{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Approximate Bayesian Computation: Synthetic likelihood (parametric approximation)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Florent Leclercq
\n", "Imperial Centre for Inference and Cosmology, Imperial College London
\n", "florent.leclercq@polytechnique.org" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "init_cell": true }, "outputs": [], "source": [ "import scipy.stats as ss\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from cycler import cycler\n", "np.random.seed(123457)\n", "%matplotlib inline\n", "plt.rcParams.update({'lines.linewidth': 2})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Setup problem" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this notebook we try to infer the unknown mean $\\mu$ of a unit-variance Gaussian distribution.\n", "\n", "The data consist of $N_\\mathrm{samp}$ realizations. For inference, we run $N$ simulations per value of $\\mu$." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def simulator(mu, sigma, Nsamp=10, random_state=None):\n", " mu, sigma = np.atleast_1d(mu, sigma)\n", " return ss.norm.rvs(mu[:, None], sigma[:, None], size=(1, Nsamp), random_state=random_state)\n", "\n", "def summary_statistic(sim):\n", " return np.mean(sim, axis=1)\n", "\n", "def neg_log_likelihood(mu, Phi_0, Nsamp):\n", " return 1/2.*np.log(2*np.pi/Nsamp) + Nsamp/2.*(Phi_0 - mu)**2\n", "\n", "def sample(mu, sigma, N):\n", " sims=np.zeros(N)\n", " for j_ in range(N):\n", " sim=simulator(mu, sigma)\n", " sims[j_]+=summary_statistic(sim)\n", " return np.mean(sims)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "data: d_0=[[1.72558743 1.96316607 3.90707517 1.95831498 1.57465709 0.93464301\n", " 0.23803412 1.5998699 2.56876862 2.08744352]]\n", "summary statistic of the data: Phi_0=1.855755990636889\n" ] } ], "source": [ "# Set the number of samples and number of simulations per mu\n", "Nsamp=10\n", "N=2\n", "\n", "# Set the generating parameters that we will try to infer\n", "mean0 = 2\n", "sigma0 = 1\n", "\n", "# Generate some data\n", "d_0 = simulator(mean0, sigma0)\n", "print(\"data: d_0=\"+str(d_0))\n", "Phi_0 = summary_statistic(d_0)\n", "print(\"summary statistic of the data: Phi_0=\"+str(Phi_0[0]))" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# Set the prior\n", "mu = ss.uniform(-2,6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Generate simulations" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# Generate some data points\n", "N_sims=100\n", "mu_sims=mu.rvs(N_sims)\n", "sims=np.zeros(N_sims)\n", "for