BayesianBlocksProject.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "library(\"repr\")\n",
    "options(warn=-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bayesian Blocks\n",
    "\n",
    "The Bayesian Block data representation is a non-parametric method based on **Bayesian statistics** to redefine binning of data. \n",
    "\n",
    "Invented by Scargle [https://arxiv.org/abs/astro-ph/9711233] in 1998 and updated in 2013 [https://arxiv.org/abs/1207.5578v3] in the context of time-series analysis, it has the following advantages:\n",
    "\n",
    "- it is able to characterize statistically significant variations, at the same time suppressing the inevitable corrupting observational errors;\n",
    "- *non parametric* : it is general, does not \"fit\" data;\n",
    "- does not require much hypothesis on signal/background shape.\n",
    "\n",
    "The key idea is to determine the _optimal segmentation_ of data, working with _posterior probabilities_ :\n",
    "\n",
    "$$ P(M | D) \\propto P(D | M)P(M)$$\n",
    "\n",
    "## Fitness function $P(D | M)$\n",
    "\n",
    "In the following work, the data were considered to follow Cash statistics just as reported in Scargle 2013: if $M(t, \\theta)$ is the considered model of the time dependence of the signal, the unbinned log-likelihood is:\n",
    "\n",
    "$$\\log L(\\theta) = \\sum_n \\log M(t_n, \\theta) − \\int M(t, \\theta)dt$$\n",
    "\n",
    "where the sum is over the events and $\\theta$ represents the model\n",
    "parameters. The integral is over the observation interval and\n",
    "is the expected number of events under the model. \n",
    "\n",
    "In the considered case, $M(t, \\lambda) = \\lambda$ (constant model), so for block $k$:\n",
    "\n",
    "$$ \\log L^{(k)}(\\lambda) = N^{(k)}\\log \\lambda − \\lambda T^{(k)}$$\n",
    "\n",
    "where $N^{(k)}$ is the number of events in block $k$ and $T^{(k)}$ is\n",
    "the length of the block. The maximum of this likelihood is at $\\lambda = N^{(k)}/T^{(k)}$, yielding:\n",
    "\n",
    "\n",
    "$$ \\log L^{(k)}_{max}+ N^{(k)} = N^{(k)}(\\log N^{(k)}− \\log T^{(k)})$$\n",
    "\n",
    "In this way the fitness function (i.e., the likelihood) will be:\n",
    "\n",
    "- scale invariant\n",
    "- block-additive\n",
    "\n",
    "## Prior\n",
    "\n",
    "Since it is more likely that $N_{blocks} \\ll N$, a _geometric prior_ is chosen:\n",
    "\n",
    "$$ P(N_{blocks})= P_0 \\gamma^{N_{blocks}} = \\frac{1-\\gamma}{1-\\gamma^{N+1}} \\gamma^{N_{blocks}} $$\n",
    "\n",
    "It has well-understood properties and is simply implemented in the algorithm. $\\gamma$ values are taken to be smaller than $1$ to avoid overfitting. Notice that putting $\\gamma=1$ equals to using a flat prior for the bins.\n",
    "\n",
    "Another possibility is to calibrate the prior as a function of the number of data points $N$ and the correct detection rate $p_0$ ($\\equiv 1 - p_1$ false positive rate) on toy pure-noise experiments, leading to the expression:\n",
    "\n",
    "$$ \\texttt{ncp_prior} = 4 - \\log(73.53 p_0 N^{-0.478})$$\n",
    "\n",
    "## The algorithm\n",
    "\n",
    "The number of possible partitions of data is $2^N$, hence computing all of them is very computationally demanding: a _dynamic programming_ approach is adopted, mimicking mathematical induction:\n",
    "\n",
    "- we can easily find the optimal binning for a single point, which of course is the optimal one;\n",
    "- we compute the optimal partition at each iteration from the previously computed ones (mathematical details in the appendices of Scargle 2013). \n",
    "\n",
    "In this way, Scargle and collaborators showed that the $2^N$ possible states can be explored in $N^2$ time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "bayesian_blocks <- function(xs, prior=7.61, nn_vec=rep(1,length(xs))){\n",
    "    \n",
    "#   Parameters\n",
    "#   ----------\n",
    "#   xs : vector, \n",
    "#         data to be histogrammed, 'old' binning\n",
    "#   prior: double,\n",
    "#         value of ncp-prior, initialized to 7.61 (p0=0.01, N=1000, value find in Scargle 2013)\n",
    "#   nn_vec: vector,\n",
    "#         counts of data, inizialized to all 1 if data in not previously binned\n",
    "\n",
    "#   Returns\n",
