{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bayesian Methods"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Environment setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Python version: 3.7.5\n",
      "NumPy version: 1.18.1\n"
     ]
    }
   ],
   "source": [
    "import platform\n",
    "\n",
    "print(f\"Python version: {platform.python_version()}\")\n",
    "assert platform.python_version_tuple() >= (\"3\", \"6\")\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "print(f\"NumPy version: {np.__version__}\")\n",
    "\n",
    "from IPython.display import YouTubeVideo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Bayes' theorem"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Thomas Bayes (1701-1761)\n",
    "\n",
    "English statistician, philosopher and presbyterian minister.\n",
    "\n",
    "[![Thomas Bayes](images/Thomas_Bayes.gif)](https://en.wikipedia.org/wiki/Thomas_Bayes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Bayes' legacy\n",
    "\n",
    "- Blaise Pascal (1623-1662) pioneered the study of probabilies of *effects* given *causes*.\n",
    "- On the contrary, Thomas Bayes proposed a formula, known as **Bayes's theorem**, for computing the probability of a *cause* given an *effect*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Intuitive explanation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
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      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"400\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/HZGCoVF3YvM\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x11560dc90>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "YouTubeVideo(\"HZGCoVF3YvM\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Quick proof"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/jpeg": 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     "execution_count": 5,
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    "YouTubeVideo(\"U_85TaXbeIo\")"
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  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Naïve Bayes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Naïve Bayes in a nutshell\n",
    "\n",
    "- Set of (supervised) learning algorithms based on applying Bayes’ theorem.\n",
    "- \"Naïve\" assumption: conditional independence between every pair of features given the value of the class variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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