deamination_estimator_simulation_20200324.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Methylation and Deamination Estimators Simulation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "author: lee.carlin@mail.huji.ac.il  \n",
    "date: 2020-03-23"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Table of Contents:  \n",
    "    * [Simple Binomial Model](#A-Simple-Binomial-Model)  \n",
    "    * [A Read Position Binomial Model](#A-Read-Position-Binomial-Model)  \n",
    "    * [A Read Position GLM Model](#A-Read-Position-GLM-Model) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# libraries:\n",
    "import numpy as np\n",
    "import scipy as sp\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import fsolve, newton\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "import statsmodels.api as sm\n",
    "from scipy.optimize import fsolve, newton"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A Simple Binomial Model  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* $n_i$ is the total coverage at position $i$  \n",
    "* $t_i, c_i$ are the total numbers of observed T and C bases at $i$ , respectively.   \n",
    "* $n_i=t_i+c_i$  \n",
    "* $m_i$ is the methylation level at position $i$, $0<=m_i<=1$  \n",
    "* $\\pi$ is the average deamination rate over all reads.   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$t_i$ is generated according to the following binomial process:    \n",
    "$t_i \\sim Bin(n_i,\\pi m_i)$   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The ML:  \n",
    "$L(\\pi m_i|n_i,t_i) = \\binom{n_i}{t_i} (\\pi m_i)^{t_i}(1-\\pi m_i)^{n_i-t_i}$m"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The MLE:  \n",
    "$\\hat{\\pi m_i}  = \\frac{t_i}{n_i}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Setting parameters \n",
    "max_n_i = 1000\n",
    "m_i = 0.7\n",
    "pi = 0.2\n",
    "n_i = 30\n",
    "# Sampling datapoints:\n",
    "t_i = np.random.binomial(1,pi*m_i,n_i)\n",
    "# Using sample to calculate estimator:\n",
    "# estimator = t_i.sum()/(n_i*pi)\n",
    "est_list = []\n",
    "rng = range(10,max_n_i,10)\n",
    "for i in rng:\n",
    "    est_list.append(np.random.binomial(1,pi*m_i,i).sum()/(i*pi))\n",
    "# Plotting simulation:\n",
    "fig = plt.figure(figsize = (15,8))\n",
    "ax = fig.add_subplot(111)\n",
    "ax.plot(list(rng),est_list,)\n",
    "ax.axhline(y=m_i, color = 'red', ls='--')\n",
    "ax.set_title('MLE Simulation for simple Binomial model')\n",
    "plt.xlabel('$n_i$', fontsize=18)\n",
    "plt.ylabel('$m_i$', fontsize=16)\n",
    "plt.ylim([0,2])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A Read Position Binomial Model "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### In this variation the deamination rate is free to vary between read position $j$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$t_{i,j} \\sim Bern(\\theta_{i,j}) \\quad \\text{where} \\quad \\theta_{i,j} = \\pi_{i,j}^1 m_i +\\pi_{i,j}^0  (1- m_i)$  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We first simplify by using   $\\quad \\theta_{i,j} = \\pi_{i,j}^1 m_i $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The FOC of the MLE is:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\frac{ \\partial \\mathbf{l}(\\theta_{i,j})}{ \\partial \\theta_{i,j}\t}  \n",
    " =\\sum_{t_{i,j}}^{k_i} t_{i,j} \\frac{\\partial \\partial (\\theta_{i,j})}{\\theta_{i,j}}\n",
    " - \\sum_{t_{i,j}}^{k_i} (1-t_{i,j}) \\frac{\\partial \\partial (\\theta_{i,j})}{1-\\theta_{i,j}} $ \n",
    "  \n",
    "  where $ \\partial \\partial (\\theta_{i,j})$ is the partial derivative of $\\theta_{i,j}$ with respect to one of its variables. \n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we choose to take the partial derivative with respect to $m_i$, then"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\frac{ \\partial \\mathbf{l}(\\theta_{i,j})}{ \\partial \\theta_{i,j}\t}  \n",
    "=  \\sum_{t_{i,j}}^{k_i} t_{i,j} \\frac{\\pi_{i,j}}{\\theta_{i,j}}\n",
    "- \\sum_{t_{i,j}}^{k_i} (1-t_{i,j}) \\frac{\\pi_{i,j}}{1-\\theta_{i,j}}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulation:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Setting Parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_i =  30 # number of coverage per read\n",
    "m_i =  0.7 # min(np.random.uniform(0.7, 0.15),1)\n",
    "p_i = 0.2\n",
    "#pi_i = np.random.binomial(1,pi_high_ratio,n_i).astype(float)\n",
    "#pi_i[pi_i==1] = pi_high\n",
    "#pi_i[pi_i==0] = pi_low"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "#help(sp.optimize.brentq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of coverage per read: 30\n",