    "#   -------\n",
    "#   change_points : vector\n",
    "#         array containing the 'new' bin edges\n",
    "\n",
    "\n",
    "#   sort input vector in order to create the starting block edges\n",
    "    xs <- sort(xs)\n",
    "    begin <- xs[1]\n",
    "    end <- xs[length(xs)]\n",
    "    \n",
    "#   remove 0s to avoid NA in the log computation\n",
    "    xs <- xs[!(nn_vec==0)]\n",
    "    nn_vec <- nn_vec[!(nn_vec==0)]\n",
    "    \n",
    "    N <- length(xs)\n",
    "    start <- xs[1]\n",
    "    stop <- xs[N]\n",
    "   \n",
    "#   starting blocks\n",
    "    blocks <- c(start, 0.5*(xs[2:N]+xs[1:N-1]), stop);\n",
    "    block_length <- stop - blocks\n",
    "\n",
    "#   start with first data cell; add one cell at each iteration\n",
    "\n",
    "    best <- NULL \n",
    "    last <- NULL\n",
    "    supp <- NULL\n",
    "    \n",
    "    for (R in 1:(N+1)){\n",
    "#       Compute fit_vec : fitness of last-known block (end at R)\n",
    "        \n",
    "#       block width and block count\n",
    "        arg_log <- block_length[1:R] - block_length[R+1]\n",
    "        \n",
    "        nn_cum_vec <- cumsum(nn_vec[R:1])\n",
    "        nn_cum_vec <- nn_cum_vec[R:1]\n",
    "        \n",
    "#       fitness\n",
    "        fit_vec <- nn_cum_vec * (log(nn_cum_vec) - log(arg_log))\n",
    "        fit_vec <- fit_vec - prior\n",
    "        \n",
    "        supp <- c(0, best) + fit_vec\n",
    "        \n",
    "#       R-th changepoint is the maximum of the fitness\n",
    "        best <- c(best, max(supp))\n",
    "        last <- c(last, which.max(supp))\n",
    "         \n",
    "}    \n",
    "    \n",
    "#   find changepoints by iteratively peeling off the last block\n",
    "    \n",
    "    index <- last[N]\n",
    "\n",
    "    change_points <- NULL\n",
    "\n",
    "    while(index > 1){\n",
    "        change_points <- c(index, change_points)\n",
    "        index <- last[index - 1]\n",
    "    }\n",
    "    \n",
    "    change_points <- c(begin, blocks[change_points], end)\n",
    "    \n",
    "    return(change_points)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Testing the algorithm\n",
    "\n",
    "Generate a random dataset to test the algorithm and its performances."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# generate some test data\n",
    "test <- c(rnorm(1000, 0, 1), rgamma(1000, 9, 2))\n",
    "test <- test[(test > -5) & (test < 10)]\n",
    "test <- sort(test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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       "\\item -1.43939039735184\n",
       "\\item -0.777721527081844\n",
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       "\\item 1.49567309165681\n",
       "\\item 2.56524166735002\n",
       "\\item 5.64385277016832\n",
       "\\item 7.25529543908165\n",
       "\\item 9.80572149859115\n",
       "\\end{enumerate*}\n"
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       "1. -3.66626825425181\n",
       "2. -2.53503663878829\n",
       "3. -1.82295815263663\n",
       "4. -1.43939039735184\n",
       "5. -0.777721527081844\n",
       "6. 0.921064482882592\n",
       "7. 1.49567309165681\n",
       "8. 2.56524166735002\n",
       "9. 5.64385277016832\n",
       "10. 7.25529543908165\n",
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       "\n",
       "\n"
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       " [1] -3.6662683 -2.5350366 -1.8229582 -1.4393904 -0.7777215  0.9210645\n",
       " [7]  1.4956731  2.5652417  5.6438528  7.2552954  9.8057215"
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     "metadata": {},
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   ],
   "source": [
    "# rebin the test data, prior values taken as suggested in Scargle paper\n",
    "cp_h <- bayesian_blocks(test, prior=7.61)\n",
    "cp_h"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "Plot with title \"Histogram of test\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "options(repr.plot.width=6, repr.plot.height=4) \n",
    "par(lwd=2)\n",
    "\n",
    "h_t  <- hist(test, breaks=100, freq=FALSE, col=rgb(0,0,1,0.4), lty='blank',\n",
    "             xlab=\"Test dataset\")\n",
    "h_bb <- hist(test, breaks=cp_h, freq=FALSE, border='blue4', add=TRUE)\n",