i_ in range(N_sims):\n", " sims[i_]=sample(mu_sims[i_], sigma0, N)\n", "S1_sims=neg_log_likelihood(sims,Phi_0,Nsamp)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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iQ2YTsLKHKjxPkiRJC6ikJezTc2ZHAvw88A+1C0mSJKn1LdmilZlXAv8fcBZwNjOzI6+udWDtwIW7JUlqX5V2K/7/zNQGGym/VhXMLtw9Pj7O+9//fk466SSTMUmS2oSzIws0d+HuUqnE/fffz/bt29m6dWvBkUmSpFqrpCVsdnbkZZn5i8B5wLtqG9bKNFv3Xm9vL52dnQfsm56eZmRkpKCIJElSvVQyML9pZkfOdu9NTU0xOTlJRDA8PFx0WAuaXbj7wx/+MHv37qVUKtHZ2UlfX1/RoUmSpBqrJJn6dER8JiIuj4jLgb+nQWdHzu3ea4YWpY6ODoaHh7nvvvu46qqr6O7upr+/n23bthUdmiRJqrFK1o68MiJ+DngJEDTw2pG9vb1MTk4yPT3dVC1Ks8lYI7faSZKk6qpo7cjM/ATwiRrHsmqz3XsjIyP09fXZoiRJkhpWZObiB0S8Dvht4FhmWsICyMx8Vu3Dm9HV1ZUTExP1up0kSdKKRcTuzOxa6rhKWsLeB1ycmXeuPixJkiRBZQPzv2sCJkmSVF0LtoSVuyEBJiLi48CngP+YfT8zP1nj2CRJklrWYt2RF895PQW8fM52AiZhkiRJK7RgEpaZ/72egUiSJLWTxbojr8rM90XEB5lp+TpAZv56TSOTJElqYYt1R84Oxrc2hCRJUpUt1h35t+XnXfULR5IkqT0s1h35t8zTDTkrM1+91MUj4tvAY8BTQCkzuyLiOcDHgZOBbwNvyMzvLytqSZKkJrdYd+TvVOkeF2bm9+ZsbwZGMvO9EbG5vH11le4lSZLUFBbrjvyn2dcR0QmcmJl3VeGerwFeWn69C7gJkzBJktRmlqyYHxEXA7cBny5vb4yIGyu8fgL/GBG7I+KK8r7nZeYDAOXnYxe47xURMRERE3v37q3wdpIkSc2hkmWL3g2cBzwCkJm3MTOeqxIvycwXAq8AfjUiLqg0sMzcmZldmdl1zDHHVHqa5lEqlRgYGKCnp4eBgQFKpVLRIUmS1PYqWcC7lJmPRsSyL56Z95efH4yI65lJ5r4bEesy84GIWAc8uOwLa1kGBwfZsWMHU1NTTE5OEhEMDw8XHZYkSW2tkpawr0bELwBrIuLUcvHWLy11UkQcHhFHzr5mZtmjrwI3ApeVD7sMuGFFkatio6OjTE1NATA9Pc3IyEjBEUmSpEqSsF8DzmBm8e6/BP4d+I0KznsecHNE3A58Bfj7zPw08F7gZRFxN/Cy8rZqqLe3l87OTgA6Ozvp6+srOCJJklRJd+SxmfkO4B2zOyLiRcA/L3ZSZn4LOHue/Q8BZgF1NDQ0REQwMjJCX18f27ZtKzokSZLaXmQuWI915oCIW4CLM/PfytsXAH+QmWfWIT4Aurq6cmLC1ZMkSVLji4jdmdm11HGVdEe+BfhURPx4RLwSuAZ45WoDlCRJamdLdkdm5j9HxK8D/wg8AbwsMy3cJUmStArLWTvyMOBR4EMRUdHakZIkSZpfPdaOlCRJ0kEqWjtSkiRJ1bVYd+TNmXl+RDzGgd2SAWRmPqvm0UmSJLWoxVrCzi8/H1m/cCRJktrDYi1hz1nsxMx8uPrhSJIktYfFBubvZqYbcr6VuxP4iZpEJEmS1AYW6448pZ6BSJIktZNKKuZLkiSpykzCmlypVGJgYICenh4GBgYolUpFhyRJkiqw5LJFamyDg4Ps2LGDqakpJicniQiGh4eLDkuSJC1hyZawiOiJiCPnbB8ZEd21DUuVGh0dZWpqCoDp6WlGRkYKjkiSJFWiku7IPwJ+MGf78fI+NYDe3l46OzsB6OzspK+vr+CIJElSJSrpjozM3F8xPzP3RYTdmA1iaGiIiGBkZIS+vj62bdtWdEiSJKkCMSe/mv+AiE8CN/Gj1q9fAS7MzNfWNrQf6erqyomJiXrdTpIkacUiYndmdi11XCXdkf8DeDHwb8AeoBu4YnXhSZIktbcluxUz80Hg0jrEIkmS1DYWWzvyqsx8X0R8kJllig6Qmb9e08gkSZJa2GItYXeWnx2MJUmSVGWLrR35t+WXU5n5N3Pfi4hLahqVJElSi6tkYP6WCvdJkiSpQouNCXsF8Erg+Ii4Zs5bzwJcoFCSJGkVFhsTdj8z48FeDeyes/8xoL+WQUmSJLW6xcaE3Q7cHhF/WT7uxMy8q26RSZIktbBKxoRdBNwGfBogIjZGxI2V3iAi1kTErRHxd+XtUyJiPCLujoiPR8QzVhS5JElSE6skCXs3cB7wCEBm3gacvIx7vJUflbsA+G