      "The true m_i: 0.700\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "m_i is = 0.7\n",
      "The solution is m_i = 0.6666666666666666\n",
      "at which the value of the expression is 0.0\n"
     ]
    }
   ],
   "source": [
    "\n",
    "# Define the expression whose roots we want to find:\n",
    "print('Number of coverage per read: {:,}'.format(n_i))\n",
    "print('The true m_i: {:.3f}'.format(m_i))\n",
    "# Plot it\n",
    "t_i = np.random.binomial(1,pi*m_i,n_i)\n",
    "def FOC(M_i,n_i,p_i):    \n",
    "    A = ((t_i*p_i)/(p_i*M_i)).sum()\n",
    "    oneMinusT = np.array([1]*n_i)-np.array(t_i)\n",
    "    oneMinusTheta = np.array([1]*n_i)-p_i*M_i\n",
    "    B = ((oneMinusT*p_i)/(oneMinusTheta)).sum()\n",
    "    return (A-B)\n",
    "#func = lambda M_i : ((t_i*pi_i)/(pi_i*M_i)).sum()-((np.array([1]*n_i)-np.array(t_i)*pi_i)/(np.array([1]*n_i)-pi_i*M_i)).sum()\n",
    "\n",
    "MM_i = np.linspace(0.01, 1, 99)\n",
    "y = []\n",
    "for i in MM_i:\n",
    "    y.append(FOC(i,n_i,p_i))\n",
    "\n",
    "plt.plot(MM_i, y)\n",
    "plt.xlabel(\"m_i\")\n",
    "plt.ylabel(\"expression value\")\n",
    "plt.grid()\n",
    "plt.show()\n",
    "\n",
    "\n",
    "m_i_initial_guess = 0.5\n",
    "m_i_solution = sp.optimize.brentq(FOC,a = 0.1, b = 0.9,args=(n_i,p_i))\n",
    "#m_i_solution = fsolve(FOC, m_i_initial_guess,args=(n_i,p_i))\n",
    "\n",
    "print(\"m_i is = {}\".format(m_i))\n",
    "print(\"The solution is m_i = {}\".format(m_i_solution))\n",
    "print(\"at which the value of the expression is {}\".format(FOC(m_i_solution,n_i,p_i)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "max_n_i = 10000\n",
    "# Plotting the simulation per coverage size:\n",
    "est_list = []\n",
    "rng = range(10,max_n_i,10)\n",
    "for i in rng:\n",
    "    t_i = np.random.binomial(1,pi*m_i,i)\n",
    "    solution = fsolve(FOC, m_i_initial_guess,args=(i,p_i))[0]\n",
    "    est_list.append(solution)\n",
    "# Plotting simulation:\n",
    "fig = plt.figure(figsize = (15,8))\n",
    "ax = fig.add_subplot(111)\n",
    "ax.plot(list(rng),est_list,)\n",
    "ax.axhline(y=m_i, color = 'red', ls='--')\n",
    "ax.set_title('MLE Simulation for Read Position Binomial model')\n",
    "plt.xlabel('$n_i$', fontsize=18)\n",
    "plt.ylabel('$m_i$', fontsize=16)\n",
    "plt.ylim([0,2])\n",
    "ax.axhline()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "max_n_i = 10000\n",
    "# Plotting the simulation per coverage size:\n",
    "est_list = []\n",
    "rng = range(10,max_n_i,10)\n",
    "for i in rng:\n",
    "    t_i = np.random.binomial(1,pi*m_i,i)\n",
    "    #solution = fsolve(FOC, m_i_initial_guess,args=(i,p_i))[0]\n",
    "    solution = sp.optimize.brentq(FOC,a = 1e-20, b = 1-1e-20,args=(i,p_i))\n",
    "    est_list.append(solution)\n",
    "# Plotting simulation:\n",
    "fig = plt.figure(figsize = (15,8))\n",
    "ax = fig.add_subplot(111)\n",
    "ax.plot(list(rng),est_list,)\n",
    "ax.axhline(y=m_i, color = 'red', ls='--')\n",
    "ax.set_title('MLE Simulation for Read Position Binomial model')\n",
    "plt.xlabel('$n_i$', fontsize=18)\n",
    "plt.ylabel('$m_i$', fontsize=16)\n",
    "plt.ylim([0,2])\n",
    "ax.axhline()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A Read Position GLM Model "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## WORK IN PROGRESS\n",
    "(I still have a few issues here)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Model:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have:  \n",
    "$t_{i,j} \\sim Bern(\\theta_{i,j}) \\quad \\text{where} \\quad \\theta_{i,j} = \\pi_{i,j}^1 m_i +\\pi_{i,j}^0  (1- m_i)$  \n",
    "Or the simplified case:   $\\quad \\theta_{i,j} = \\pi_{i,j}^1 m_i $\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$t_{i,j}∼Bernoulli(\\theta_{i,j})$    \n",
    "and \n",
    "$\\theta_{i} = \\pi_i \\beta$ \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\theta_{i,j}=\\alpha+\\beta*\\pi_{i,j}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "nothing is normal, so least squares,t and F tests, and so forth make no sense.  \n",
    "But maximum likelihood, the asymptotics of maximum likelihood estimates,   \n",
    "and likelihood ratio tests do make sense."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The maximum likelihood estimates can be found using an iteratively   \n",
    "reweighted least squares algorithm or a Newton's method "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\"quasi-likelihood\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We generate $t_{i,j}$ according to $Bern(\\theta_{i,j})$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Setting Parameters:\n",
