar_plot(posterior)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In other words, we have to compute 10 multiplications to get this result. For a real filter with large arrays in multiple dimensions we'd require billions of multiplications, and vast amounts of memory. \n",
    "\n",
    "But this distribution looks like a Gaussian. What if we use a Gaussian instead of an array? I'll compute the mean and variance of the posterior and plot it against the bar chart."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean: 5.88 var: 1.24\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = np.arange(0, 10, .01)\n",
    "\n",
    "def mean_var(p):\n",
    "    x = np.arange(len(p))\n",
    "    mean = np.sum(p * x,dtype=float)\n",
    "    var = np.sum((x - mean)**2 * p)\n",
    "    return mean, var\n",
    "\n",
    "mean, var = mean_var(posterior)\n",
    "book_plots.bar_plot(posterior)\n",
    "plt.plot(xs, gaussian(xs, mean, var, normed=False), c='r');\n",
    "print('mean: %.2f' % mean, 'var: %.2f' % var)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is impressive. We can describe an entire distribution of numbers with only two numbers. Perhaps this example is not persuasive, given there are only 10 numbers in the distribution. But a real problem could have millions of numbers, yet still only require two numbers to describe it.\n",
    "\n",
    "Next, recall that our filter implements the update function with\n",
    "```python\n",
    "def update(likelihood, prior):\n",
    "    return normalize(likelihood * prior)\n",
    "```\n",
    "\n",
    "If the arrays contain a million elements, that is one million multiplications. However, if we replace the arrays with a Gaussian then we would perform that calculation with\n",
    "\n",
    "$$\\begin{aligned}\\mu &=\\frac{\\sigma_1^2\\mu_2 + \\sigma_2^2\\mu_1}{\\sigma_1^2+\\sigma_2^2}\\\\\n",
    "\\sigma^2 &=\\frac{\\sigma_1^2\\sigma_2^2}{\\sigma_1^2+\\sigma_2^2} \n",
    "\\end{aligned}$$\n",
    "\n",
    "which is three multiplications and two divisions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bayes Theorem\n",
    "\n",
    "In the last chapter we developed an algorithm by reasoning about the information we have at each moment, which we expressed as discrete probability distributions. In the process we discovered [*Bayes' Theorem*](https://en.wikipedia.org/wiki/Bayes%27_theorem). Bayes theorem tells us how to compute the probability of an event given prior information. \n",
    "\n",
    "We implemented the `update()` function with this probability calculation:\n",
    "\n",
    "$$ \\mathtt{posterior} = \\frac{\\mathtt{likelihood}\\times \\mathtt{prior}}{\\mathtt{normalization}}$$ \n",
    "\n",
    "It turns out that this is Bayes' theorem. In a second I will develop the mathematics, but in many ways that obscures the simple idea expressed in this equation. We read this as:\n",
    "\n",
    "$$ updated\\,knowledge = \\big\\|likelihood\\,of\\,new\\,knowledge\\times prior\\, knowledge \\big\\|$$\n",
    "\n",
    "where $\\| \\cdot\\|$ expresses normalizing the term.\n",
    "\n",
    "We came to this with simple reasoning about a dog walking down a hallway. Yet, as we will see, the same equation applies to a universe of filtering problems. We will use this equation in every subsequent chapter.\n",
    "\n",
    "\n",
    "To review, the *prior* is the probability of something happening before we include the probability of the measurement (the *likelihood*) and the *posterior* is the probability we compute after incorporating the information from the measurement.\n",
    "\n",
    "Bayes theorem is\n",
    "\n",
    "$$P(A \\mid B) = \\frac{P(B \\mid A)\\, P(A)}{P(B)}$$\n",
    "\n",
    "$P(A \\mid B)$ is called a [*conditional probability*](https://en.wikipedia.org/wiki/Conditional_probability). That is, it represents the probability of $A$ happening *if* $B$ happened. For example, it is more likely to rain today compared to a typical day if it also rained yesterday because rain systems usually last more than one day. We'd write the probability of it raining today given that it rained yesterday as $P$(rain today $\\mid$ rain yesterday).\n",
    "\n",
    "\n",
    "I've glossed over an important point. In our code above we are not working with single probabilities, but an array of probabilities - a *probability distribution*. The equation I just gave for Bayes uses probabilities, not probability distributions. However, it is equally valid with probability distributions. We use a lower case $p$ for probability distributions\n",
