GalacticDNSMass

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commit cf02464a1c59fed08af76bcb85d69aba59879f9b
parent 53b3d7c6e12fb82986ad119cf8b8433a3ecded6c
Author: NicholasFarrow <nicholas.w.farrow@gmail.com>
Date:   Thu, 31 Jan 2019 22:57:00 +1100

Remove jupyter trash

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D.ipynb_checkpoints/Inference Demo-checkpoint.ipynb | 556-------------------------------------------------------------------------------
1 file changed, 0 insertions(+), 556 deletions(-)

diff --git a/.ipynb_checkpoints/Inference Demo-checkpoint.ipynb b/.ipynb_checkpoints/Inference Demo-checkpoint.ipynb @@ -1,556 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Inference on the Mass Distribution of Galactic Double Neutron Stars\n", - "In this demo we investigate mass distribution models under the hypothesis that Recycled and Non-recycled neutron stars have differing mass distributions. We compare two sub-hypotheses for the mass distribution of *recycled (fast)* and *non-recycled (slow)* Neutron Stars from Galactic Double Neutron Star (DNS) systems. The sub-hypotheses we compare are:\n", - "\n", - "1. Recycled NS distribution is two-Gaussian (bimodal) and non-recycled is uniform. (Most favoured hypothesis in our findings)\n", - "2. Recycled & non-recycled are both single-Gaussian distributions. (Conventional)\n", - "\n", - "However this code can easily be altered to compare any other two sub-hypotheses by changing the models investigated through replacing occurences of:\n", - "> models.uniformList\n", - ">\n", - "> models.___________List\n", - "\n", - "into models of your choosing. Infact you can investigate your own models by writing a function in models.py (as long as you introduce an appropriate prior!)\n", - "\n", - "### Requirements (Imports)" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "# We require functions for uniform, truncated gaussian, and truncated two-gaussian models.\n", - "import models\n", - "\n", - "# We sample using pymultinest\n", - "import pymultinest\n", - "\n", - "# Useful librarys for mathematical operations\n", - "import numpy as np\n", - "from scipy import stats\n", - "from scipy.special import erf\n", - "import random\n", - "\n", - "# Filesystem operations\n", - "import os\n", - "import sys" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We also load the mass samples:" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "# Load DNS mass samples\n", - "bothMassSamples = np.load('Demo Files/Samples/bothMassSamples.npy')\n", - "# For each DNS, pulsar & companion samples are grouped in pairs.\n", - "# Creates array of shape like (17x10000x2) (17 DNSs x 10000 observation samples x 2 (pulsar + companion))\n", - "\n", - "# Only use 200 samples for faster sampling\n", - "massSamples = bothMassSamples[:,:200,:]\n", - "\n", - "# Define the nMeasurements and nSamples per mass measurement\n", - "nSamples, nMeasurements = len(massSamples[0]), len(massSamples)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Prior\n", - "\n", - "Here we define prior used in this hypothesis. In this demo as we are exploring sub-hypotheses between **pairs of models**, therefore we run PyMultiNest with a set of hyperparameters which contains the parameters describing both models." