5_Frequentist_Analysis.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#The linear model is considered as the null hypothesis\n",
    "#Import the required modules\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "from scipy import optimize, stats\n",
    "import csv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Convert the dat file to csv file\n",
    "# read testdata.dat to a list of lists\n",
    "datContent = [i.strip().split() for i in open(\"./testdata.dat\").readlines()]\n",
    "\n",
    "# write it as a new CSV file\n",
    "with open(\"./testdata.csv\", \"w\") as f:\n",
    "    writer = csv.writer(f)\n",
    "    writer.writerows(datContent)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#read the csv file\n",
    "global data, x, y, sigma_y, val1, val2, val3  #defined as global so all functions can access these values\n",
    "data = pd.read_csv('testdata.csv')\n",
    "x = data['x']\n",
    "y = data['y']\n",
    "sigma_y = data['sigma_y']\n",
    "\n",
    "#initialise theta for all the fits to zero\n",
    "val1 = np.array([0, 0])\n",
    "val2 = np.array([0, 0, 0])\n",
    "val3 = np.array([0, 0, 0, 0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Defining the required functions for fitting\n",
    "def linearFunc(x, val1):\n",
    "    return val1[1]*x+val1[0]\n",
    "\n",
    "def quadraticFunc(x, val2):\n",
    "    return val2[2]*x**2 + val2[1]*x + val2[0]\n",
    "\n",
    "def cubicFunc(x, val3):\n",
    "    return val3[3]*x**3 + val3[2]*x**2 + val3[1]*x + val3[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#The log-likelihood function\n",
    "#The log-likelihood function is maximum for best fitting value of theta\n",
    "def logL(theta, n):\n",
    "    if n==1:\n",
    "        y_fit = linearFunc(x, theta)\n",
    "    elif n==2:\n",
    "        y_fit = quadraticFunc(x, theta)\n",
    "    elif n==3:\n",
    "        y_fit = cubicFunc(x, theta)\n",
    "    return sum(stats.norm.logpdf(*args)\n",
    "               for args in zip(y, y_fit, sigma_y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "#This function returns the best theta for the fitting\n",
    "def best_theta(n, theta_val):\n",
    "    if n==1:\n",
    "        theta_0 = (n+1)*[0]\n",
    "        neg_logL = lambda theta: -logL(theta, 1)\n",
    "        return optimize.fmin_bfgs(neg_logL, theta_0, disp=False)\n",
    "    if n==2:\n",
    "        theta_0 = (n+1)*[0]\n",
    "        neg_logL = lambda theta: -logL(theta, 2)\n",
    "        return optimize.fmin_bfgs(neg_logL, theta_0, disp=False)\n",
    "    if n==3:\n",
    "        theta_0 = (n+1)*[0]\n",
    "        neg_logL = lambda theta: -logL(theta, 3)\n",
    "        return optimize.fmin_bfgs(neg_logL, theta_0, disp=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "#compute chi2 likelihood for frequentist\n",
    "def compute_chi2(n):\n",
    "    if n==1:\n",
    "        theta = best_theta(n, val1)\n",
    "        resid = ((y - linearFunc(x, theta)) / sigma_y)\n",
    "    elif n==2:\n",
    "        theta = best_theta(n, val2)\n",
    "        resid = ((y - quadraticFunc(x, theta)) / sigma_y)\n",
    "    elif n==3:\n",
    "        theta = best_theta(n, val3)\n",
    "        resid = ((y - cubicFunc(x, theta)) / sigma_y)\n",
    "\n",
    "    return np.sum(resid ** 2)\n",
    "\n",
    "def compute_dof(degree, data=data):\n",
    "    return data.shape[0] - (degree + 1)\n",
    "\n",
    "def chi2_likelihood(n):\n",
    "    chi2 = compute_chi2(n)\n",
    "    dof = compute_dof(n)\n",
    "    return stats.chi2(dof).pdf(chi2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Compute the p value for the fit using linear model as the null hypothesis\n",
    "def p_val(n):\n",
    "    return 1-stats.chi2(n-1).cdf(compute_chi2(1) - compute_chi2(n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Compute the optimized values of the parameters\n",
    "r1 = best_theta(1, val1)\n",
    "r2 = best_theta(2, val2)\n",
    "r3 = best_theta(3, val3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Log L values\n",
      "linear model:    logL = 22.01834340803627\n",
      "quadratic model: logL = 22.924910312002723\n",
      "cubic model:    logL = 23.13040925879735\n"
     ]
    }
   ],
   "source": [
    "print(\"Log L values\")\n",
    "print(\"linear model:    logL =\", logL(best_theta(1, val1), 1))\n",
    "print(\"quadratic model: logL =\", logL(best_theta(2, val2), 2))\n",
    "print(\"cubic model:    logL =\", logL(best_theta(3, val3), 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "chi2 likelihood\n",
      "- linear model:     0.045383795585920046\n",
      "- quadratic model:  0.036608447550142253\n",
      "- cubic model:  0.04215280601014979\n"
     ]
    }
   ],
   "source": [
    "print(\"chi2 likelihood\")\n",
    "print(\"- linear model:    \", chi2_likelihood(1))\n",
    "print(\"- quadratic model: \", chi2_likelihood(2))\n",