    "\n",
    "$$p(A \\mid B) = \\frac{p(B \\mid A)\\, p(A)}{p(B)}$$\n",
    "\n",
    "In the equation above $B$ is the *evidence*, $p(A)$ is the *prior*, $p(B \\mid A)$ is the *likelihood*, and $p(A \\mid B)$ is the *posterior*. By substituting the mathematical terms with the corresponding words you can see that Bayes theorem matches our update equation. Let's rewrite the equation in terms of our problem. We will use $x_i$ for the position at *i*, and $z$ for the measurement. Hence, we want to know $P(x_i \\mid z)$, that is, the probability of the dog being at $x_i$ given the measurement $z$. \n",
    "\n",
    "So, let's plug that into the equation and solve it.\n",
    "\n",
    "$$p(x_i \\mid z) = \\frac{p(z \\mid x_i) p(x_i)}{p(z)}$$\n",
    "\n",
    "That looks ugly, but it is actually quite simple. Let's figure out what each term on the right means. First is $p(z \\mid x_i)$. This is the likelihood, or the probability for the measurement at every cell $x_i$. $p(x_i)$ is the *prior* - our belief before incorporating the measurements. We multiply those together. This is just the unnormalized multiplication in the `update()` function:\n",
    "\n",
    "```python\n",
    "def update(likelihood, prior):\n",
    "    posterior = prior * likelihood   # p(z|x) * p(x)\n",
    "    return normalize(posterior)\n",
    "```\n",
    "\n",
    "The last term to consider is the denominator $p(z)$. This is the probability of getting the measurement $z$ without taking the location into account. It is often called the *evidence*. We compute that by taking the sum of $x$, or `sum(belief)` in the code. That is how we compute the normalization! So, the `update()` function is doing nothing more than computing Bayes' theorem.\n",
    "\n",
    "The literature often gives you these equations in the form of integrals. After all, an integral is just a sum over a continuous function. So, you might see Bayes' theorem written as\n",
    "\n",
    "$$p(A \\mid B) = \\frac{p(B \\mid A)\\, p(A)}{\\int p(B \\mid A_j) p(A_j) \\,\\, \\mathtt{d}A_j}\\cdot$$\n",
    "\n",
    "This denominator is usually impossible to solve analytically; when it can be solved the math is fiendishly difficult. A recent [opinion piece ](http://www.statslife.org.uk/opinion/2405-we-need-to-rethink-how-we-teach-statistics-from-the-ground-up)for the Royal Statistical Society called it a \"dog's breakfast\" [8].  Filtering textbooks that take a Bayesian approach are filled with integral laden equations with no analytic solution. Do not be cowed by these equations, as we trivially handled this integral by normalizing our posterior. We will learn more techniques to handle this in the **Particle Filters** chapter. Until then, recognize that in practice it is just a normalization term over which we can sum. What I'm trying to say is that when you are faced with a page of integrals, just think of them as sums, and relate them back to this chapter, and often the difficulties will fade. Ask yourself \"why are we summing these values\", and \"why am I dividing by this term\". Surprisingly often the answer is readily apparent. Surprisingly often the author neglects to mention this interpretation.\n",
    "\n",
    "It's probable that the strength of Bayes' theorem is not yet fully apparent to you. We want to compute $p(x_i \\mid Z)$. That is, at step i, what is our probable state given a measurement. That's an extraordinarily difficult problem in general. Bayes' Theorem is general. We may want to know the probability that we have cancer given the results of a cancer test, or the probability of rain given various sensor readings. Stated like that the problems seem unsolvable.\n",
    "\n",
    "But Bayes' Theorem lets us compute this by using the inverse  $p(Z\\mid x_i)$, which is often straightforward to compute\n",
    "\n",
    "$$p(x_i \\mid Z) \\propto p(Z\\mid x_i)\\, p(x_i)$$\n",
    "\n",
    "That is, to compute how likely it is to rain given specific sensor readings we only have to compute the likelihood of the sensor readings given that it is raining! That's a ***much*** easier problem! Well, weather prediction is still a difficult problem, but Bayes makes it tractable. \n",
    "\n",
    "Likewise, as you saw in the Discrete Bayes chapter, we computed the likelihood that Simon was in any given part of the hallway by computing how likely a sensor reading is given that Simon is at position `x`. A hard problem becomes easy. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Total Probability Theorem\n",
    "\n",