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [], - "source": [ - "def prior(cube, ndim, nparams):\n", - " # cube is initially a unit hypercube which is to be mapped onto the relevant prior space.\n", - " \n", - " # j is the hyperparameter index. We map the priors beginning with the parameters of model1,\n", - " # and then incriment j by the number of parameters in that model1. Then mapping\n", - " # the parameters of the next model2.\n", - " j = 0\n", - " \n", - " # Loop over both models in the sub-hypothesis.\n", - " for modelBeingMapped in [modelName1, modelName2]:\n", - " if modelBeingMapped == 'singleGaussian':\n", - " cube[j] = 0.8 + cube[j] * (2 - 0.8)\n", - " cube[j+1] = 0.005 + cube[j+1] * (0.5 - 0.005)\n", - " j += 2\n", - " if modelBeingMapped == 'twoGaussian':\n", - " cube[j] = 0.8 + cube[j] * (2 - 0.8)\n", - " cube[j+1] = cube[j] + cube[j+1] * (2 - cube[j])\n", - " cube[j+2] = 0.005 + cube[j+2] * (0.5 - 0.005)\n", - " cube[j+3] = 0.005 + cube[j+3] * (0.5 - 0.005)\n", - " cube[j+4] = cube[j+4] * 1\n", - " j += 5\n", - " if modelBeingMapped == 'uniform':\n", - " cube[j] = 0.8 + cube[j] * (2 - 0.8)\n", - " cube[j+1] = cube[j] + cube[j+1] * (2 - cube[j])\n", - " j += 2\n", - "\n", - " return" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Likelihood Function\n", - "\n", - "Here we impliment the likelihood function given by *Equation 11*.\n" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [], - "source": [ - "def likelihood(cube, ndim, nparams):\n", - " \n", - " # Create lists of the parameters for each model. Model1 has parameters in cube from 0 to ndim1-1, Model2 has parameters in cube from ndim1 to ndim-1.\n", - " paramList1 = [cube[i] for i in range(ndim1)]\n", - " paramList2 = [cube[i] for i in range(ndim1, ndim)]\n", - " \n", - " # Initial list to contain the sum of the products of the probability for each m_r and m_s sample in their respective models.\n", - " pdfProductSumList = []\n", - " \n", - " # For the m_r and m_s pairs in each BNS system. (eg. 1000x2)\n", - " for massSample in massSamples:\n", - " \n", - " # Evaluate the PDF function down the m_r and m_s samples of the BNS\n", - " mrProbabilities = modelEval1(paramList1, massSample[:,0])\n", - " msProbabilities = modelEval2(paramList2, massSample[:,1])\n", - " \n", - " # Evaluate the product of the m_r and m_s probability for each pair.\n", - " probabilityProduct = mrProbabilities*msProbabilities\n", - " \n", - " # Append the sum over all the probability products of each pair.\n", - " pdfProductSumList.append(np.sum(probabilityProduct))\n", - " \n", - " # If either the m_r or the m_s samples are completely outside their model then return a log-likelihood of -inf.