{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "73f0db79",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iminuit version: 2.16.0\n"
     ]
    }
   ],
   "source": [
    "# Example of Bayesian parameter estimation using iminuit to find\n",
    "# posterior mode (MAP) estimators and MCMC for intervals.\n",
    "# pdf is a mixture of Gaussian (signal) and exponential (background),\n",
    "# truncated in [xMin,xMax].\n",
    "# G. Cowan / RHUL Physics / December 2022\n",
    "\n",
    "import numpy as np\n",
    "import scipy.stats as stats\n",
    "from scipy.stats import truncexpon\n",
    "from scipy.stats import truncnorm\n",
    "from scipy.stats import chi2\n",
    "from scipy.special import logsumexp\n",
    "from scipy.signal import correlate\n",
    "import iminuit\n",
    "from iminuit import Minuit\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams[\"font.size\"] = 14\n",
    "print(\"iminuit version:\", iminuit.__version__)  # need 2.x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "6c1df433",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define pdf\n",
    "np.random.seed(seed=1234567)        # fix random seed\n",
    "theta = 0.2                         # fraction of signal\n",
    "mu = 10.                            # mean of Gaussian\n",
    "sigma = 2.                          # std. dev. of Gaussian\n",
    "xi = 5.                             # mean of exponential\n",
    "xMin = 0.\n",
    "xMax = 20.\n",
    "\n",
    "def f(x, par):\n",
    "    theta   = par[0]\n",
    "    mu      = par[1]\n",
    "    sigma   = par[2]\n",
    "    xi      = par[3]\n",
    "    fs = stats.truncnorm.pdf(x, a=(xMin-mu)/sigma, b=(xMax-mu)/sigma, loc=mu, scale=sigma)\n",
    "    fb = stats.truncexpon.pdf(x, b=(xMax-xMin)/xi, loc=xMin, scale=xi)\n",
    "    return theta*fs + (1-theta)*fb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1428ade9",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate data\n",
    "numVal = 400\n",
    "xData = np.empty([numVal])\n",
    "for i in range (numVal):\n",
    "    r = np.random.uniform();\n",
    "    if r < theta:\n",
    "        xData[i] = stats.truncnorm.rvs(a=(xMin-mu)/sigma, b=(xMax-mu)/sigma, loc=mu, scale=sigma)\n",
    "    else:\n",
    "        xData[i] = stats.truncexpon.rvs(b=(xMax-xMin)/xi, loc=xMin, scale=xi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "872cae6f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Specify parameters, initial values, limits, etc.\n",
    "parin   = np.array([theta, mu, sigma, xi]) # initial values (here = true values)\n",
    "parname = [r'theta', r'mu', r'sigma', r'xi']\n",
    "parname_latex = [r'$\\theta$', r'$\\mu$', r'$\\sigma$', r'$\\xi$']\n",
    "parstep = np.array([0.1, 1., 1., 1.])      # initial step sizes for iminuit\n",
    "parfix  = [False, False, False, False]     # change these to fix/free parameters\n",
    "numFreePar = sum(1 for i in parfix if parfix[i] == False)\n",
    "parlim  = [(0.,1.), (None, None), (0., None), (0., None)]    # set limits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "bbb208cc",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Negative log-likelihood\n",
    "def negLogL(par):\n",
    "    fx = f(xData, par)\n",
    "    return -np.sum(np.log(fx))\n",
    "\n",
    "# Prior pdf\n",
    "def prior(par):\n",
    "    theta    = par[0]\n",
    "    mu       = par[1]\n",
    "    sigma    = par[2]\n",
    "    xi       = par[3]\n",
    "    pi_theta = 1. if theta >= 0. and theta <= 1. else 0.\n",
    "    pi_mu    = 1. if mu >= 0. else 0.\n",
    "    pi_sigma = 1. if sigma > 0. else 0.\n",
    "    pi_xi    = 1. if xi > 0. else 0.\n",
    "    piArr = np.array([pi_theta, pi_mu, pi_sigma, pi_xi])\n",
    "    pi = np.prod(piArr[np.array(parfix) == False])   # exclude fixed par\n",
    "    return pi\n",
    "    \n",
    "# Negative log of posterior pdf\n",
    "def negLogPost(par):\n",
    "    return negLogL(par) - np.log(prior(par))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e53c149d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "par index, name, MAP estimate, standard deviation:\n",