    "We now know the formal mathematics behind the `update()` function; what about the `predict()` function? `predict()` implements the [*total probability theorem*](https://en.wikipedia.org/wiki/Law_of_total_probability). Let's recall what `predict()` computed. It computed the probability of being at any given position given the probability of all the possible movement events. Let's express that as an equation. The probability of being at any position $i$ at time $t$ can be written as $P(X_i^t)$. We computed that as the sum of the prior at time $t-1$ $P(X_j^{t-1})$ multiplied by the probability of moving from cell $x_j$ to $x_i$. That is\n",
    "\n",
    "$$P(X_i^t) = \\sum_j P(X_j^{t-1})  P(x_i | x_j)$$\n",
    "\n",
    "That equation is called the *total probability theorem*. Quoting from Wikipedia [6] \"It expresses the total probability of an outcome which can be realized via several distinct events\". I could have given you that equation and implemented `predict()`, but your chances of understanding why the equation works would be slim. As a reminder, here is the code that computes this equation\n",
    "\n",
    "```python\n",
    "for i in range(N):\n",
    "    for k in range (kN):\n",
    "        index = (i + (width-k) - offset) % N\n",
    "        result[i] += prob_dist[index] * kernel[k]\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computing Probabilities with scipy.stats\n",
    "\n",
    "In this chapter I used code from [FilterPy](https://github.com/rlabbe/filterpy) to compute and plot Gaussians. I did that to give you a chance to look at the code and see how these functions are implemented.  However, Python comes with \"batteries included\" as the saying goes, and it comes with a wide range of statistics functions in the module `scipy.stats`. So let's walk through how to use scipy.stats to compute statistics and probabilities.\n",
    "\n",
    "The `scipy.stats` module contains a number of objects which you can use to compute attributes of various probability distributions. The full documentation for this module is here: http://docs.scipy.org/doc/scipy/reference/stats.html. We will focus on the  norm variable, which implements the normal distribution. Let's look at some code that uses `scipy.stats.norm` to compute a Gaussian, and compare its value to the value returned by the `gaussian()` function from FilterPy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.13114657203397997\n",
      "0.13114657203397995\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import norm\n",
    "import filterpy.stats\n",
    "print(norm(2, 3).pdf(1.5))\n",
    "print(filterpy.stats.gaussian(x=1.5, mean=2, var=3*3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The call `norm(2, 3)` creates what scipy calls a 'frozen' distribution - it creates and returns an object with a mean of 2 and a standard deviation of 3. You can then use this object multiple times to get the probability density of various values, like so:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pdf of 1.5 is       0.1311\n",
      "pdf of 2.5 is also  0.1311\n",
      "pdf of 2 is         0.1330\n"
     ]
    }
   ],
   "source": [
    "n23 = norm(2, 3)\n",
    "print('pdf of 1.5 is       %.4f' % n23.pdf(1.5))\n",
    "print('pdf of 2.5 is also  %.4f' % n23.pdf(2.5))\n",
    "print('pdf of 2 is         %.4f' % n23.pdf(2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The documentation for  [scipy.stats.norm](http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html#scipy.stats.normfor) [2] lists many other functions. For example, we can generate $n$ samples from the distribution with the `rvs()` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 3.026  7.51  -2.588  6.081 -3.413 -1.11   6.484\n",
      "  5.935  2.313  1.912  1.895  7.964  4.876 -0.841\n",
      " -0.174]\n"
     ]
    }
   ],
   "source": [
    "np.set_printoptions(precision=3, linewidth=50)\n",
    "print(n23.rvs(size=15))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can get the [*cumulative distribution function (CDF)*](https://en.wikipedia.org/wiki/Cumulative_distribution_function), which is the probability that a randomly drawn value from the distribution is less than or equal to $x$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5\n"
     ]
    }
   ],
   "source": [
    "# probability that a random value is less than the mean 2\n",
    "print(n23.cdf(2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can get various properties of the distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "variance is 9.0\n",
      "standard deviation is 3.0\n",