3g9zLzVOD7wJuWcS1JkqSWUEkSVsrMR1dy8YhYD/wM8Kfl7QB6gevKh+wC6rYGpSRJUqOoJAn7akT8ArAmIk4tV9D/UoXX3w5cBewrbx8NPJKZs7Mr9wDHLydgSZKkVlBJEvZrwBnAfwAfA/4d+I2lToqIVwEPZubcmZUxz6FPWxKpfP4VETERERN79+6tIExJkqTmUckC3lPAO8qP5XgJ8OqIeCWwlpn6YtuBZ0dER7k1bD0zpTDmu+9OYCdAV1fXvImaJElSs1qyJSwiXhAROyPiHyNidPax1HmZuSUz12fmycClwGhm/lfg88Dry4ddBtywivibVqlUYmBggJ6eHgYGBiiVrH8rSVI7WbIlDPgb4I+ZGVz/VBXueTXwVxHxHuBW4ENVuGbTGRwcZMeOHUxNTTE5OUlEMDw8XHRYLa1UKjE4OMjo6Ci9vb0MDQ3R0VHJfwFJkqqvkt9Apcz8o9XcJDNvAm4qv/4WMyUv2tro6ChTU1MATE9PMzIyYhJWYwcnvplJRJiUSZIKsdjakc8pv/zbiPgV4HpmBucDkJkP1zi2ltbb28vk5CTT09N0dnbS19dXdEgt7+DEd9euXTz66KO2RkqSCrHYn/27mZm5ODuj8co57yXwE7UKqh0MDQ0REYyMjNDX18e2bduKDqnmiu4OPDjxjQhbIyVJhVls7chTACJibWY+Mfe9iFhb68BaXUdHB8PDw3X5pV908jOr6HFwBye+Tz31FNdcc42tkZKkQlTym/hLwAsr2KcGVXTyM6vocXAHJ76lUok1a9a0VWukJKlxLFiiIiJ+PCLOBToj4pyIeGH58VLgsLpFqFWbL/kpQm9vL52dnQAN0fI0m5SNjY0xPDzsoHxJUl0t9lvnPwOXM1NQ9QNz9j8GDNQwJlXZciYB1LLrsh3HwUmStJDIXLwYfUT8XGZ+ok7xzKurqysnJiaKDKGplUoltm7dekDys1BiNTAwsL/rsrOzk/7+fgerS5K0DBGxOzO7ljyugiTsmcDPASczp+UsM4dWGWPFTMLqp6enh/Hx8f3b3d3djI2NFRiRJEnNpdIkrJIFvG8AXgOUgMfnPNSCGm3cliRJraqSwT7rM/OimkeihlCLcVuNUiJDkqRGUkl35E7gg5l5R31Cejq7I5ub48wkSe2kmt2R5wO7I+KuiJiMiDsiYnL1IapdNEqJDEmSGkklSdgrgFOBlwMXA68qP0sVOXic2SGHHEJPTw8DAwOUSqWCo5MkqRiVDMz5NeDPMvNrtQ5GradUKrFv3z6OOuoonv3sZ3PSSSdx2223MT097aLZkqS2VklL2NeBP4mI8Yj4HxHxY7UOSq1jcHCQD37wg9x///088sgj3HfffUxPTwN2TUqS2tuSSVhm/mlmvgT4RWZqhU1GxF9GxIW1Dk7NoVQqMTAwMG8X48HjwTLTEhiSJFFZdyQRsQb4T+XH94DbgbdFxFsy89IaxqcmsNgC4QcvmXTZZZdxyCGHuHSRJKntVVKi4gPMDMQfBT6UmV+Z895dmfmTtQ3REhWNbrEq+8tZMkmSpFZQaYmKSn4bfhV4Z2ZOzfPeecuOTC1nsQXCOzo6GB4edvC9JEkHqWRg/l1AAETEGyPiAxFxEkBmPlrL4NQchoaG6O/vp7u7m/7+/lV1MS42vmw5x0iS1OgqaQn7I+DsiDgbuAr4EPAR4P+uZWBqHtVs7VpsfNlyjpEkqdFV0hJWypmBY68BdmTmDuDI2oaldlVJdX0r8EuSWkElSdhjEbEFeCPw9+WZkofWNiy1q4Or689XwqKSYyRJanSVdEf+PPALwJsy839HxInA+2sbltrV0NAQEbFoCYtKjpEkqdEtWaLigIMjXpWZf1fDeOZliQpJktQsKi1RUUl35FxDK4xHakjOtJQkFWW5VTOjJlGoLZVKJQYHBxkdHaW3t5ehoaG6F3J1pqUkqSjLbQl7S6UHRsTaiPhKRNweEf8SEdvK+08pLwZ+d0R8PCKescwY1CJmE6Dx8XG2b9/O1q1b6x6DMy0lSUVZMgmLiNfNPoD15dd9EXHsEqf+B9CbmWcDG4GLIqIH+G3g9zLzVOD7wJtW+TWoSTVCAuRMS0lSUSrp+3kTsAn4fHn7pcAY8IKIGMrMP5/vpHJtsR+UNw8tPxLoZWa2JcAu4N3MFIRVm1lsuaN6caalJKkolSRh+4DTMvO7ABHxPGaSpm7gC8C8SVj52DXAbuD5wB8A3wQeyczZ0c97gONXHL2aWiMkQK5tKUkqypIlKiLijsw8c852AHdk5oaIuDUzz1nyJhHPBq4HBoEPZ+bzy/tPAP5h7vXnnHMFcAXAiSeeeO699967jC9LkiSpGJWWqKikJeyLEfF3wN+Ut18PfCEiDgceqSSYzHwkIm4CeoBnR0RHuTVsPXD/AufsBHbCTJ2wSu4jSZLULCqZHfmrwIeZGVx/DjPjuH41Mx/PzAsXOikijim3gBERncBPA3cyM7bs9eXDLgNuWHn4kiRJzWnJJKw8wP5mYBT4HPCFrKzM/jrg8xExCfwz8Nlytf2rgbdFxDeAo4EPrTR4tT6LqUqSWtWS3ZER8QZm1oq8iZlirR+MiCsz87rFzsvMSWZazg7e/y3gvBVFq7ZjMVVJUquqpDvyHcCLMvOyzPxFZhKod9U2LGlGI9QSkySpFipJwg7JzAfnbD9U4XnSqh1cTPXCCy+0e1KS1BIqmR356Yj4DPCx8vbPA/9Qu5DUila6TuTBtcSeeuoprrnmGrsnJUlNb8k6YQAR8XPAS5gZE/aFzLy+1oHN1dXVlRMTE/W8papsYGBg/9iuzs5O+vv7V5Q89fT0MD4+vn+7u7ubsbGxaoYqSWpBK20MWIlq1gkjMz8BfGLVUaltzTe2ayVJWCMsdSRJaj6NONFrwSQsIh5jZq3Hp73FTOWKZ9UsKrWcaiVPjbDUkSSp+VSrMaCaFkzCMvPIegai1lat5Mm1HiVJK9GIPSkVjQkrmmPCJEnSapRKJbZu3XpAY0DRY8JMwiRJkqqo0iTMel+SJEll9VwurzbtcJIkSU3o4FmUmUlE1KS0RSVrR843S/JRYAL4zfJakJIkSU3v4FmUu3bt4tFHH61JaYtKuiM/AFwJHA+sB94O/AnwV8CfVSUKSZKkBnDwcnkRUbM1jCtpT7soM7vnbO+MiLHMHIqIgapFIkmSVLCFlsurRWmLSpKwfRHxBuC68vbr57zX+FMrJUmSKnRwPcpSqcSaNWtqUiR8yRIVEfETwA5gEzNJ1xjQD/wbcG5m3ly1aBZgiQpJktQsqlaiIjO/lZkXZ+ZzM/OY8utvZOZ0PRIwSatTz+nWkqTKLZmERcQLImIkIr5a3j4rIt5Z+9Ck5tVIic/sdOvx8XG2b9/O1q1bC4tFkvQjlcyO/BNgC/AkQGZOApfWMiip2TVS4jPforWSpOJVkoQdlplfOWif/RnSIhop8Tl4unUjLForSapsduT3IuL/ojwTMiJeDzxQ06ikJtfb28vk5GRNpjQv18HTras5s0eStHKVzo7cCbwY+D5wD/DGzPx2zaMrc3akKlEqlRgcHKzJ0hIriWXr1q0HJD5FxSJJqq9KZ0cumYTNueDhwCGZ+dhqg1sukzBVYmBgYP96X52dnfT391dtaQlJkipVtRIVEfHMiPgF4K1Af0QMRsRgNYKUqqmRxmFJkrSUSgbm3wC8hpnB+I/PeUgNxQHokqRmUskglfWZeVHNI5FWyQHokqRmUsnA/J3ABzPzjvqE9HSOCVM9NdIAf0lS86l0TFglv1nOBy6PiHuA/wACyMw8a4kATgA+Avw4sA/YmZk7IuI5wMeBk4FvA2/IzO9XEIdUF7OFVqemppgZROVcAAAQRUlEQVScnCQiHOAvSaq6SsaEvQI4FXg5cDHwqvLzUkrAb2bmaUAP8KsRcTqwGRjJzFOBkfK21DAc4C9JqodKFvC+d75HBec9kJm3lF8/BtwJHM/MIP9d5cN2Aa9defhS9TXCAP9GWntSklQbdRnoEhEnA+cA48DzMvMBmEnUIuLYesQgVaoRBvjbJSpJ82ulcbsVF2td8Q0ijgD+CRjOzE9GxCOZ+ew5738/M4+a57wrgCsATjzxxHPvvXfJxjepZfT09DA+Pr5/u7u7m7GxsQIjkqTG0AyFuatWrHWVQRwKfAL4i8z8ZHn3dyNiXfn9dcCD852bmTszsyszu4455phahik1nFp0idrFKakVtNK43Zq130VEAB8C7szMD8x560bgMuC95ecbahWD1Kyq3SVaKpW44IILGB8fZ9++fXZxSmpavb29TE5OMj093fSFuWvWHRkR5wNfBO5gpkQFwAAz48L+GjgRuA+4JDMfXuxa1gmTVmdgYID3vve9zP3/bhenpGZUKpXYunXrAX+kNtqYsGrWCVuRzLyZmZpi82netFVaQiMOGh0dHT0gAYuIpv7rUVL76ujoYHh4mOHh4Yb8ebsczROp1CQacWZjb28vt99+O0888QQRwaZNm1zWSVLTa8Sft8tR04H5UjtayaDRWg+aHxoa4m1vexvd3d1s2bKFf/qnf2qqvxYlaT7NPkjfJEyqspXMbJz9a258fJzt27ezdevWBY9dScI223w/NjbG8PCwCZikljD3521EcMghhzTVzG+TMKnKhoaG6O/vp7u7m/7+/oq6/Zbz19xyEjZJamVDQ0Ns3LiRiCAzufXWW5vqZ6JJmFRlK2l1Wk7rWbM3v0tStXR0dLBv3779E4+eeOKJpvqZaJ+E1ACWUxeslWrkSNJqNfPPxJovW1QN1gmTfqQZauRIUr004s/ESuuEmYRJkiRVUUOsHSlJkqT5mYRJkiQVwCRMkiSpACZhkiRJBTAJk9pErZdGktTa/BlSfc5rl9pAqVTiggsuYGxsjMzk9ttvb7qFbiUVq9kXy25EtoRJbWBwcJDx8fGmrSotqXiu1lF9JmFSGxgdHWXfvn37tyOiqapKSyrecpZXm0+1uzNXc71G6Vq1O1JqA3OX9YgINm3aVNHC4pI0aznLq82n2t2Zq7leo3StWjFfagONuKyHpPbS09PD+Pj4/u3u7m7GxsaWfZ1SqcTg4CDXXHMNjz/++IquV61YFmLFfEn7dXR0MDw8zNjYGMPDwyZgkuputd2Zs2ZbseYmYMu9XrViWS1/EkuSpJpbbXfmrLkTBAAOP/xw3vrWty7retWKZbXsjpQkSU1jYGCA7du3Mz09TWdnJ/39/Q1XKqPS7khbwiRJUtNolFasarAlTJIkqYocmC9JktTATMIkSZIKYBImSZJUAJMwqY00ylIdkqQaJmER8WcR8WBEfHXOvudExGcj4u7y81G1ur+kp5stcjg+Ps727dvZunVr0SFJqiH/8GpstWwJuxa46KB9m4GRzDwVGClvS6qTuUUOp6enGRkZKTgiSbXkH16NrWZJWGZ+AXj4oN2vAXaVX+8CXlur+0t6ukZZqkNS7cxt/br22mv9w6uB1btY6/My8wGAzHwgIo6t8/2lttZKRQ4lzW+29Wtqaoo1a9bQ0dFBqVSq6x9es4tsj46O0tvby9DQkGvWzqNhP5GIuAK4AuDEE08sOBqpNcwu5N1oS3xIqp65ww6eeuopjjvuOE444YS6/uE1NxGcnJwkIvy5M496z478bkSsAyg/P7jQgZm5MzO7MrPrmGOOqVuAkiQ1s4OHHVx++eWMjY0xPDxct9Yox59Wpt4tYTcClwHvLT/fUOf7S5LU0hph2EFvby+Tk5P7F9l2/On8arZ2ZER8DHgp8Fzgu8BW4FPAXwMnAvcBl2TmwYP3n8a1IyVJah6lUomtW7cekAi205iwSteOdAFvSZKkKnIBb0mSpAZmEiZJklQAkzBJkqQCmIRJqrpK1qtzTTtJ7a59pipIqptKCjVazFFSu7MlTFLVVVKo0WKOktqdSZikBa20y7CShcJdTFxSu7M7UtKCVtplWEnF7kao6i01MhfBbn0Wa5W0oJ6eHsbHx/dvd3d3MzY2VmBEUvsYGBjY/0dQZ2cn/f39jptsEhZrlbRqdhlKxXHcZOuzXVPSguwylIrjItitz+5ISZKqpJrjuNp9EexmZnekJElVVMls4dnJLOPj42zfvp2tW7eu+H4dHR0MDw9z8803k5mcf/75FjZuMSZhkhqWVfXVSCpJsFYyjmup7/NqJnZqLCZhkmpqNYmUv3zUSCpJsFYymWWx7/NSqcS1117rAP0WZRImqabe+c538v73v5/x8XHe97738a53vavic50dpkZSSYI1NDREf38/3d3d9Pf3VzSZZbHv88HBQfbu3bt/u6OjwwH6LcQkTFJNfeQjH9nf+vXUU0/xkY98pOJzLZGhRlJJgjU7jmtsbIzh4eGKBtIv9n0+Ojp6QOvxscceu/++dtc3P6dZSGpYlshQI5lNsKpdMHWx7/ODy1Rcfvnl+xO7la5oocZhiQpJNbV582Z+93d/l1KpREdHB29/+9v5rd/6raLDkubVaEsFLVamwhUtGlelJSpsCZNUU+95z3tYs2aNrVlqCo3WurRY65vFXJufLWGSWk49WjMarcVE1dFMrUsWc21ctoRJalqrTXDq0ZrRaC0mqo5mal2q1Rg11Y+zIyU1nNXWB6tHaYtGKZ/hDLnqWkmJCWmlTMIkNZzVJjj1KG3RKOUzLGhbPbMtsCMjI/T29tq9p5rzu0tSw1ltl1A9Sls0SvmM+RLWandPtcv4N7uYVW+t979IUtNbbYJTj7EyHR0dbNu2jcxkZGSEzCwkOanHGKZ2SU7mS2i3bdvWFgmoiuF3kqSG0ygDjpdqAWqE5KQeLXL1aG1rBPMltI3wb6zW5ZgwSVrAUuOtFhq7Nt9g+YUG0K92YP1KlslZruWMf6v2RIF6TjyYb1B+o0zAUIvKzLo/gIuAu4BvAJuXOv7cc89NSaq37u7uBPY/uru7D3h/y5Yt2dnZmUB2dnbmpk2bsru7Ozdt2nTA/oGBgdyyZUsedthhB+ybvcZ8+xvJk08+mQMDA9nd3Z0DAwP55JNPLnhstb+eoj+fg/+NG/HfR40HmMhK8qFKDqrmA1gDfBP4CeAZwO3A6YudYxImqQhL/QKem5zMTbwi4mnJ20IJ3VKJ3pNPPplbtmzJ7u7u3LJly6IJUBEOju+8885b9OtZrqU+n1pbTgIqzWrkJGwT8Jk521uALYudYxImqQjL+QV8cLIwm4jNbQmbL6Gbb//cxGbTpk1VawlaKKFbLNF78skn8+qrr85169blunXr8uqrrz7g/SuvvPKApHPdunXzfj2LXWOx+9sSpWbUyEnY64E/nbP934DfX+wckzBJje7gZOHFL37xAcnbQgndfPvndsHN16q2UldffXV2dHQkkB0dHbl58+b9sS+U6G3ZsmX/ObPnzX3/8MMPPyA+4Glf+1LXWOz+tkSpGTVyEnbJPEnYB+c57gpgApg48cQTa/QxSVJ1VDNZWKpVbaXWrVt3wHWPO+64ee83N9E7+L2D3z/00EMXfb+SaxTd5ShVW6VJWBGzI/cAJ8zZXg/cf/BBmbkzM7sys+uYY46pW3CStBLVnKU4dzbi2rVr2bRpU02X0Vls9mNvb+8BX0tHR8cB75977rkHXCsinjZ7sre3lzVr