      "   0 theta       =  0.197936  +/-  0.057880\n",
      "   1 mu          =  9.309286  +/-  0.555300\n",
      "   2 sigma       =  2.347174  +/-  0.509533\n",
      "   3 xi          =  5.054644  +/-  0.534132\n"
     ]
    }
   ],
   "source": [
    "# Find maximum of posterior and its covariance\n",
    "m = Minuit(negLogPost, parin, name=parname)\n",
    "m.errors = parstep\n",
    "m.fixed = parfix\n",
    "m.limits = parlim\n",
    "m.errordef = 0.5                          # errors from lnL = lnLmax - 0.5\n",
    "m.migrad()                                # minimize -logPost\n",
    "MAP = m.values                            # posterior mode\n",
    "sigmaMAP = m.errors                       # standard deviations\n",
    "cov = m.covariance                        # covariance matrix\n",
    "rho = m.covariance.correlation()          # correlation coeffs.\n",
    "    \n",
    "print(r\"par index, name, MAP estimate, standard deviation:\")\n",
    "for i in range(m.npar):\n",
    "    if not m.fixed[i]:\n",
    "        print(\"{:4d}\".format(i), \"{:<10s}\".format(m.parameters[i]), \" = \",\n",
    "         \"{:.6f}\".format(MAP[i]), \" +/- \", \"{:.6f}\".format(sigmaMAP[i]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "20a67395",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot fitted pdf (MAP estimators)\n",
    "yMin = 0.\n",
    "yMax = f(0., MAP)*1.1\n",
    "fig = plt.figure(figsize=(8,6))\n",
    "xCurve = np.linspace(xMin, xMax, 100)\n",
    "yCurve = f(xCurve, MAP)\n",
    "plt.plot(xCurve, yCurve, color='dodgerblue')\n",
    "plt.xlabel(r'$x$')\n",
    "plt.ylabel(r'$f(x)$')\n",
    "y_fitval = 0.8\n",
    "delta_y_fitval = 0.08\n",
    "plt.figtext(0.6, y_fitval, 'MAP Estimators')\n",
    "for i in range(len(parin)):\n",
    "    y_fitval -= delta_y_fitval\n",
    "    if not parfix[i]:\n",
    "        plt.figtext(0.6, y_fitval, parname_latex[i] + ' = ' + f'{MAP[i]:.4f}' + r'$\\pm$' + f'{sigmaMAP[i]:.4f}')\n",
    "\n",
    "# Add data as tick marks\n",
    "tick_height = 0.05*(yMax - yMin)\n",
    "xvals = [xData, xData]\n",
    "yvals = [np.zeros_like(xData), tick_height * np.ones_like(xData)]\n",
    "plt.plot(xvals, yvals, color='black', linewidth=1)\n",
    "plt.xlim(xMin, xMax)\n",
    "plt.ylim(yMin, yMax)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "ed1a0725",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "posterior covariance = \n",
      "┌───────┬─────────────────────────────────┐\n",
      "│       │   theta      mu   sigma      xi │\n",
      "├───────┼─────────────────────────────────┤\n",
      "│ theta │ 0.00337 -0.0118  0.0197 -0.0208 │\n",
      "│    mu │ -0.0118   0.308  -0.114  0.0137 │\n",
      "│ sigma │  0.0197  -0.114    0.26  -0.124 │\n",
      "│    xi │ -0.0208  0.0137  -0.124   0.285 │\n",
      "└───────┴─────────────────────────────────┘\n",
      "proposal covariance = \n",
      "┌───────┬─────────────────────────────────┐\n",
      "│       │   theta      mu   sigma      xi │\n",
      "├───────┼─────────────────────────────────┤\n",
      "│ theta │ 0.00478 -0.0167  0.0279 -0.0294 │\n",
      "│    mu │ -0.0167   0.437  -0.162  0.0193 │\n",
      "│ sigma │  0.0279  -0.162   0.369  -0.176 │\n",
      "│    xi │ -0.0294  0.0193  -0.176   0.404 │\n",
      "└───────┴─────────────────────────────────┘\n"
     ]
    }
   ],
   "source": [
    "# Set up MCMC\n",
    "# see J. Rosenthal, http://probability.ca/jeff/ftpdir/galinart.pdf\n",
    "scale_prop = 2.38**2/numFreePar      # or adjust to minimize acf\n",
    "cov_prop = scale_prop*cov\n",
    "print('posterior covariance = ')\n",
    "print(cov)\n",
    "print('proposal covariance = ')\n",
    "print(cov_prop)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "9b2a0a74",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Start MCMC iterations: ...............................................................................................\n",
      " MCMC acceptance fraction =  0.3737\n"
     ]
    }
   ],
   "source": [
    "# Iterate with Metropolis-Hastings algorithm\n",
    "chain = [np.array(MAP)]         # start point is MAP estimate\n",
    "numIterate = 10000\n",
    "numBurn = 100\n",