      "mean is 2.0\n"
     ]
    }
   ],
   "source": [
    "print('variance is', n23.var())\n",
    "print('standard deviation is', n23.std())\n",
    "print('mean is', n23.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Limitations of Using Gaussians to Model the World\n",
    "\n",
    "Earlier I mentioned the *central limit theorem*, which states that under certain conditions the arithmetic sum of any independent random variable will be normally distributed, regardless of how the random variables are distributed. This is important to us because nature is full of distributions which are not normal, but when we apply the central limit theorem over large populations we end up with normal distributions. \n",
    "\n",
    "However, a key part of the proof is “under certain conditions”. These conditions often do not hold for the physical world. For example, a kitchen scale cannot read below zero, but if we represent the measurement error as a Gaussian the left side of the curve extends to negative infinity, implying a very small chance of giving a negative reading. \n",
    "\n",
    "This is a broad topic which I will not treat exhaustively. \n",
    "\n",
    "Let's consider a trivial example. We think of things like test scores as being normally distributed. If you have ever had a professor “grade on a curve” you have been subject to this assumption. But of course test scores cannot follow a normal distribution. This is because the distribution assigns a nonzero probability distribution for *any* value, no matter how far from the mean. So, for example, say your mean is 90 and the standard deviation is 13. The normal distribution assumes that there is a large chance of somebody getting a 90, and a small chance of somebody getting a 40. However, it also implies that there is a tiny chance of somebody getting a grade of -10, or 150. It assigns an extremely small chance of getting a score of $-10^{300}$ or $10^{32986}$. The tails of a Gaussian distribution are infinitely long.\n",
    "\n",
    "But for a test we know this is not true. Ignoring extra credit, you cannot get less than 0, or more than 100. Let's plot this range of values using a normal distribution to see how poorly this represents real test scores distributions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = np.arange(10, 100, 0.05)\n",
    "ys = [gaussian(x, 90, 30) for x in xs]\n",
    "plt.plot(xs, ys, label='var=0.2')\n",
    "plt.xlim(0, 120)\n",
    "plt.ylim(-0.02, 0.09);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The area under the curve cannot equal 1, so it is not a probability distribution. What actually happens is that more students than predicted by a normal distribution get scores nearer the upper end of the range (for example), and that tail becomes “fat”. Also, the test is probably not able to perfectly distinguish minute differences in skill in the students, so the distribution to the left of the mean is also probably a bit bunched up in places. \n",
    "\n",
    "Sensors measure the world. The errors in a sensor's measurements are rarely truly Gaussian. It is far too early to be talking about the difficulties that this presents to the Kalman filter designer. It is worth keeping in the back of your mind the fact that the Kalman filter math is based on an idealized model of the world.  For now I will present a bit of code that I will be using later in the book to form distributions to simulate various processes and sensors. This distribution is called the [*Student's $t$-distribution*](https://en.wikipedia.org/wiki/Student%27s_t-distribution). \n",
    "\n",
    "Let's say I want to model a sensor that has some white noise in the output. For simplicity, let's say the signal is a constant 10, and the standard deviation of the noise is 2. We can use the function `numpy.random.randn()` to get a random number with a mean of 0 and a standard deviation of 1. I can simulate this with:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy.random import randn\n",
    "def sense():\n",
    "    return 10 + randn()*2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot that signal and see what it looks like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "zs = [sense() for i in range(5000)]\n",
    "plt.plot(zs, lw=1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That looks like what I would expect. The signal is centered around 10. A standard deviation of 2 means that 68% of the measurements will be within $\\pm$ 2 of 10, and 99% will be within $\\pm$ 6 of 10, and that looks like what is happening. \n",
