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Update Bayesianism.ipynb
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notebooks/Bayesianism.ipynb

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"id": "Kzu5pR2q_MuU"
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"source": [
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"Notice how, in this second approach, the normal likelihood for data $x$ became a normal prior for parameters $\\epsilon$.\n",
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"\n",
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"Bayes' theorem is like the [honey badger](https://www.youtube.com/watch?v=4r7wHMg5Yjg), it simply doesn't care!"
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"Notice how, in this second approach, the normal likelihood for data $x$ became a normal prior for parameters $\\epsilon$."
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"In a way this is a consequence of their academic backgrounds and original goals. Statistics methods were designed as scientific tools and, without surprise, they are widely used in Science. Machine Learning -- as a branch of Artificial Intelligence -- focused more on engineering problems, which naturally found their niche in Business (cf. [Statistical Modeling: The Two Cultures](https://projecteuclid.org/journals/statistical-science/volume-16/issue-3) by Leo Breiman)."
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"cell_type": "markdown",
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"metadata": {},
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"Using a predictive method to get an answer should not be seen as the final goal. It is important to understand why the data is as it is. And to list the assumptions that must be made to build a model able to generate similar data. This is a process of interpretation that conveys understanding about the original problem, something pure prediction is unable to provide."
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"cell_type": "markdown",
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"<center>* * *</center>\n",
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"\n",
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"However, it is perfectly possible to deal with prediction in a Bayesian setting.\n",
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"\n",
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"Consider we wish to predict the probability of a future value $y$, with parameters $\\theta$ representing the current model knowledge. The *predictive distribution* is the distribution of possible unobserved values conditional on the evidence of observed values. We can compute the predictive distribution by integrating out the model parameters,\n",

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