\n", - " if 0 in pdfProductSumList:\n", - " #print(\"Zero probability value - Parameters: {}, {}\".format(paramList1,paramList2))\n", - " return -np.inf\n", - " \n", - " # The log-likelihood is the log of the normalised sum over the log of each pdfProductSum\n", - " loglikelihood = nMeasurements * np.log(1.0/nSamples) + np.sum(np.log(pdfProductSumList))\n", - " return loglikelihood" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Inference\n", - "\n", - "## Hypothesis #1, that recycled NS distribution is two-Gaussian (bimodal) and non-recycled is uniform.\n", - "\n", - "This sampling can be quite computationally expensive, sampling speed can be an issue particularly inside Jupyter notebooks. Therefore for this demonstration the number of livepoints is reduced to 500. If this takes too long try 100 livepoints which should take 10-15 minutes. However reducing the livepoints will result in less continuous and more jagged posterior distributions.\n", - "\n", - "\n", - "Unfortunately the ouput from pymultinest is directed to the terminal (where jupyter is started), so it can not be seen in this notebook. However an example of the output is given below:" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [], - "source": [ - "modelName1, modelEval1, ndim1, paramNames1 = models.twoGaussianList\n", - "modelName2, modelEval2, ndim2, paramNames2 = models.uniformList\n", - "\n", - "# Define the total number of hyperparameters\n", - "ndimHyp1 = ndim1 + ndim2\n", - "\n", - "### Inference\n", - "# Directory to send output to. Create it if it does not exist.\n", - "directoryNameHyp1 = 'Demo Files/hypo1/' + modelName1[:4] + \"/\" + modelName2[:4]\n", - "if not os.path.exists(directoryNameHyp1):\n", - " os.makedirs(directoryNameHyp1)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "**Uncomment this cell if you wish to run the sampling. NOTE: This may take a while!**" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [], - "source": [ - "#pmObject = pymultinest.run(likelihood, prior, ndimHyp1, n_live_points=500, sampling_efficiency=0.3, importance_nested_sampling=False, outputfiles_basename=directoryNameHyp1 + '/', verbose=True, resume=False)" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [], - "source": [ - "egOutput = '''\n", - "*****************************************************\n", - "MultiNest v3.10\n", - "Copyright Farhan Feroz & Mike Hobson\n", - "Release Jul 2015\n", - "\n", - "no. of live points = 100\n", - "dimensionality = 7\n", - "resuming from previous job\n", - "*****************************************************\n", - "Starting MultiNest\n", - "generating live points\n", - "live points generated, starting sampling\n", - "Acceptance Rate: 0.955414\n", - "Replacements: 150\n", - "Total Samples: 157\n", - "Nested Sampling ln(Z): -6.272028\n", - "Acceptance Rate: 0.271370\n", - "Replacements: 400\n", - "Total Samples: 1474\n", - "Nested Sampling ln(Z): 10.303706\n", - "'''" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Hypothesis #2, that recycled & non-recycled are both single-Gaussian distributions. " - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [], - "source": [ - "modelName1, modelEval1, ndim1, paramNames1 = models.singleGaussianList\n", - "modelName2, modelEval2, ndim2, paramNames2 = models.singleGaussianList\n", - "\n", - "# Define the total number of hyperparameters\n", - "ndimHyp2 = ndim1 + ndim2\n", - "\n", - "### Inference\n", - "# Directory to send output to. Create it if it does not exist.