    "\n",
    "Now let's look at distribution generated with the Student's $t$-distribution. I will not go into the math, but just give you the source code for it and then plot a distribution using it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "import math\n",
    "\n",
    "def rand_student_t(df, mu=0, std=1):\n",
    "    \"\"\"return random number distributed by Student's t \n",
    "    distribution with `df` degrees of freedom with the \n",
    "    specified mean and standard deviation.\n",
    "    \"\"\"\n",
    "    x = random.gauss(0, std)\n",
    "    y = 2.0*random.gammavariate(0.5*df, 2.0)\n",
    "    return x / (math.sqrt(y / df)) + mu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def sense_t():\n",
    "    return 10 + rand_student_t(7)*2\n",
    "\n",
    "zs = [sense_t() for i in range(5000)]\n",
    "plt.plot(zs, lw=1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see from the plot that while the output is similar to the normal distribution there are outliers that go far more than 3 standard deviations from the mean (7 to 13). \n",
    "\n",
    "It is unlikely that the Student's $t$-distribution is an accurate model of how your sensor (say, a GPS or Doppler) performs, and this is not a book on how to model physical systems. However, it does produce reasonable data to test your filter's performance when presented with real world noise. We will be using distributions like these throughout the rest of the book in our simulations and tests. \n",
    "\n",
    "This is not an idle concern. The Kalman filter equations assume the noise is normally distributed, and perform sub-optimally if this is not true. Designers for mission critical filters, such as the filters on spacecraft, need to master a lot of theory and empirical knowledge about the performance of the sensors on their spacecraft. For example, a presentation I saw on a NASA mission stated that while theory states that they should use 3 standard deviations to distinguish noise from valid measurements in practice they had to use 5 to 6 standard deviations. This was something they determined by experiments.\n",
    "\n",
    "The code for rand_student_t is included in `filterpy.stats`. You may use it with\n",
    "\n",
    "```python\n",
    "from filterpy.stats import rand_student_t\n",
    "```\n",
    "\n",
    "While I'll not cover it here, statistics has defined ways of describing the shape of a probability distribution by how it varies from an exponential distribution. The normal distribution is shaped symmetrically around the mean - like a bell curve. However, a probability distribution can be asymmetrical around the mean. The measure of this is called [*skew*](https://en.wikipedia.org/wiki/Skewness). The tails can be shortened, fatter, thinner, or otherwise shaped differently from an exponential distribution. The measure of this is called [*kurtosis*](https://en.wikipedia.org/wiki/Kurtosis). the `scipy.stats` module contains the function `describe` which computes these statistics, among others."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DescribeResult(nobs=5000, minmax=(1.7707248080804092, 17.824961707265643), mean=10.004201301507253, variance=2.721973140216924, skewness=-0.03534037712630867, kurtosis=1.583968849611276)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import scipy\n",
    "scipy.stats.describe(zs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's examine two normal populations, one small, one large:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DescribeResult(nobs=10, minmax=(-1.1170056026895896, 1.0389413316321683), mean=-0.14317693801053674, variance=0.63137454114842, skewness=0.23966670696111078, kurtosis=-1.3702119526058378)\n",
      "\n",
      "DescribeResult(nobs=300000, minmax=(-4.262303362805642, 4.603650808299195), mean=-0.00040808441709135014, variance=0.998953112076118, skewness=-0.0010979017079029859, kurtosis=-0.00030025117171517124)\n"
     ]
    }
   ],
   "source": [
    "print(scipy.stats.describe(np.random.randn(10)))\n",
    "print()\n",
    "print(scipy.stats.describe(np.random.randn(300000)))"
   ]
  },
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    "The small sample has very non-zero skew and kurtosis because the small number of samples is not well distributed around the mean of 0. You can see this also by comparing the computed mean and variance with the theoretical mean of 0 and variance 1. In comparison the large sample's mean and variance are very close to the theoretical values, and both the skew and kurtosis are near zero."