    "\n",
    "legend('top', col=c(rgb(0,0,1,0.4), 'blue4'), bty='n', \n",
    "       lty=c(NA, 1), pch=c(15, NA), cex=0.7, horiz = TRUE,\n",
    "       legend = c(\"Test data\", \"Bayesian blocks\")\n",
    "         )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Varying the value of `ncp_prior`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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rCzckLGnn+LH5/XP2IIGcGHFvjQYNLPY58/jZBW4EMLfCgw7+eBD81HSEPwoQU+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\n3AAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title \"\"prior\" == 4.02820683085348\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ULtd7B/H+mDCrtA4uSRHrBzUGHzoLCO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\nwqCwAIRBYQEIg8ICEMZ/mqsxgO6BKdAAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"\"prior\" == 13.1125620953892\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ncp_prior <- function(p0, N){ 4 - log(73.53 * p0 * N^(-0.478))}\n",
    "\n",
    "p0 <- c(1e-6, 0.001, 0.01, 0.1, 0.25, 0.5)\n",
    "N  <- c(10, 1000, 2000, 10000, 100000, 1e8)\n",
    "\n",
    "options(repr.plot.width=10, repr.plot.height=6) \n",
    "par(mfrow=c(2,3), lwd=1.5)\n",
    "\n",
    "for (i in 1:length(p0)){\n",
    "    cp <- bayesian_blocks(xs = test, prior=ncp_prior(p0[i], length(test)))\n",
    "    h_t  <- hist(test, breaks=100, freq=FALSE, col=rgb(0,0,1,0.4), lty='blank',\n",
    "                 xlab= parse(text = paste0(' p[0] == ', p0[i])), \n",
    "                 main= parse(text = paste0(' \"prior\" == ', ncp_prior(p0[i], length(test)) ) ) )\n",
    "    h_bb <- hist(test, breaks=cp, freq=FALSE, border='blue4', add=TRUE)\n",
    "\n",
    "}\n",
    "\n",
    "for (i in 1:length(N)){\n",
    "    cp <- bayesian_blocks(xs = test, prior=ncp_prior(0.01, N[i]))\n",
    "    h_t  <- hist(test, breaks=100, freq=FALSE, col=rgb(1,0,0,0.4), lty='blank',\n",
    "                 xlab= parse(text = paste0(' N == ', N[i])), \n",
    "                 main= parse(text = paste0(' \"prior\" == ', ncp_prior(0.01, N[i]) ) ) )\n",
    "    h_bb <- hist(test, breaks=cp, freq=FALSE, border='firebrick3', add=TRUE)\n",
    "\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Varying the $\\gamma$ value with geometric prior\n",
    "\n",
    "The contribute of the geometric prior in the algorithm simply consist of adding the constant $\\log \\gamma$ to the fitness of each block, meaning that the input parameter in the previously defined function needs to be equal to $-\\log \\gamma$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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1YKYd2l8llChLWj9bOE7oSVo4NJWIeC2JNHWO6LZIeesD5RYaXlkSYs8viCsCIg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",
      "text/plain": [
       "Plot with title \"\"prior\" == 0\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gamma <- c(1e-5, 1e-4, 1e-3, 1e-2, 0.1 ,1)\n",
    "\n",
    "options(repr.plot.width=10, repr.plot.height=6) \n",
    "par(mfrow=c(2,3), lwd=1.5)\n",
    "\n",
    "for (i in 1:length(gamma)){\n",
    "    cp <- bayesian_blocks(xs = test, prior=-log(gamma[i]))\n",
    "    h_t  <- hist(test, breaks=100, freq=FALSE, col=rgb(0,1,0,0.4), lty='blank',\n",
    "                 xlab= parse(text = paste0(' ~gamma == ', gamma[i])), \n",
    "                 main= parse(text = paste0(' \"prior\" == ', -log(gamma[i]) ) ) )\n",
    "    h_bb <- hist(test, breaks=cp, freq=FALSE, border='chartreuse4', add=TRUE)\n",
    "\n",
    "}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test on other datasets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# generate some test data\n",
    "test1 <- c(rnorm(2000, 0, 4))\n",
    "test1 <- test1[(test1 > -10) & (test1 < 10)]\n",
    "\n",
    "test2 <- c(rbeta(2000, 0.7, 0.7))\n",
    "test2 <- test2[(test2 > 0) & (test2 < 15)]\n",
    "\n",
    "test3 <- c(rcauchy(1000, 1, 0.7), rgamma(1000, 7.5, 1))\n",
    "test3 <- test3[(test3 > -5) & (test3 < 10)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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W9bhrDqsP4WnOfPTARVUI4hhZUlHwjL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\ngg==",
      "text/plain": [
       "Plot with title \"Histogram of test3\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "options(repr.plot.width=10, repr.plot.height=4) \n",
