environment.yml

name: example-environment

dependencies:
  - numpy
  - scipy
  - matplotlib

homework1-code.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.stats import expon\n",
    "from scipy import stats\n",
    "import random\n",
    "def proposal(x):\n",
    "    return x + random.randint(-5,5)\n",
    "\n",
    "n = 100\n",
    "\n",
    "density = lambda k: stats.binom.pmf(k, n, 0.75)\n",
    "\n",
    "def accept(x, y):\n",
    "    acceptance_proba = min(1, density(y)/density(x))\n",
    "    if np.random.uniform(0,1) < acceptance_proba:\n",
    "        return True\n",
    "    else:\n",
    "        return False\n",
    "\n",
    "def next_state(x):\n",
    "    y = proposal(x)\n",
    "    if accept(x, y):\n",
    "        return y\n",
    "    else:\n",
    "        return x\n",
    "\n",
    "def run_chain(n, x0):\n",
    "    states = []\n",
    "    current = x0\n",
    "    for i in range(n):\n",
    "        current = next_state(current)\n",
    "        states.append(current)\n",
    "    return states\n",
    "\n",
    "output = run_chain(1000, 1.0)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.bar(range(n+1), np.bincount(output, minlength=n+1))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f681dc5e1d0>]"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Here we plot the exact pmf of the binomial(100,0.75) distribution\n",
    "plt.plot(range(n+1), [density(k) for k in range(n+1)]) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}