   ]
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    "## Product of Gaussians (Optional)\n",
    "\n",
    "It is not important to read this section. Here I derive the equations for the product of two Gaussians.\n",
    "\n",
    "You can find this result by multiplying the equation for two Gaussians together and combining terms. The algebra gets messy. I will derive it using Bayes theorem. We can state the problem as: let the prior be $N(\\bar\\mu, \\bar\\sigma^2)$, and measurement be $z \\propto N(z, \\sigma_z^2)$. What is the posterior  x given the measurement z?\n",
    "\n",
    "Write the posterior as $p(x \\mid z)$. Now we can use Bayes Theorem to state\n",
    "\n",
    "$$p(x \\mid z) = \\frac{p(z \\mid x)p(x)}{p(z)}$$\n",
    "\n",
    "$p(z)$ is a normalizing constant, so we can create a proportinality\n",
    "\n",
    "$$p(x \\mid z) \\propto p(z|x)p(x)$$\n",
    "\n",
    "Now we subtitute in the equations for the Gaussians, which are\n",
    "\n",
    "$$p(z \\mid x) = \\frac{1}{\\sqrt{2\\pi\\sigma_z^2}}\\exp \\Big[-\\frac{(z-x)^2}{2\\sigma_z^2}\\Big]$$\n",
    "\n",
    "$$p(x) = \\frac{1}{\\sqrt{2\\pi\\bar\\sigma^2}}\\exp \\Big[-\\frac{(x-\\bar\\mu)^2}{2\\bar\\sigma^2}\\Big]$$\n",
    "\n",
    "We can drop the leading terms, as they are constants, giving us\n",
    "\n",
    "$$\\begin{aligned}\n",
    "p(x \\mid z) &\\propto \\exp \\Big[-\\frac{(z-x)^2}{2\\sigma_z^2}\\Big]\\exp \\Big[-\\frac{(x-\\bar\\mu)^2}{2\\bar\\sigma^2}\\Big]\\\\\n",
    "&\\propto \\exp \\Big[-\\frac{(z-x)^2}{2\\sigma_z^2}-\\frac{(x-\\bar\\mu)^2}{2\\bar\\sigma^2}\\Big] \\\\\n",
    "&\\propto \\exp \\Big[-\\frac{1}{2\\sigma_z^2\\bar\\sigma^2}[\\bar\\sigma^2(z-x)^2+\\sigma_z^2(x-\\bar\\mu)^2]\\Big]\n",
    "\\end{aligned}$$\n",
    "\n",
    "Now we multiply out the squared terms and group in terms of the posterior $x$.\n",
    "\n",
    "$$\\begin{aligned}\n",
    "p(x \\mid z) &\\propto \\exp \\Big[-\\frac{1}{2\\sigma_z^2\\bar\\sigma^2}[\\bar\\sigma^2(z^2 -2xz + x^2) + \\sigma_z^2(x^2 - 2x\\bar\\mu+\\bar\\mu^2)]\\Big ] \\\\\n",
    "&\\propto \\exp \\Big[-\\frac{1}{2\\sigma_z^2\\bar\\sigma^2}[x^2(\\bar\\sigma^2+\\sigma_z^2)-2x(\\sigma_z^2\\bar\\mu + \\bar\\sigma^2z) + (\\bar\\sigma^2z^2+\\sigma_z^2\\bar\\mu^2)]\\Big ]\n",
    "\\end{aligned}$$\n",
    "\n",
    "The last parentheses do not contain the posterior $x$, so it can be treated as a constant and discarded.\n",
    "\n",
    "$$p(x \\mid z) \\propto \\exp \\Big[-\\frac{1}{2}\\frac{x^2(\\bar\\sigma^2+\\sigma_z^2)-2x(\\sigma_z^2\\bar\\mu + \\bar\\sigma^2z)}{\\sigma_z^2\\bar\\sigma^2}\\Big ]\n",
    "$$\n",
    "\n",
    "Divide numerator and denominator by $\\bar\\sigma^2+\\sigma_z^2$ to get\n",
    "\n",
    "$$p(x \\mid z) \\propto \\exp \\Big[-\\frac{1}{2}\\frac{x^2-2x(\\frac{\\sigma_z^2\\bar\\mu + \\bar\\sigma^2z}{\\bar\\sigma^2+\\sigma_z^2})}{\\frac{\\sigma_z^2\\bar\\sigma^2}{\\bar\\sigma^2+\\sigma_z^2}}\\Big ]\n",
    "$$\n",
    "\n",
    "Proportionality allows us create or delete constants at will, so we can factor this into\n",
    "\n",
    "$$p(x \\mid z) \\propto \\exp \\Big[-\\frac{1}{2}\\frac{(x-\\frac{\\sigma_z^2\\bar\\mu + \\bar\\sigma^2z}{\\bar\\sigma^2+\\sigma_z^2})^2}{\\frac{\\sigma_z^2\\bar\\sigma^2}{\\bar\\sigma^2+\\sigma_z^2}}\\Big ]\n",
    "$$\n",
    "\n",
    "A Gaussian is\n",
    "\n",
    "$$N(\\mu,\\, \\sigma^2) \\propto \\exp\\Big [-\\frac{1}{2}\\frac{(x - \\mu)^2}{\\sigma^2}\\Big ]$$\n",
    "\n",
    "So we can see that $p(x \\mid z)$ has a mean of\n",
    "\n",