    "print(\"- cubic model: \", chi2_likelihood(3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p_values\n",
      "- quadratic model:  0.1781327569531711\n",
      "- cubic model:  0.32887884419649793\n"
     ]
    }
   ],
   "source": [
    "print(\"p_values\") #The p value for null hypothesis will not be defined as the delta chi square value is zero\n",
    "print(\"- quadratic model: \", p_val(2))\n",
    "print(\"- cubic model: \", p_val(3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'\\nFrom the p values of frequentist analysis, as both the p values are greater than 0.05, we can not reject our\\nNull Hypothesis.\\n'"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "From the p values of frequentist analysis, as both the p values are greater than 0.05, we can not reject our\n",
    "Null Hypothesis.\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"Bayesian Analysis\"\"\"\n",
    "#Compute the AICc values as number of data points is considerably small\n",
    "AIC1 = -2*logL(r1, 1) + (2.0*2*20)/(17.0)\n",
    "AIC2 = -2*logL(r2, 2) + (2.0*3*20)/(16.0)\n",
    "AIC3 = -2*logL(r3, 3) + (2.0*4*20)/(15.0)\n",
    "\n",
    "#Compute the BIC values\n",
    "BIC1 = -2*logL(r1, 1) + 2*np.log(x.shape[0])\n",
    "BIC2 = -2*logL(r2, 2) + 3*np.log(x.shape[0])\n",
    "BIC3 = -2*logL(r3, 3) + 4*np.log(x.shape[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AICc values\n",
      "- linear model:     -39.330804463131365\n",
      "- quadratic model:  -38.349820624005446\n",
      "- cubic model:  -35.594151850928036\n"
     ]
    }
   ],
   "source": [
    "print(\"AICc values\")\n",
    "print(\"- linear model:    \", AIC1)\n",
    "print(\"- quadratic model: \", AIC2)\n",
    "print(\"- cubic model: \", AIC3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Delta AIC values\n",
      "- linear model:     0.0\n",
      "- quadratic model:  0.9809838391259191\n",
      "- cubic model:  3.7366526122033292\n"
     ]
    }
   ],
   "source": [
    "#Computing delta AIC\n",
    "AIC_min = min(AIC1, AIC2, AIC3)\n",
    "print(\"Delta AIC values\")\n",
    "print(\"- linear model:    \", AIC1-AIC_min)\n",
    "print(\"- quadratic model: \", AIC2-AIC_min)\n",
    "print(\"- cubic model: \", AIC3-AIC_min)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'\\nFor quadratic model, 0 < delta AIC < 2, which implies that quadratic model also has a substantial support.\\nFor cubic model, 2 < delta AIC < 4, which implies that cubic model has cosiderably less support.\\n'"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "For quadratic model, 0 < delta AIC < 2, which implies that quadratic model also has a substantial support.\n",
    "For cubic model, 2 < delta AIC < 4, which implies that cubic model has cosiderably less support.\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "BIC vlaues\n",
      "- linear model:     -38.04522226896456\n",
      "- quadratic model:  -36.862623803343475\n",
      "- cubic model:  -34.27788942337874\n"
     ]
    }
   ],
   "source": [
    "print(\"BIC vlaues\")\n",
    "print(\"- linear model:    \", BIC1)\n",
    "print(\"- quadratic model: \", BIC2)\n",
    "print(\"- cubic model: \", BIC3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Delta BIC values\n",
      "- linear model:     0.0\n",
      "- quadratic model:  1.1825984656210835\n",
      "- cubic model:  3.7673328455858197\n"
     ]
    }
   ],
   "source": [
    "#Computing delta BIC\n",
    "BIC_min = min(BIC1, BIC2, BIC3)\n",
    "print(\"Delta BIC values\")\n",
    "print(\"- linear model:    \", BIC1-BIC_min)\n",
    "print(\"- quadratic model: \", BIC2-BIC_min)\n",
    "print(\"- cubic model: \", BIC3-BIC_min)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'\\nFor quadratic model, 0 < delta BIC < 2, which implies that there is no evidence against quadratic model.\\nFor cubic model, 2 < delta AIC < 4, which implies that there is positive evidence against cubic model.\\n'"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "For quadratic model, 0 < delta BIC < 2, which implies that there is no evidence against quadratic model.\n",
    "For cubic model, 2 < delta AIC < 4, which implies that there is positive evidence against cubic model.\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"Plotting\"\"\"\n",
    "t =  np.linspace(0, 1, 1000)\n",
    "fig, ax = plt.subplots(figsize=(10, 10))\n",
    "plt.plot(t, linearFunc(t, r1), label='linear_fitting')\n",
    "plt.plot(t, quadraticFunc(t, r2), label='quadratic_fitting')\n",
    "plt.plot(t, cubicFunc(t, r3), label='cubic_fitting')\n",
    "plt.legend()\n",
    "plt.xlabel('$x$')\n",
    "plt.ylabel('$y$')\n",
    "plt.title(\"Curve fitting using Linear, Quadratic and Cubic Models\", size=15)\n",
    "ax.errorbar(x, y, sigma_y, fmt='ok', ecolor = 'gray')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.15rc1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}