1ix4jUZZfUCqu0oytWo+mKlN9i3gFH40MP+Mxc6xO1JSO6lVF9xC3ZGL3e/JJ5/MzZs353HHHZfHHXdcbt68+YD3p6enc9OmTXnooYfmEUcckVddddXT4l3qGnY5qtVQYUtYzBxbXxHxSmA7MzMl/ywzF61819XVlRMTE3WJTZJaValUYuvWrQcUdrX6u1R9EbE7M7uWPK6IJGy5TMIkSVKzqDQJs2K+JElSAUzCJEmSCmASJkmSVACTMEmSpAKYhEmSJBXAJEySJKkAJmGSJEkFMAmTJEkqgEmYJElSAUzCJEmSCmASJkmSVACTMEmSpAKYhEmSJBUgMrPoGJYUEXuBe5c47LnA9+oQTrvzc64PP+f68HOuDz/n+vBzro9KPueTMvOYpS7UFElYJSJiIjO7io6j1fk514efc334OdeHn3N9+DnXRzU/Z7sjJUmSCmASJkmSVIBWSsJ2Fh1Am/Bzrg8/5/rwc64PP+f68HOuj6p9zi0zJkySJKmZtFJLmCRJUtNoqSQsIt4fEV+PiMmIuD4inl10TK0oIi6JiH+JiH0R4UycKoqIiyLiroj4RkRsLjqeVhURfxYRD0bEV4uOpVVFxAkR8fmIuLP88+KtRcfUiiJibUR8JSJuL3/O24qOqZVFxJqIuDUi/q4a12upJAz4LLAhM88C/hXYUnA8reqrwOuALxQdSCuJiDXAHwCvAE4H/ktEnF5sVC3rWuCiooNocSXgNzPzNKAH+FW/n2viP4DezDwb2AhcFBE9BcfUyt4K3Fmti7VUEpaZ/5iZpfLmGLC+yHhaVWbemZl3FR1HCzoP+EZmfiszfwj8FfCagmNqSZn5BeDhouNoZZn5QGbeUn79GDO/uI4vNqrWkzN+UN48tPxwsHcNRMR64GeAP63WNVsqCTvI/wP8r6KDkJbheOA7c7b34C8ttYCIOBk4BxgvNpLWVO4iuw14EPhsZvo518Z24CpgX7Uu2FGtC9VLRHwO+PF53npHZt5QPuYdzDSF/0U9Y2sllXzOqrqYZ59/0aqpRcQRwCeA38jMfy86nlaUmU8BG8vjoK+PiA2Z6XjHKoqIVwEPZubuiHhpta7bdElYZv70Yu9HxGXAq4C+tP7Gii31Oasm9gAnzNleD9xfUCzSqkXEocwkYH+RmZ8sOp5Wl5mPRMRNzIx3NAmrrpcAr46IVwJrgWdFxEcz842ruWhLdUdGxEXA1cCrM3Oq6HikZfpn4NSIOCUingFcCtxYcEzSikREAB8C7szMDxQdT6uKiGNmKwFERCfw08DXi42q9WTmlsxcn5knM/OzeXS1CRi0WBIG/D5wJPDZiLgtIv646IBaUUT8bETsATYBfx8Rnyk6plZQnlTyP4HPMDOI+a8z81+Kjao1RcTHgC8DPxkReyLiTUXH1IJeAvw3oLf88/i2ciuCqmsd8PmImGTmD7nPZmZVyieo9qyYL0mSVIBWawmTJElqCiZhkiRJBTAJkyRJKoBJmCRJUgFMwiRJkgpgEiZJklQAkzBJkqQCmIRJajsRcVNE/GT59dER4RIvkurOJExSO3o+cHf59VnAHQXGIqlNmYRJaisRcRLwb5m5r7zrLGCywJAktSmTMEntZiMHJl3nYhImqQAmYZLazdnAWoCIOBV4DXZHSiqASZikdrMROCQibgcGgTuBy4oNSVI7iswsOgZJqpuI+AZwTmY+VnQsktqbLWGS2kZEHAnsMwGT1AhsCZMkSSqALWGSJEkFMAmTJEkqgEmYJElSAUzCJEmSCmASJkmSVACTMEmSpAKYhEmSJBXAJEySJKkA/wcvs2s7rMQIugAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "(xmin,xmax)=(-2.1,4.1)\n", "(ymin,ymax)=(-5,85)\n", "plt.figure(figsize=(10,6))\n", "plt.xlim([xmin,xmax])\n", "plt.ylim([ymin,ymax])\n", "plt.plot(mu_sims, S1_sims, linestyle=\"\", marker=\"o\", markersize=3.5, color=\"black\", label=\"realizations at $\\mu$\")\n", "plt.xlabel(\"$\\mu$\")\n", "plt.ylabel(\"neg log-synthetic likelihood\")\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The synthetic likelihood as a stochastic process" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using the true variance (unity), the synthetic likelihood is given by\n", "\\begin{equation}\n", "-2\\log \\mathcal{L}_\\mathrm{s}^N(\\mu) = -\\frac{1}{2} \\log\\left( \\frac{2\\pi}{N_\\mathrm{samp}} \\right) - \\frac{N_\\mathrm{samp}}{2} (\\Phi_0 - \\hat{\\Phi}_\\mu)^2,\n", "\\end{equation}\n", "where $\\hat{\\Phi}_\\mu$ is the stochastic process from which realizations are plotted above.