    "$$\\mu_\\mathtt{posterior} = \\frac{\\sigma_z^2\\bar\\mu + \\bar\\sigma^2z}{\\bar\\sigma^2+\\sigma_z^2}$$\n",
    "\n",
    "and a variance of\n",
    "$$\n",
    "\\sigma_\\mathtt{posterior} = \\frac{\\sigma_z^2\\bar\\sigma^2}{\\bar\\sigma^2+\\sigma_z^2}\n",
    "$$\n",
    "\n",
    "I've dropped the constants, and so the result is not a normal, but proportional to one. Bayes theorem normalizes with the $p(z)$ divisor, ensuring that the result is normal. We normalize in the update step of our filters, ensuring the filter estimate is Gaussian.\n",
    "\n",
    "$$\\mathcal N_1 = \\| \\mathcal N_2\\cdot \\mathcal N_3\\|$$"
   ]
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    "## Sum of Gaussians (Optional)\n",
    "\n",
    "Likewise, this section is not important to read. Here I derive the equations for the sum of two Gaussians.\n",
    "\n",
    "The sum of two Gaussians is given by\n",
    "\n",
    "$$\\begin{gathered}\\mu = \\mu_1 + \\mu_2 \\\\\n",
    "\\sigma^2 = \\sigma^2_1 + \\sigma^2_2\n",
    "\\end{gathered}$$\n",
    "\n",
    "There are several proofs for this. I will use convolution since we used convolution in the previous chapter for the histograms of probabilities. \n",
    "\n",
    "To find the density function of the sum of two Gaussian random variables we sum the density functions of each. They are nonlinear, continuous functions, so we need to compute the sum with an integral. If the random variables $p$ and $z$ (e.g. prior and measurement) are independent we can compute this with\n",
    "\n",
    "$p(x) = \\int\\limits_{-\\infty}^\\infty f_p(x-z)f_z(z)\\, dx$\n",
    "\n",
    "This is the equation for a convolution. Now we just do some math:\n",
    "\n",
    "\n",
    "$p(x) = \\int\\limits_{-\\infty}^\\infty f_2(x-x_1)f_1(x_1)\\, dx$\n",
    "\n",
    "$=  \\int\\limits_{-\\infty}^\\infty \n",
    "\\frac{1}{\\sqrt{2\\pi}\\sigma_z}\\exp\\left[-\\frac{(x - z - \\mu_z)^2}{2\\sigma^2_z}\\right]\n",
    "\\frac{1}{\\sqrt{2\\pi}\\sigma_p}\\exp\\left[-\\frac{(x - \\mu_p)^2}{2\\sigma^2_p}\\right] \\, dx$\n",
    "\n",
    "$=  \\int\\limits_{-\\infty}^\\infty\n",
    "\\frac{1}{\\sqrt{2\\pi}\\sqrt{\\sigma_p^2 + \\sigma_z^2}} \\exp\\left[ -\\frac{(x - (\\mu_p + \\mu_z)))^2}{2(\\sigma_z^2+\\sigma_p^2)}\\right]\n",
    "\\frac{1}{\\sqrt{2\\pi}\\frac{\\sigma_p\\sigma_z}{\\sqrt{\\sigma_p^2 + \\sigma_z^2}}} \\exp\\left[ -\\frac{(x - \\frac{\\sigma_p^2(x-\\mu_z) + \\sigma_z^2\\mu_p}{}))^2}{2\\left(\\frac{\\sigma_p\\sigma_x}{\\sqrt{\\sigma_z^2+\\sigma_p^2}}\\right)^2}\\right] \\, dx$\n",
    "\n",
    "$= \\frac{1}{\\sqrt{2\\pi}\\sqrt{\\sigma_p^2 + \\sigma_z^2}} \\exp\\left[ -\\frac{(x - (\\mu_p + \\mu_z)))^2}{2(\\sigma_z^2+\\sigma_p^2)}\\right] \\int\\limits_{-\\infty}^\\infty\n",
    "\\frac{1}{\\sqrt{2\\pi}\\frac{\\sigma_p\\sigma_z}{\\sqrt{\\sigma_p^2 + \\sigma_z^2}}} \\exp\\left[ -\\frac{(x - \\frac{\\sigma_p^2(x-\\mu_z) + \\sigma_z^2\\mu_p}{}))^2}{2\\left(\\frac{\\sigma_p\\sigma_x}{\\sqrt{\\sigma_z^2+\\sigma_p^2}}\\right)^2}\\right] \\, dx$\n",
    "\n",
    "The expression inside the integral is a normal distribution. The sum of a normal distribution is one, hence the integral is one. This gives us\n",
    "\n",
    "$$p(x) = \\frac{1}{\\sqrt{2\\pi}\\sqrt{\\sigma_p^2 + \\sigma_z^2}} \\exp\\left[ -\\frac{(x - (\\mu_p + \\mu_z)))^2}{2(\\sigma_z^2+\\sigma_p^2)}\\right]$$\n",
    "\n",
    "This is in the form of a normal, where\n",
    "\n",
    "$$\\begin{gathered}\\mu_x = \\mu_p + \\mu_z \\\\\n",
    "\\sigma_x^2 = \\sigma_z^2+\\sigma_p^2\\, \\square\\end{gathered}$$"