    "par(lwd=2, mfrow=c(1,3))\n",
    "\n",
    "cp_h1 <- bayesian_blocks(test1, prior=7.90708)\n",
    "\n",
    "h_t1  <- hist(test1, breaks=100, freq=FALSE, col=rgb(0.6,0.6,0,0.4), lty='blank',\n",
    "             xlab=\"Test dataset 1\")\n",
    "h_bb1 <- hist(test1, breaks=cp_h1, freq=FALSE, border='darkmagenta', add=TRUE)\n",
    "\n",
    "legend('top', col=c(rgb(0.6,0.6,0,0.4), 'darkmagenta'), bty='n', \n",
    "       lty=c(NA, 1), pch=c(15, NA), cex=0.7, horiz = TRUE,\n",
    "       legend = c(\"Test data\", \"Bayesian blocks\")\n",
    "         )\n",
    "\n",
    "cp_h2 <- bayesian_blocks(test2, prior=7.90708)\n",
    "\n",
    "h_t2  <- hist(test2, breaks=100, freq=FALSE, col=rgb(0.6,0.6,0,0.4), lty='blank',\n",
    "             xlab=\"Test dataset 2\")\n",
    "h_bb2 <- hist(test2, breaks=cp_h2, freq=FALSE, border='darkmagenta', add=TRUE)\n",
    "\n",
    "legend('top', col=c(rgb(0.6,0.6,0,0.4), 'darkmagenta'), bty='n', \n",
    "       lty=c(NA, 1), pch=c(15, NA), cex=0.7, horiz = TRUE,\n",
    "       legend = c(\"Test data\", \"Bayesian blocks\")\n",
    "         )\n",
    "\n",
    "cp_h3 <- bayesian_blocks(test3, prior=7.90708)\n",
    "\n",
    "h_t3  <- hist(test3, breaks=100, freq=FALSE, col=rgb(0.6,0.6,0,0.4), lty='blank',\n",
    "             xlab=\"Test dataset 3\")\n",
    "h_bb3 <- hist(test3, breaks=cp_h3, freq=FALSE, border='darkmagenta', add=TRUE)\n",
    "\n",
    "legend('top', col=c(rgb(0.6,0.6,0,0.4), 'darkmagenta'), bty='n', \n",
    "       lty=c(NA, 1), pch=c(15, NA), cex=0.7, horiz = TRUE,\n",
    "       legend = c(\"Test data\", \"Bayesian blocks\")\n",
    "         )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Application on a real dataset\n",
    "\n",
    "Being the algorithm really flexible and easily applicable, the bayesian blocks method is applied to an energy spectrum, differently from what done in Scargle 2013, where only time based events are treated.\n",
    "\n",
    "The dataset analysed is collected via a Germanium detector, and concerns the energy spectrum of a $Am241$, $ Co60$ and $Cs137$ radioactive source. In the experimental setting, the source was well sealed and hence we can consider the detected signals as photons emitted by $\\gamma$ decay of the source, while the contribute of normally produced $\\alpha$ particles can be considered negligible since they were absorbed by the sealing system.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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X0Zp1CyfmoOwlLDSmEtyav5/CSsasOy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\nADUgLABQA8ICADUgLABQA8ICADX8Ax3yR8UzWPMfAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"AmCoCs energy spectrum, logscale\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# skip the first two lines as they are only a header\n",
    "data   <- read.table(\"./Data/B19036_AmCsCo_20180316.dat\", skip=2)\n",
    "counts <- data[,1]\n",
    "\n",
    "#set the initial bins as reported in the header of the data file\n",
    "bins   <- c(0:8191)\n",
    "\n",
    "# Preliminary computation: start data at the first non-empty bin\n",
    "\n",
    "idx    <- which(counts >0)[1]\n",
    "counts <- counts[idx:length(counts)]\n",
    "bins   <- bins[idx:length(bins)]\n",
    "\n",
    "options(repr.plot.width=10, repr.plot.height=4)  #to set graph size\n",
    "par(mfrow=c(1,2))\n",
    "\n",
    "plot(bins, counts, type='s', lwd=0.5, col= 'azure4',\n",
    "     xlab=\"ADC channels\", ylab=\"Counts\", main=\"AmCoCs energy spectrum\")\n",
    "plot(bins, counts, type='s', lwd=0.5, col= 'azure4', log='y',\n",
    "     xlab=\"ADC channels\", ylab=\"Counts\", main=\"AmCoCs energy spectrum, logscale\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before applying the algorithm, a function to assign the proper bin value to rebinned histogram is defined: this is necessary due to the structure of the collected data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "rebin_bb <- function(bins, counts, change_points){\n",
    "\n",
    "#   Parameters\n",
    "#   ----------\n",
    "#   bins : vector, \n",
    "#         'old' bin edges\n",
    "#   counts: vector,\n",
    "#         counts assigned to old binning\n",
