Sampling and MCMC.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import plotly.graph_objects as go\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import scipy as sp\n",
    "from sklearn import linear_model\n",
    "import math\n",
    "from scipy.optimize import minimize\n",
    "from scipy.optimize import Bounds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def genSample(iterrations, mean, sd):\n",
    " track  = np.empty(((iterrations), 3))\n",
    " cumSum = 0   \n",
    " for i in range(iterrations):\n",
    "        track[i, 0] = i+1\n",
    "        track[i, 1] = np.random.normal(mean, sd, 1)\n",
    "        cumSum = cumSum + track[i, 1]\n",
    "        track[i, 2] = cumSum/(i+1)\n",
    " return(track)    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
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\"#E5ECF6\", \"caxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}}, \"title\": {\"x\": 0.05}, \"xaxis\": {\"automargin\": true, \"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\", \"title\": {\"standoff\": 15}, \"zerolinecolor\": \"white\", \"zerolinewidth\": 2}, \"yaxis\": {\"automargin\": true, \"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\", \"title\": {\"standoff\": 15}, \"zerolinecolor\": \"white\", \"zerolinewidth\": 2}}}, \"width\": 500},\n",
       "                        {\"responsive\": true}\n",
       "                    ).then(function(){\n",
       "                            \n",
       "var gd = document.getElementById('dff3e89a-fc72-4f5b-972f-391fd1c58abe');\n",
       "var x = new MutationObserver(function (mutations, observer) {{\n",
       "        var display = window.getComputedStyle(gd).display;\n",
       "        if (!display || display === 'none') {{\n",
       "            console.log([gd, 'removed!']);\n",
       "            Plotly.purge(gd);\n",
       "            observer.disconnect();\n",
       "        }}\n",
       "}});\n",
       "\n",
       "// Listen for the removal of the full notebook cells\n",
       "var notebookContainer = gd.closest('#notebook-container');\n",
       "if (notebookContainer) {{\n",
       "    x.observe(notebookContainer, {childList: true});\n",
       "}}\n",
       "\n",
       "// Listen for the clearing of the current output cell\n",
       "var outputEl = gd.closest('.output');\n",
       "if (outputEl) {{\n",
       "    x.observe(outputEl, {childList: true});\n",
       "}}\n",
       "\n",
       "                        })\n",
       "                };\n",
       "                });\n",
       "            </script>\n",
       "        </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "p1 = go.Figure()\n",
    "track = genSample(1000, 10, 2)\n",
    "p1.add_trace(go.Scatter(x = track[:,0], y = track[:,2],\n",
    "                    mode='lines',\n",
    "                    name = 'sample 1'                            \n",
    "                    ))\n",
    "track = genSample(1000, 10, 2)\n",
    "p1.add_trace(go.Scatter(x = track[:,0], y = track[:,2],\n",
    "                    mode='lines',\n",
    "                    name = 'sample 2'                            \n",
    "                    ))\n",
    "track = genSample(1000, 10, 2)\n",
    "p1.add_trace(go.Scatter(x = track[:,0], y = track[:,2],\n",
    "                    mode='lines',\n",
    "                    name = 'sample 3'                            \n",
    "                    ))\n",
    "p1.update_layout(autosize = False, width = 500, height = 400, \n",
    "                 plot_bgcolor = '#FFFFFF')\n",
    "\n",
    "p1.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = np.random.normal(10, 2, 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def llNorm(parameters):\n",
    " mu = parameters[0]\n",
    " sigma = parameters[1]\n",
    " NLL = -len(data)/2 * np.log(2 * np.pi) - (len(data)/2) * np.log(sigma**2)\n",
    " tmp = 0\n",
    " for val in data:\n",
    "  tmp = tmp + ((val-mu)**2)\n",
    " NLL = NLL + -(1/(2*(sigma**2)))*tmp\n",
    " return(-NLL) \n",
    "\n",
    "def proposalfunction(param, t):\n",
    " return(float(np.random.uniform((param - t),(param + t),1))) # be more careful with Python more stongly typed\n",
    "\n",
    "def MCMC(startval, iterrations, t):\n",
    "#    chain  = np.zeros(((iterrations+1), 2))\n",
    "    chain  = np.empty(((iterrations+1), 2))\n",
    "    chain[0,1] = startval\n",
    "    sigma = 2 \n",
    "    for i in range(iterrations):\n",
    "     chain[i, 0] = i\n",
    "     proposal = proposalfunction(chain[i,1], t)\n",
    "     if (llNorm(np.array([chain[i,1],sigma])) < llNorm(np.array([proposal,sigma]))):\n",
    "        chain[i+1,1] = chain[i,1]\n",
    "     else:\n",
    "        chain[i+1,1] = proposal\n",
    "    return(chain)\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "config": {
        "plotlyServerURL": "https://plot.ly"