    "n_i = 30\n",
    "m_i = 0.7\n",
    "p_i = [1*0.2]*n_i\n",
    "t_i = []\n",
    "for k in p_i:\n",
    "    t_i.append(np.random.binomial(1,k*m_i,1)[0])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                 Generalized Linear Model Regression Results                  \n",
      "==============================================================================\n",
      "Dep. Variable:                    t_i   No. Observations:                   30\n",
      "Model:                            GLM   Df Residuals:                       29\n",
      "Model Family:                Binomial   Df Model:                            0\n",
      "Link Function:               identity   Scale:                          1.0000\n",
      "Method:                          IRLS   Log-Likelihood:                -16.298\n",
      "Date:                Thu, 26 Mar 2020   Deviance:                       32.596\n",
      "Time:                        08:58:16   Pearson chi2:                     30.0\n",
      "No. Iterations:                     2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "p_i            1.1667      0.386      3.022      0.003       0.410       1.923\n",
      "==============================================================================\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.7/site-packages/ipykernel_launcher.py:4: DeprecationWarning: Calling Family(..) with a link class as argument is deprecated.\n",
      "Use an instance of a link class instead.\n",
      "  after removing the cwd from sys.path.\n",
      "/usr/local/lib/python3.7/site-packages/statsmodels/genmod/generalized_linear_model.py:278: DomainWarning: The identity link function does not respect the domain of the Binomial family.\n",
      "  DomainWarning)\n"
     ]
    }
   ],
   "source": [
    "df = pd.DataFrame({\"t_i\": t_i,\n",
    "                   \"p_i\": p_i})\n",
    "\n",
    "model = sm.formula.glm(\"t_i ~ 0 + p_i\",family=sm.families.Binomial(link=sm.families.links.identity), data=df ).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ToDo:  \n",
    "* How to add a constant ? Every example has a different link function.  \n",
    "* Check what optimization method suits best.  \n",
    "* A glm with a different link function\n",
    "* Check parity between methods  \n",
    "* Vary Pi maybe using gamma.   \n",
    "* How many reads do we need for consistent.  \n",
    "* Weighted GLM - "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [],
   "source": [
    "#model.params['p_i']+model.params['Intercept']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                 Generalized Linear Model Regression Results                  \n",
      "==============================================================================\n",
      "Dep. Variable:                    t_i   No. Observations:                   30\n",
      "Model:                            GLM   Df Residuals:                       29\n",
      "Model Family:                Gaussian   Df Model:                            0\n",
      "Link Function:               identity   Scale:                         0.18506\n",
      "Method:                          IRLS   Log-Likelihood:                -16.753\n",
      "Date:                Thu, 26 Mar 2020   Deviance:                       5.3667\n",
      "Time:                        08:59:18   Pearson chi2:                     5.37\n",
      "No. Iterations:                     3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "p_i            1.1667      0.393      2.971      0.003       0.397       1.936\n",
      "==============================================================================\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.7/site-packages/ipykernel_launcher.py:1: DeprecationWarning: Calling Family(..) with a link class as argument is deprecated.\n",
      "Use an instance of a link class instead.\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    }
   ],
   "source": [
    "model = sm.formula.glm(\"t_i ~ 0+ p_i\",family=sm.families.Gaussian(link=sm.families.links.identity), data=df ).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1416166394393.821"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.params['p_i']+model.params['Intercept']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 290,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intercept when fit_intercept=False : 0.00000\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[ 1.03349116e+11, -5.16745579e+11]])"
      ]
     },