\n", - "directoryNameHyp2 = 'Demo Files/hypo2/' + modelName1[:4] + \"/\" + modelName2[:4]\n", - "if not os.path.exists(directoryNameHyp2):\n", - " os.makedirs(directoryNameHyp2)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "**Uncomment this cell if you wish to run the sampling. NOTE: This may take a while!**" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [], - "source": [ - "#pmObject = pymultinest.run(likelihood, prior, ndimHyp2, n_live_points=500, sampling_efficiency=0.3, importance_nested_sampling=False, outputfiles_basename=directoryNameHyp2 + '/', verbose=True, resume=False)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Analysis" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - " analysing data from Demo Files/hypo1/twoG/unif/.txt\n", - " analysing data from Demo Files/hypo2/sing/sing/.txt\n", - "For Hypothesis 1 we find a log-Bayes Evidence: 24.2533062226\n", - "For Hypothesis 2 we find a log-Bayes Evidence: 19.4291942354\n", - "\n", - "Here we have shown that Hypothesis 1 (two-Gaussian recycled, uniform non-recycled) is strongly favoured\n", - "over the alternative hypothesis (single-gaussian distributions) with a Bayes Factor of 121.5, (log-BF: 4.8)\n", - "\n" - ] - } - ], - "source": [ - "# We load the results for each hypothesis which were created by pymultinest\n", - "hyp1Res = pymultinest.analyse.Analyzer(ndimHyp1, outputfiles_basename=directoryNameHyp1 + '/')\n", - "hyp1Stats = hyp1Res.get_stats()\n", - "hyp2Res = pymultinest.analyse.Analyzer(ndimHyp2, outputfiles_basename=directoryNameHyp2 + '/')\n", - "hyp2Stats = hyp2Res.get_stats()\n", - "\n", - "print(\"For Hypothesis 1 we find a log-Bayes Evidence: {}\".format(hyp1Stats['global evidence']))\n", - "print(\"For Hypothesis 2 we find a log-Bayes Evidence: {}\".format(hyp2Stats['global evidence']))\n", - "\n", - "logBF = np.round(hyp1Stats['global evidence'] - hyp2Stats['global evidence'], 1)\n", - "\n", - "print(\n", - "\"\"\"\n", - "Here we have shown that Hypothesis 1 (two-Gaussian recycled, uniform non-recycled) is strongly favoured\n", - "over the alternative hypothesis (single-gaussian distributions) with a Bayes Factor of {}, (log-BF: {})\n", - "\"\"\".format(np.round(np.exp(logBF), 1), logBF))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## We can also explore the parameter posteriors to view their distributions:\n", - "We make use of a library called corner plots which allows us to create corner plots, showing joint distributions which allows us to view slices of the sampling parameter space." - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [], - "source": [ - "# We import plotting tools\n", - "%matplotlib inline\n", - "import matplotlib.pyplot as plt\n", - "\n", - "# Corner module provides great visualisations for our purpose.