   ]
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   "source": [
    "## Summary and Key Points\n",
    "\n",
    "This chapter is a poor introduction to statistics in general. I've only covered the concepts that  needed to use Gaussians in the remainder of the book, no more. What I've covered will not get you very far if you intend to read the Kalman filter literature. If this is a new topic to you I suggest reading a statistics textbook. I've always liked the Schaum series for self study, and Alan Downey's *Think Stats* [5] is also very good and freely available online. \n",
    "\n",
    "The following points **must** be understood by you before we continue:\n",
    "\n",
    "* Normals express a continuous probability distribution\n",
    "* They are completely described by two parameters: the mean ($\\mu$) and variance ($\\sigma^2$)\n",
    "* $\\mu$ is the average of all possible values\n",
    "* The variance $\\sigma^2$ represents how much our measurements vary from the mean\n",
    "* The standard deviation ($\\sigma$) is the square root of the variance ($\\sigma^2$)\n",
    "* Many things in nature approximate a normal distribution, but the math is not perfect.\n",
    "* In filtering problems computing $p(x\\mid z)$ is nearly impossible, but computing $p(z\\mid x)$ is straightforward. Bayes' lets us compute the former from the latter. \n",
    "\n",
    "The next several chapters will be using Gaussians with Bayes' theorem to help perform filtering. As noted in the last section, sometimes Gaussians do not describe the world very well. Latter parts of the book are dedicated to filters which work even when the noise or system's behavior is very non-Gaussian. "
   ]
  },
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   "source": [
    "## References"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[1] https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/Supporting_Notebooks/Computing_and_plotting_PDFs.ipynb\n",
    "\n",
    "[2] http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html\n",
    "\n",
    "[3] http://docs.scipy.org/doc/scipy/reference/tutorial/stats.html\n",
    "\n",
    "[4] Huber, Peter J. *Robust Statistical Procedures*, Second Edition. Society for Industrial and Applied Mathematics, 1996.\n",
    "\n",
    "[5] Downey, Alan. *Think Stats*, Second Edition. O'Reilly Media.\n",
    "\n",
    "https://github.com/AllenDowney/ThinkStats2\n",
    "\n",
    "http://greenteapress.com/thinkstats/"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Useful Wikipedia Links\n",
    "\n",
    "https://en.wikipedia.org/wiki/Probability_distribution\n",
    "\n",
    "https://en.wikipedia.org/wiki/Random_variable\n",
    "\n",
    "https://en.wikipedia.org/wiki/Sample_space\n",
    "\n",
    "https://en.wikipedia.org/wiki/Central_tendency\n",
    "\n",
    "https://en.wikipedia.org/wiki/Expected_value\n",
    "\n",
    "https://en.wikipedia.org/wiki/Standard_deviation\n",
    "\n",
    "https://en.wikipedia.org/wiki/Variance\n",
    "\n",
    "https://en.wikipedia.org/wiki/Probability_density_function\n",
    "\n",
    "https://en.wikipedia.org/wiki/Central_limit_theorem\n",
    "\n",
    "https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule\n",
    "\n",
    "https://en.wikipedia.org/wiki/Cumulative_distribution_function\n",
    "\n",
    "https://en.wikipedia.org/wiki/Skewness\n",
    "\n",
    "https://en.wikipedia.org/wiki/Kurtosis"
   ]
  }
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