    "#   change_points: vector,\n",
    "#         'new' binning\n",
    "\n",
    "#   Returns\n",
    "#   -------\n",
    "#   rebin : vector\n",
    "#         values assigned to the new bins\n",
    "    \n",
    "    rebin <- NULL\n",
    "    y <- 0\n",
    "#   assume that old binning is evenly spaced\n",
    "    dn <- bins[2]-bins[1]\n",
    "    \n",
    "    for (i in 1:(length(change_points))){\n",
    "        ifelse( ( bins < change_points[i+1] ) & ( bins > change_points[i] ),\n",
    "               { y <- sum(counts[bins < change_points[i+1] & bins > change_points[i]])\n",
    "                 y <- y/(dn*length(counts[bins < change_points[i+1] & bins > change_points[i]]))\n",
    "                 rebin <- c(rebin, y)},\n",
    "               next\n",
    "            )\n",
    "    }\n",
    "#   neededor proper data presentation\n",
    "    rebin <- c(0,rebin)\n",
    "    \n",
    "    if (length(rebin) == length(change_points)){ \n",
    "        return(rebin)\n",
    "    }\n",
    "    else { \n",
    "        return(c(rebin, rebin[length(rebin)])) \n",
    "    }\n",
    "    \n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we can perform the rebinning of the dataset. We will use as prior the computed value of $7.61$ at first, then we will also analyze some different values of the prior."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "Plot with title \"AmCoCs energy spectrum\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cp <- bayesian_blocks(xs = bins, prior = 7.61, nn_vec = counts)\n",
    "rebin <- rebin_bb(bins = bins, counts = counts, change_points = cp)\n",
    "\n",
    "options(repr.plot.width=6, repr.plot.height=4)  #to set graph size\n",
    "\n",
    "plot(bins, counts, col= 'azure4', type='s', lwd=0.1, log='y',\n",
    "     xlab=\"ADC channels\", ylab=\"Counts\", main=\"AmCoCs energy spectrum\")\n",
    "lines(cp, rebin, type='s', col='red')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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susRNomYmFNBl2tTm1YesuGNT0EwppKy69iFlZ40NViYFjKpr0SYU1l94aFroKA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\nYQGAGDAsABADhgUAYvgPBorcd7U9YfMAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"\"AmCoCs energy spectrum, prior\" == 1\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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fhdFYg1ierOr3J6m4GFV6tT3p9TTm81sC4q+Xvoqec9UZevqkCsaVSPzco3HFh4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\nQmCC",
      "text/plain": [
       "Plot with title \"\"AmCoCs energy spectrum, prior\" == 5\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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bRKVyx5klwp3SjwisDSiAKx5ElypXSjwCsCSyMKxJInyZXSjQKvCCyNxMX6l5JY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\nNfwHmRHau2RY1VUAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"\"AmCoCs energy spectrum, prior\" == 8.61469327977946\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "Plot with title \"\"AmCoCs energy spectrum, prior\" == 1000\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "test_priors <- c(1e-3, 1, 2, 5, 7.61, ncp_prior(p0 = 0.01, N = 8192), 50, 1000)\n",
    "\n",
    "options(repr.plot.width=10, repr.plot.height=4)  #to set graph size\n",
    "par(mfrow=c(1,2))\n",
    "\n",
    "for (i in 1:length(test_priors)){\n",
    "    cp <- NULL\n",
    "    rebin <- NULL\n",
    "    cp <- bayesian_blocks(xs = bins, prior = test_priors[i], nn_vec = counts)\n",
    "    rebin <- rebin_bb(bins = bins, counts = counts, change_points = cp)\n",
    "\n",
    "    plot(bins, counts, col= 'azure4', type='s', lwd=0.1, log='y',\n",
    "         xlab=\"ADC channels\", ylab=\"Counts\",\n",
    "         main= parse(text = paste0(' \"AmCoCs energy spectrum, prior\" == ', test_priors[i] ) ) )\n",
    "    lines(cp, rebin, type='s', col='red')\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Further studies\n",
    "\n",
    "- data that contain highly-repeated unique values may result pathological for the algorithm. See https://medium.com/@janplus/stratified-bayesian-blocks-2bd77c1e6cc7 for a possible solution (Stratified Bayesian Blocks)\n",
    "- try different fitness functions (see Appendix of Scargle 2013)\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}