\n", - "import corner\n", - "\n", - "\n", - "def cornerPlot(samples, bounds, parameterNames):\n", - " plt.rcParams.update({'font.size': 15})\n", - " return corner.corner(samples, bins=50, smooth=0.9, label_kwargs=dict(fontsize=16), show_titles=True, range=bounds, title_kwargs=dict(fontsize=16), color='#3fcca6', labels=parameterNames, plot_density=False, plot_datapoints=True, fill_contours=True, max_n_ticks=5)\n", - "\n", - "hyp1Posterior = np.asarray([param for param in hyp1Res.get_equal_weighted_posterior()])\n", - "hyp2Posterior = np.asarray([param for param in hyp2Res.get_equal_weighted_posterior()])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Hypothesis #2 Posterior" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": { - "scrolled": false - }, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "<Figure size 698.4x698.4 with 16 Axes>" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# We have to reset the model information back to hypothesis 2 information\n", - "modelName1, modelEval1, ndim1, paramNames1 = models.singleGaussianList\n", - "modelName2, modelEval2, ndim2, paramNames2 = models.singleGaussianList\n", - "paramNames1 = [r'$m_r$ ' + pName for pName in paramNames1]\n", - "paramNames2 = [r'$m_s$ ' + pName for pName in paramNames2]\n", - "\n", - "cornerPlt = cornerPlot(hyp2Posterior[:,:ndim1 + ndim2], bounds=[[1.3,1.6],[0,0.5], [1.2,1.4],[0,0.5]], parameterNames=paramNames1+paramNames2)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Posterior Predictive Distributions (PPD)\n", - "\n", - "The goal is to now summarise the findings into a mass distributions from our inference sampling.\n", - "\n", - "We can see above that some parameter distributions cover a wide range of possible values. It would be unwise to take take the maximum likelihood parameters or the mode parameters (maximum a posteriori (MAP) estimate), as this would ignore the uncertainties within each parameter.\n", - "\n", - "Instead we take another approach by creating a posterior predictive distibution:\n", - "See paper or https://en.wikipedia.org/wiki/Posterior_predictive_distribution." - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": {}, - "outputs": [], - "source": [ - "def postPredDist(model1List, model2List, hypPost, plotrange=[0.8, 2], thinningFactor=10):\n", - " paramList = hypPost[:,:-1].tolist()\n", - " \n", - " # Randomly take totalSamples/thinningFactor sets of the hyperparameters from the posterior.\n", - " drawnParams = [random.choice(paramList) for i in range(len(paramList)/thinningFactor)]\n", - " \n", - " # Here we are creating two PPDs, one for recycled NS and one for non recycled NS.\n", - " # We need to keep track of whether we are looking at reclyed or non-reclyed model parameters.