    "numAccept = 0\n",
    "print(\"Start MCMC iterations: \", end=\"\")\n",
    "while len(chain) < numIterate:\n",
    "    par = chain[-1]\n",
    "    log_post = -negLogL(par) + np.log(prior(par))\n",
    "    par_prop = np.random.multivariate_normal(par, cov_prop)\n",
    "    if prior(par_prop) <= 0:\n",
    "        chain.append(chain[-1])    # never accept if prob<=0.\n",
    "    else:\n",
    "        log_post_prop = -negLogL(par_prop) + np.log(prior(par_prop))\n",
    "        alpha = np.exp(log_post_prop - log_post)\n",
    "        u = np.random.uniform(0, 1)\n",
    "        if u <= alpha:\n",
    "            chain.append(par_prop)\n",
    "            numAccept += 1\n",
    "        else:\n",
    "            chain.append(chain[-1])\n",
    "        if len(chain)%(numIterate/100) == 0:\n",
    "            print(\".\", end=\"\", flush=True)\n",
    "chain = np.array(chain)\n",
    "print('\\n MCMC acceptance fraction = ', numAccept/numIterate)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b66bba58",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Show trace plots\n",
    "fig, axes = plt.subplots(sharex=True, nrows=4, figsize=(8,6))\n",
    "plt.xlim(0, numIterate)\n",
    "for i, (ax, label) in enumerate(zip(axes, parname_latex)):\n",
    "    ax.plot(chain[:, i], color=\"dodgerblue\")\n",
    "    ax.axvline(numBurn, color=\"orange\")\n",
    "    ax.set_ylabel(label)\n",
    "axes[-1].set_xlabel(\"iteration number\")\n",
    "fig.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "bc4f8db3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Show marginal distributions\n",
    "fig, axes = plt.subplots(nrows=4, figsize=(8,6))\n",
    "for i, (ax, label, sim) in enumerate(zip(axes, parname_latex, np.array(MAP))):\n",
    "    ax.hist(chain[numBurn:, i], bins=50, density=True, color=\"dodgerblue\")\n",
    "    ax.set(xlabel=label, ylabel=\"pdf\")\n",
    "    ax.axvline(sim, color=\"orange\")\n",
    "fig.tight_layout(pad=0.3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "b79529e7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Find autocorrelation and plot\n",
    "var = chain[numBurn:,].var(axis=0)\n",
    "x   = chain[numBurn:,] - chain[numBurn:,].mean(axis=0)\n",
    "max_lag = 200\n",
    "N   = len(x[:,0])\n",
    "acf = np.zeros(shape=[max_lag, len(chain[0])])\n",
    "for i in range(len(chain[0])):\n",
    "    if var[i] > 0:\n",
    "        acf[:,i] = np.correlate(x[:,i], x[:,i], mode='full')[N-1:N-1+max_lag]\n",
    "        acf[:,i] /= (var[i]*N)\n",
    "    \n",
    "fig, axes = plt.subplots(sharex=True, nrows=4, figsize=(8,6))\n",
    "for i, (ax, label) in enumerate(zip(axes, parname_latex)):\n",
    "    ax.plot(acf[:,i], color=\"dodgerblue\")\n",
    "    ax.set_ylabel('ACF[' + label + ']')\n",
    "    ax.set_yticks([0., 0.5, 1.])\n",
    "    ax.grid()\n",
    "axes[-1].set_xlabel(\"lag\")\n",
    "plt.xlim(0, max_lag)\n",
    "plt.subplots_adjust(left=0.15, bottom=0.1, right=0.9, top=0.9, wspace=0.4, hspace=0.4)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "1fc33d96",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Functions for computing intervals\n",
    "# input:  values = numpy array with MCMC chain, e.g., chain[:,0]\n",
    "#         CL = credibility level, e.g., 0.683\n",
    "\n",
    "# Central credible interval\n",
    "def cc_interval(values, CL):\n",
    "    alpha = np.array([(1.-CL)/2., (1.+CL)/2.])\n",
    "    return np.quantile(values, alpha)\n",
    "\n",
    "# Highest Probability Density (HPD) interval from MCMC chain\n",
    "def HPD_interval(values, CL):\n",
    "    sorted = np.sort(np.copy(values))\n",
    "    nPoints = len(values)\n",
    "    nCovered = np.floor(0.683 * nPoints).astype(int)\n",
    "    intWidth = sorted[nCovered:] - sorted[:nPoints-nCovered]\n",
    "    minWidth = np.argmin(intWidth)\n",
    "    hpdLo = sorted[minWidth]\n",
    "    hpdHi = sorted[minWidth+nCovered]\n",
    "    return np.array([hpdLo, hpdHi])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fe79498a",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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