     "execution_count": 290,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.datasets import make_regression\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "df = pd.DataFrame({\"t_i\": t_i,\n",
    "                   \"p_i\": pi})\n",
    "from patsy import dmatrices\n",
    "y, X = dmatrices('t_i ~ p_i', df, return_type = 'dataframe')\n",
    "\n",
    "\n",
    "lr_fi_true = LinearRegression(fit_intercept=True)\n",
    "lr_fi_false = LinearRegression(fit_intercept=False)\n",
    "\n",
    "lr_fi_true.fit(X, y)\n",
    "lr_fi_false.fit(X, y)\n",
    "\n",
    "#print('Intercept when fit_intercept=True : {:.5f}'.format(lr_fi_true.intercept_))\n",
    "print('Intercept when fit_intercept=False : {:.5f}'.format(lr_fi_false.intercept_))\n",
    "lr_fi_false.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                 Generalized Linear Model Regression Results                  \n",
      "==============================================================================\n",
      "Dep. Variable:                    t_i   No. Observations:                 9990\n",
      "Model:                            GLM   Df Residuals:                     9989\n",
      "Model Family:                Gaussian   Df Model:                            0\n",
      "Link Function:               identity   Scale:                         0.11740\n",
      "Method:                          IRLS   Log-Likelihood:                -3474.5\n",
      "Date:                Thu, 26 Mar 2020   Deviance:                       1172.7\n",
      "Time:                        06:33:37   Pearson chi2:                 1.17e+03\n",
      "No. Iterations:                     3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept   9.719e+10   2.45e+11      0.396      0.692   -3.83e+11    5.78e+11\n",
      "p_i         -4.86e+11   1.23e+12     -0.396      0.692   -2.89e+12    1.92e+12\n",
      "==============================================================================\n"
     ]
    }
   ],
   "source": [
    "\n",
    "df = pd.DataFrame({\"t_i\": t_i,\n",
    "                   \"p_i\": pi})\n",
    "\n",
    "model = sm.formula.glm(\"t_i ~ p_i\",family=sm.families.Gaussian(), data=df ).fit()\n",
    "#model = sm.formula.ols(\"t_i ~ p_i\" , data=df ).fit()\n",
    "print(model.summary())\n",
    "#pi_high = 0.4 # pi at beginning of read\n",
    "#pi_low = 0.2 # pi at rest of read\n",
    "#pi_high_ratio = 0.3 # ratio of beginning of read as part of the whole read"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept   -2.794747\n",
       "p_i          5.300730\n",
       "dtype: float64"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 248,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2.571389192934744"
      ]
     },
     "execution_count": 248,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tmp = model.params['Intercept']+model.params['p_i']*np.array(t_i)\n",
    "tmp.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "unexpected EOF while parsing (<ipython-input-67-4ff56f1d3984>, line 1)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;36m  File \u001b[0;32m\"<ipython-input-67-4ff56f1d3984>\"\u001b[0;36m, line \u001b[0;32m1\u001b[0m\n\u001b[0;31m    1/(1+np.exp(tmp.mean())\u001b[0m\n\u001b[0m                           ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m unexpected EOF while parsing\n"
     ]
    }
   ],
   "source": [
    "#1/(1+np.exp(tmp.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Trying with a different package:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 249,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.7/site-packages/sklearn/linear_model/logistic.py:432: FutureWarning: Default solver will be changed to 'lbfgs' in 0.22. Specify a solver to silence this warning.\n",
      "  FutureWarning)\n",
      "/usr/local/lib/python3.7/site-packages/sklearn/utils/validation.py:724: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "  y = column_or_1d(y, warn=True)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[-1.06532323, -0.21306465]])"
      ]
     },
     "execution_count": 249,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from patsy import dmatrices\n",
    "y, X = dmatrices('t_i ~ p_i', df, return_type = 'dataframe')\n",
    "model = LogisticRegression(fit_intercept = True)\n",
    "mdl = model.fit(X, y)\n",
    "mdl.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0565406146754943"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.exp(0.055)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.2213750375685026"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.log(9.22)"
   ]
  }
 ],
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