\n", - " paramsPassed = 0\n", - " \n", - " titleList = [r'Recycled NS Posterior Predictive Distribution $m_r$ - {}', r' Non-Recyled Posterior Predictive Distribution $m_s$ - {}']\n", - " \n", - " # Loop over each model for recycled and non-recycled\n", - " for index, (modelName, modelEval, ndim, paramNames) in enumerate([model1List, model2List]):\n", - " \n", - " # X-axis plot range\n", - " xValues = np.linspace(plotrange[0], plotrange[1], 10000)\n", - " plt.xlim(plotrange[0], plotrange[1])\n", - " \n", - " # For each set of hyperparameters we evaluate the function they describe.\n", - " yValueList = []\n", - " for params in drawnParams:\n", - " yValues = modelEval(params[paramsPassed:paramsPassed + ndim], xValues)\n", - " yValueList.append(yValues)\n", - " \n", - " # We incriment paramsPassed by the number of parameters belonging to this model.\n", - " paramsPassed += ndim\n", - " \n", - " # We turn these function values into an array and then take the mean of each function value at each x.\n", - " yValueArray = np.asarray(yValueList)\n", - " meanyValues = np.mean(yValueArray, axis=0)\n", - "\n", - " plt.title(titleList[index].format(modelName))\n", - " plt.plot(xValues, meanyValues)\n", - " plt.show()\n", - " \n", - " return" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Hypothesis #1 PPD" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "<Figure size 432x288 with 1 Axes>" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "<Figure size 432x288 with 1 Axes>" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "postPredDist(models.twoGaussianList, models.uniformList, hyp1Posterior)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Hypothesis #2 PPD" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "<Figure size 432x288 with 1 Axes>" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "image/png": 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QDdZSdhJeMlHk93V8Olkx+mKtF8lwI149/ZmZLcPbr/PwhqJoJLYWzpjfU865TjN7Fd6dqXeaN6ZXePiZCrwxxt6El8BEHos/4A30fp+Z3enP+1YGH8U+1jobSzmP9ljEE/foucRv072AIW4FB8rwmnAdUcNX+K/X4o2B0+DvWAPeUBIToua7lqFvqX4E2DnaWP3X5+NVoIcjphUCH8I7QR3zH8/jtQy8Imr5Urzm2g14lbfFX+59Q2zv7348bx8h3mujpscT03S8ytTmP+7GGzNtJ0m61T/eY4p3N85X8E6AR/Bu7d2JNw7RnKj1vQOvA3KPH8dt8ZbDcPVnhHIedf1MRrnGEH9K6sMw5RJTPR/q2A213oi6ccR//cej3d8Ryj786MdL+jbgJYKXxlJPSEI9TqRuRixzCd5dt7v9ba8jakgHf/6T8MaJ6vCP1e/w+ri85JgnctxI03kcLylwwFsGeW0/8LdBpoeHGZgWMW0Z3p3JzXiXnk+L9X0b43s7nnox3PGNqZzwEos7gaN47+m7/GmNRA3bMMwxjOs9hde5//14Hd8b/ePegvcLO18D5kbNXwB8Cu+yYjfeMCtfw/vMdcAN8dbZWMo5Ccci5rjjPW6DPcyfWdLIzO7Fa42Y4jL/9zlFRHKGeSOj/wCY7JxLdEDRjOS3JDUCP3LOvSfoeCQ2qegjJsMws9l4fcSy4UfSRUSynpn9u5nNN7MQ3hWbSUT1K8s2Nvi4eeE+TA+mMxYZnaBuY847ZnYmXrPmh/Ca/m8KNiIRkbxxNt4QKTV4l6p+gzeSeza718x24fWDC+Fdwn013p2i0X0sJYPp0mSamPcDutfg3db9CefcncFGJCIi2crMPob3mVKP13erAa/P2OfcS3/nUzKYEjERERGRgOjSpMRkwoQJrr6+PugwRESyyqpVqxqdc9E/lSRynBIxiUl9fT0rV64MOgwRkazi9+MSGZLumhQREREJiBIxERERkYAoERMREREJiBIxERERkYAoERMREREJiBIxERERkYAoERMREREJiMYRE5GEOed4akcTq3Y1U1tewqULT6CitCjosEREsoYSMRFJSGtnLx/57TP8Y9Oh49O+ct9zfOctizlvjgYSFxGJhS5Nikjcunr7edfPV/LP5w/z2VfNZ/3nXsmf338ukypKue62lTy5/UjQIYqIZAUlYiISt6/et4mndzbxrTedxvXnzaS8pJDTplXxm3efxbSaMXzgjjU0H+sJOkwRkYynRExE