\n", "\n", "Since a realization at $\\mu$ is the average of $N$ realizations of the summary statistics (themselves Gaussian-distributed with mean $\\mu$ and variance $1/N_\\mathrm{samp}$), realizations of $\\hat{\\Phi}_\\mu$ are Gaussian-distributed with mean $\\mu$ and variance $1/(N\\times N_\\mathrm{samp})$. We can therefore write the synthetic likelihood as a quadratic function subject to a random shift $g$,\n", "\\begin{equation}\n", "-2\\log \\mathcal{L}_\\mathrm{s}^N(\\mu) = -\\frac{1}{2} \\log\\left( \\frac{2\\pi}{N_\\mathrm{samp}} \\right) - \\frac{N_\\mathrm{samp}}{2} (\\Phi_0 - \\mu - g)^2, \\quad g \\sim \\mathcal{G}\\left(0, \\frac{1}{N\\times N_\\mathrm{samp}}\\right).\n", "\\end{equation}" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "def neg_log_synthetic_likelihood(mu, Phi_0, g, Nsamp):\n", " return 1/2.*np.log(2*np.pi/Nsamp) + Nsamp/2.*(Phi_0 - mu - g)**2\n", "# this is likelihood(Phi_0, mu+g)\n", "# equation (17) in Gutmann & Corander 2016" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### One realization" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "# Get the synthetic likelihood for one particular realization\n", "sigma_g=1/np.sqrt(N*Nsamp)\n", "g=ss.norm(0, sigma_g).rvs()\n", "(xmin,xmax)=(-2.1,4.1)\n", "mu_arr=np.linspace(xmin,xmax,200)\n", "l_mu_one_res=neg_log_synthetic_likelihood(mu_arr, Phi_0, g, Nsamp)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,6))\n", "plt.xlim([xmin,xmax])\n", "plt.ylim([ymin,ymax])\n", "plt.plot(mu_sims, S1_sims, linestyle=\"\", marker=\"o\", markersize=3.5, color=\"black\", label=\"realizations at $\\mu$\")\n", "plt.plot(mu_arr, l_mu_one_res, linestyle=\":\", color=\"black\", label=\"one realization of stochastic process\")\n", "plt.xlabel(\"$\\mu$\")\n", "plt.ylabel(\"neg log-synthetic likelihood\")\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Mean and quantiles" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The mean and quantiles of the stochastic process can be obtained using the Percent Point Function (Inverse of the CDF)." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "g_m=ss.norm(0, sigma_g).ppf(0.1) # g value for the 0.1 quantile\n", "g_p=ss.norm(0, sigma_g).ppf(0.9) # g value for the 0.9 quantile\n", "g_0=ss.norm(0, sigma_g).ppf(0.5) # g value for the mean\n", "l_mu_m=neg_log_synthetic_likelihood(mu_arr, Phi_0, g_m, Nsamp)\n", "l_mu_p=neg_log_synthetic_likelihood(mu_arr, Phi_0, g_p, Nsamp)\n", "l_mu_0=neg_log_synthetic_likelihood(mu_arr, Phi_0, g_0, Nsamp)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,6))\n", "plt.xlim([xmin,xmax])\n", "plt.ylim([ymin,ymax])\n", "plt.plot(mu_sims, S1_sims, linestyle=\"\", marker=\"o\", markersize=3.5, color=\"black\", label=\"realizations at $\\mu$\")\n", "plt.plot(mu_arr, l_mu_one_res, linestyle=\":\", color=\"black\", label=\"one realization of stochastic process\")\n", "plt.plot(mu_arr, l_mu_0, linestyle=\"-\", label=\"mean of stochastic process\")\n", "plt.fill_between(mu_arr, l_mu_m, l_mu_p, alpha=0.2, label=\"0.1 and 0.9 quantiles\")\n", "plt.xlabel(\"$\\mu$\")\n", "plt.ylabel(\"neg log-synthetic likelihood\")\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Distribution of the maximum synthetic likelihood estimator" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The randomness makes the maximum synthetic likelihood estimator $\\check{\\mu} = \\mathrm{argmax}_\\mu \\mathcal{L}_\\mathrm{s}^N(\\mu)$ a random variable: it depends on $g$ via $\\check{\\mu} = \\Phi_0 - g$, i.e.\n", "\\begin{equation}\n", "\\check{\\mu} \\sim \\mathcal{G}\\left( \\Phi_0, \\frac{1}{N \\times N_\\mathrm{samp}} \\right).\n", "\\end{equation}\n", "As expected, this randomness is reduced as $N$ increases." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "def max_synthetic_likelihood(Phi_0, N):\n", " sigma_g=1/np.sqrt(N*Nsamp)\n", " return ss.norm(Phi_0, sigma_g)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "(ymin,ymax)=(-10,700)\n", "plt.figure(figsize=(10,6))\n", "plt.xlim([xmin,xmax])\n", "plt.ylim([ymin,ymax])\n", "plt.plot([Phi_0,Phi_0],[0,ymax], linestyle=\"--\", color=\"black\", label=\"$\\Phi_0$\")\n", "plt.plot(mu_arr, -max_synthetic_likelihood(Phi_0, 2).logpdf(mu_arr), label=\"N=2\")\n", "plt.plot(mu_arr, -max_synthetic_likelihood(Phi_0, 10).logpdf(mu_arr), label=\"N=10\")\n", "plt.plot(mu_arr, -max_synthetic_likelihood(Phi_0, 100).logpdf(mu_arr), label=\"N=100\")\n", "plt.xlabel(\"$\\mu$\")\n", "plt.ylabel(\"neg log-pdf of max synthetic likelihood estimator\")\n", "plt.legend(loc=\"best\")" ] } ], "metadata": { "celltoolbar": "Initialization Cell", "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": "3.7.3" }, "toc": { "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": true, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": true, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 2 }