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{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattergeo\"}], \"scattergl\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattergl\"}], \"scattermapbox\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattermapbox\"}], \"scatterpolar\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatterpolar\"}], \"scatterpolargl\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatterpolargl\"}], \"scatterternary\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatterternary\"}], \"surface\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"surface\"}], \"table\": [{\"cells\": {\"fill\": {\"color\": \"#EBF0F8\"}, \"line\": {\"color\": \"white\"}}, \"header\": {\"fill\": {\"color\": \"#C8D4E3\"}, \"line\": {\"color\": \"white\"}}, \"type\": \"table\"}]}, \"layout\": {\"annotationdefaults\": {\"arrowcolor\": \"#2a3f5f\", \"arrowhead\": 0, \"arrowwidth\": 1}, \"coloraxis\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"colorscale\": {\"diverging\": [[0, \"#8e0152\"], [0.1, \"#c51b7d\"], [0.2, \"#de77ae\"], [0.3, \"#f1b6da\"], [0.4, \"#fde0ef\"], [0.5, \"#f7f7f7\"], [0.6, \"#e6f5d0\"], [0.7, \"#b8e186\"], [0.8, \"#7fbc41\"], [0.9, \"#4d9221\"], [1, \"#276419\"]], \"sequential\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"sequentialminus\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]]}, \"colorway\": [\"#636efa\", \"#EF553B\", \"#00cc96\", \"#ab63fa\", \"#FFA15A\", \"#19d3f3\", \"#FF6692\", \"#B6E880\", \"#FF97FF\", \"#FECB52\"], \"font\": {\"color\": \"#2a3f5f\"}, \"geo\": {\"bgcolor\": \"white\", \"lakecolor\": \"white\", \"landcolor\": \"#E5ECF6\", \"showlakes\": true, \"showland\": true, \"subunitcolor\": \"white\"}, \"hoverlabel\": {\"align\": \"left\"}, \"hovermode\": \"closest\", \"mapbox\": {\"style\": \"light\"}, \"paper_bgcolor\": \"white\", \"plot_bgcolor\": \"#E5ECF6\", \"polar\": {\"angularaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"bgcolor\": \"#E5ECF6\", \"radialaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}}, \"scene\": {\"xaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}, \"yaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}, \"zaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}}, \"shapedefaults\": {\"line\": {\"color\": \"#2a3f5f\"}}, \"ternary\": {\"aaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"baxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"bgcolor\": \"#E5ECF6\", \"caxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}}, \"title\": {\"x\": 0.05}, \"xaxis\": {\"automargin\": true, \"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\", \"title\": {\"standoff\": 15}, \"zerolinecolor\": \"white\", \"zerolinewidth\": 2}, \"yaxis\": {\"automargin\": true, \"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\", \"title\": {\"standoff\": 15}, \"zerolinecolor\": \"white\", \"zerolinewidth\": 2}}}, \"width\": 500},\n",
       "                        {\"responsive\": true}\n",
       "                    ).then(function(){\n",
       "                            \n",
       "var gd = document.getElementById('12bb4dab-fb89-4bb7-a0e8-4a5a3c01dc7f');\n",
       "var x = new MutationObserver(function (mutations, observer) {{\n",
       "        var display = window.getComputedStyle(gd).display;\n",
       "        if (!display || display === 'none') {{\n",
       "            console.log([gd, 'removed!']);\n",
       "            Plotly.purge(gd);\n",
       "            observer.disconnect();\n",
       "        }}\n",
       "}});\n",
       "\n",
       "// Listen for the removal of the full notebook cells\n",
       "var notebookContainer = gd.closest('#notebook-container');\n",
       "if (notebookContainer) {{\n",
       "    x.observe(notebookContainer, {childList: true});\n",
       "}}\n",
       "\n",
       "// Listen for the clearing of the current output cell\n",
       "var outputEl = gd.closest('.output');\n",
       "if (outputEl) {{\n",
       "    x.observe(outputEl, {childList: true});\n",
       "}}\n",
       "\n",
       "                        })\n",
       "                };\n",
       "                });\n",
       "            </script>\n",
       "        </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "iterations = 100\n",
    "p1 = go.Figure()\n",
    "chain = MCMC(6, iterations, 1)\n",
    "p1.add_trace(go.Scatter(x = chain[:,0], y = chain[:,1],\n",
    "                    mode='lines',\n",
    "                    name = 'sample 1'                            \n",
    "                    ))\n",
    "chain = MCMC(11, iterations, 1)\n",
    "\n",
    "p1.add_trace(go.Scatter(x = chain[:,0], y = chain[:,1],\n",
    "                    mode='lines',\n",
    "                    name = 'sample 2'                            \n",
    "                    ))\n",
    "chain = MCMC(20, iterations, 1)\n",
    "p1.add_trace(go.Scatter(x = chain[:,0], y = chain[:,1],\n",
    "                    mode='lines',\n",
    "                    name = 'sample 3'                            \n",
    "                    ))\n",
    "p1.update_layout(autosize = False, width = 500, height = 400, \n",
    "                 plot_bgcolor = '#FFFFFF')\n",
    "\n",
    "p1.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.5"
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 "nbformat": 4,
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