4rJqVxM//9dO3nH2DF69aMqLXqsqK+Z7b11Ca2cPn79nYzABiohkESViIhIz5xxfvncTk8aV8olL5w06z/zJFbzrvJn8ac1e1u9tTXOEIiLZRYmYiMTskS2HWbWrmQ9ePJuxJUPf6/OeC2ZRVVbETQ9sTmN0IiLZR4mYiMTsBw9vZWr1GK46fdqw81WUFnHduSfy8ObDbD10NE3RiYhkHyViIhKTjfvaWLGzmWvPqae4cORTx9VnzaCkMMSty3emPjgRkSylRExEYvLLJ3dSWhQasTUsrGZsMW9YUsedqxto6+pNcXQiItlJiZiIjKi9u48/r9nHFafWUVkW+8j5b1w6je6+Ae5btz+F0YmIZC8lYiIyogc2HKCzt583njE1ruVOm1bFzNqx/HHV3hRFJiKS3ZSIiciI7npmH1Orx7BkenVcy5kZ/75kKk/vbGL3kY4URScikr2UiInIsI60d7N8ayOvOXUKZhb38q9bXAfAvet1eVJEJJoSMREZ1r3r9tM/4LjitCkjzzyIuqoxLKyr5P71B5IcmYhI9lMiJiLDemDjQWbWjmXeCRUJr+PSBSfwzJ4WDrR2JTEyEZHsp0RMRIbU3t3Hk9uPcMn8SaNazytP8ZZ/cKNaxUREIikRE5Eh/XPLYXr7HRfPmziq9cyeOI6ZtWP524aDSYpMRCQ3KBETkSH9fdMhKscUcfqM+O6WHMzF8yby9I4mOnr6khCZiEhuUCImIoPqH3A8vOkQF8ytpbBg9KeK8+bU0tM/wFM7mpIQnYhIblAiJiKDerahhSPHerholJclw5adWENJYYjHthxOyvpERHKBEjERGdTy5xsxg/Pn1CZlfaVFBZw5c7wSMRGRCErERGRQT2xr5OTJFVSPLU7aOs+fM4Fth4+xt6UzaesUEclmSsRE5CU6e/pZvauFc2dPSOp6X36S17qmVjEREY8SMRF5iZW7mujpH+DsWeOTut7ZE8upHVfCk9uPJHW9IiLZSolYnjKzOjNrNzNnZuVBxyOZ5fGtRygMGcvqa5K6XjPjzBNreGp7E865pK5bRCQbKRHLX18H2oMOQjLTE9saWTy9irElhUlf95kzx3OgrYvdTR1JX7eISLZRIpaHzOx84FLgG0HHIpmntaOXdXtbOWdWcvuHhZ11otfK9tR2jScmIqJELM+YWQHwXeDzQGPA4UgGemrHEZyDc5LcPyxs9sRyxo8t5skd6icmIqJELP+8BygBvh90IJKZVu5qprggxKnTqlKyfjNjmd9PTEQk3ykRyyNmNh74AvBR51xvDPO/28xWmtnKw4c13EC+WLmziYVTKyktKkjZNs48sYa9LZ00NKufmIjkNyVi+eVLwJPOuXtjmdk5d4tzbqlzbmltbXJGV5fM1tXbz7q9rSytH/2PfA/nzJneZc+n9buTIpLnlIjlCTM7BfgP4PNmVmVmVUCZ/3KlmY0JLjrJFGsbWuntdyydkdxhK6KdNGkc5SWFrNrVnNLtiIhkuuTfmy6Zag5QBPxrkNcagFuB69MakWScFTu9FqrTZ6S2RawgZJw2rYrVu1tSuh0RkUynRCx/LAcujJp2KfBJ4HJge9ojkoyzalczs2rHUpPE35ccypLpVXzv4a20d/dRnoLxykREsoHOfnnCOdcIPBI5zczq/T//6ZzT4K55bmDAsXJnE5cvnJyW7S2eUc2Ag7V7Wjgnyb9pKSKSLdRHTEQA2Hq4nbauvpRflgxbMs3bzurd6icmIvlLiVgec87d5pwztYYJvNA/7Iwk/77kUCrLiphVO1b9xEQkrykRExEAVu1sZkJ5MTPGl408c5IsmV7Nmt3N+gFwEclbSsREBIBnGlo4bVo1Zpa2bS6ZUU1zRy87Go+lbZsiIplEiZiIcLSrl+2Hj3Hq1Mq0bnfJ9HA/MV2eFJH8pERMRFi3txWARSn6fcmhzJlYzriSQnXYF5G8pURMRFjX4CViC+vS2yIWChmLplWytkEtYiKSn5SIiQhrG1qZWj0mLQO5RltYV8XmA0fp6u1P+7ZFRIKmRExEWLu3hVOnpveyZNipUyvp7XdsOnA0kO2LiARJiZhInms+1sOepk4Wprmjflh4u+t0eVJE8pASMZE8tzbcUT/N/cPC6qrGMH5sMc/6/dRERPKJEjGRPBduiVoQUIuYmbFwauXxGwZERPKJEjGRPLe2oZWZE8ZSUVoUWAyLplbx/KGjdPT0BRaDiEgQlIiJ5Lm1Da0sCqg1LGxRXSUDDtbvbQs0DhGRdFMiJpLHDrV1caCti4UB3TEZtmialwhqPDERyTdKxETy2Fq/X1bQLWITx5UyubL0eDwiIvlCiZhIHlu7t5WQwSlTKoIOhYV1lcd/aklEJF8oERPJY+saWpgzcRxlxYVBh8Kp06rY0XiM1s7eoEMREUkbJWIieco5x9qG1sAGco0W/p3L9WoVE5E8okRMJE/ta+3iyLEeTs2QRCzcT+1ZddgXkTyiREwkT4UHcg36jsmwqrJipteUsUFDWIhIHlEiJpKnnm1opajAmD95XNChHLegrkId9kUkrygRE8lT6xpamXvCOEoKC4IO5bhTplSyu6mD1g512BeR/KBETCQPeR31W1hYlxmXJcMW+B32N+xXq5iI5AclYiJ5aNeRDtq6+jKmo35YeDwz9RMTkXyhREwkD631+2FlytAVYRPKS5hcWcr6fWoRE5H8oERMJA+t3dNCSWGIkyZlTkf9sFOmVGosMRHJG0rERPLQ2r2tnDylgqKCzDsFLKirYHvjMY519wUdiohIymXeWVhEUqp/wLFhbyuL6jLrsmTYgimVOAfP7Vc/MRHJfUrERPLM9sPtHOvpZ1GGDOQabYF+6khE8ogSMZE8s7bBS3AWZVhH/bBJFSVMKC9m/T61iIlI7lMilifM7Eoze8LMjphZl5ltNrPPmllx0LFJeq1taKGsuICZteVBhzIoM1OHfRHJG0rE8sd44B/A9cBlwE+BzwDfDDIoSb+1e1tZUFdJQciCDmVIC+oqeP5QO129/UGHIiKSUoVBByDp4Zz7UdSkh82sAni/mX3QOeeCiEvSq7d/gI372nj7WTOCDmVYC6ZU0j/g2HzgKKdOy8y+bCIiyaAWsfx2BNClyTyy5eBRuvsGMm4g12jHO+xrYFcRyXFqEcszZlYAlABLgA8BP1RrWP5Y53fUPzVD75gMm1o9hsoxRazXTx2JSI5TIpZ/juElYgC/AP5rqBnN7N3AuwGmT5+e+sgk5dbubaWitJAZ48uCDmVYZsaCugo2qEVMRHKcLk3mn3OA84CPAVcA3xtqRufcLc65pc65pbW1temKT1JobUMLi6ZWYZa5HfXDFkypZNP+o/T2DwQdiohIyigRyzPOudXOueXOuW/iXZp8r5nNCjouSb2u3n42Hzia8f3Dwk6pq6Snf4DnD7YHHYqISMooEctvq/3nEwONQtJi04Gj9Pa7jP1po2gLplQA6rAvIrlNiVh+O9d/3hFoFJIW6xpaAFiUJcNB1I8fy9jiAjZoYFcRyWHqrJ8nzOx+4CFgA9CPl4R9DPitc25bkLFJeqxtaGX82GKmVJYGHUpMQiF/hH391JGI5DAlYvljBXAtUA/0AduBTwE3BxeSpNPahlYWTq3Mio76YafUVfCbp/fQP+Ay+pcAREQSpUuTecI59z/OuQXOuXLnXJVzbolz7rvOud6gY5PU6+jp4/lDR1mU4eOHRVswpZLO3n52NKrDvojkJiViInlg4742BhxZ01E/7PgI+xrYVURylBIxkTzwrD+i/qIsGboibFbtWEoKQ6xXh30RyVFKxETywLqGFk6oKGViRXZ01A8rLAgxf3KFhrAQkZylREwkD4Q76mejBXUVbNjbxsCAfhJVRHKPEjGRHNfW1cv2xmNZ1z8sbMGUSo5297GnuSPoUEREkk6JmEiOWx/uH5YlA7lGC3fYX6d+YiKSg5SIieS44x31s7RF7KRJ4yguCOnOSRHJSUrERHLc2oYWpteUUT22OOhQElJcGGLe5HGs29sSdCgiIkmnREwkx61taM26YSuiLairZG1DK86pw76I5BYlYiI5rLG9m70tnZyaZSPqR1tUV8nRrj52HVGHfRHJLUrERHLY2gbvcl62t4iFh95Qh30RyTVKxERy2LN7WgnZC3ceZquTJo2juDCkRExEco4SMZEctrahhdkTyxlbUhh0KKNS5I+wH27hExHJFUrERHKUc87vqJ/d/cPCFtVVsl4j7ItIjlEiJpKj9rZ0cuRYD6dmef+wsIVTK2nv7mPHkWNBhyIikjRKxERy1NrwQK650iLmJ5Tr1U9MRHKIEjGRHPVsQwtFBca8yeOCDiUpZteWU1oUOp5giojkAiViIjnq2T0tzJ9cQUlhQdChJEVhQYiTJ1ewTomYiOQQJWIiOWhgwLF+b1vWjx8WbdHUKtbva6VfHfZFJEcoERPJQdsb22nv7suZ/mFhC+oq6ejpZ0dje9ChiIgkhRIxkRz07B7v8l22/7RRtHALn/qJiUiuUCImkoPWNrQwpqiA2RPLgw4lqWbVljOmqECJmIjkDCViIjlozZ4WFk2tpCBkQYeSVAUhY0FdhX7qSERyhhIxkRzT1dvPxn1tLJlRHXQoKbGgrpKN+9ro6x8IOhQRkVFTIiaSY9btbaVvwLFkem4mYoumVtLZ28+2wxphX0SynxIxkRyzelczAIun51ZH/bCFdd5+6QfARSQXKBETyTFrdrcwvaaMCeUlQYeSEjMnjKW8pJBnlYiJSA5QIiaSQ5xzrN7dnLOtYQChkHHqtEqe2aNETESynxIxkRyyr7WLQ0e7c7Z/WNhp06p4bv9ROnv6gw5FRGRUlIjlCTO7ysz+YmZ7zazdzFYZQCqcAAAZkElEQVSZ2VuCjkuSK9f7h4UtnlZN/4DTMBYikvWUiOWPjwLtwEeA1wIPA3eY2QcDjUqSas3uFkoKQ8yfXBF0KCl1mp9oPrOnOeBIRERGpzDoACRtXuOca4z4/x9mNgUvQftuQDFJkq3e3cyiqZUUFeT2d6wJ5SVMryljzW71ExOR7JbbZ2s5LioJC1sDTEl3LJIaXb39bNjXmvP9w8JOm1alRExEsp4Ssfx2NrAl6CAkOTbsa6O337E4TxKxxdOrONDWxf7WzqBDERFJmBKxPGVmFwOvA24aZp53m9lKM1t5+PDh9AUnCVmz2+svtSTHO+qHhRNOtYqJSDZTIpaHzKweuAO4yzl321DzOeducc4tdc4tra2tTVN0kqgVO5uYWj2GiRWlQYeSFidPrqC4MHQ8ARURyUZKxPKMmdUA9wG7gKsDDkeSxDnHyp3NLDuxJuhQ0qa4MMSCKRUa2FVEspoSsTxiZmXAPUAx8GrnXEfAIUmSbDt8jCPHelhWnz+JGMBp06pZ29BKb/9A0KGIiCREiVieMLNC4PfAHOBS59yhgEOSJHp6RxNAXrWIgddhv7tvgE37jwYdiohIQjSOWP74AXA58GFgvJmNj3htjXOuO5iwJBlW7GxiQnkxJ04YG3QoaRX+BYHVu5tZOLUy4GhEROKnRCx/vMJ//r9BXjsR2Jm+UCTZnt7RxBn1NZhZ0KGkVV3VGCaOK2HVrmbecU590OGIiMRNlybzhHOu3jlnQzx2Bh2fJG5fSyd7Wzo5I8/6hwGYGWfU17ByZ1PQoYiIJESJmEiWW7EzP/uHhZ1RX82+1i4amnXviYhkHyViIlnu6R1NjCspzPkf+h7KGX4CukKtYiKShZSIiWS5FTubWDKjmoJQfvUPC5t3QgXjSgp5eocGdhWR7KNETCSLNR/rYcvB9ry9LAlQEDJOr69WPzERyUpKxESy2L+2HwHgrJnjR5gzt51RX8Pzh9ppPtYTdCgiInFRIiaSxZ7Y1sjY4gIW5fkYWsvUT0xEspQSMZEs9sTWI5w5czxFBfn9Vl5YV0lxQUiJmIhknfw+e4tksf2tnWxvPMY5s/L7siRAaVEBp06rZMVOddgXkeyiREwkSz2+1esfdu7sCQFHkhnOqK9h/d5WOnr6gg5FRCRmSsREstQTWxupGVvM3Enjgg4lIyw7sYa+AcfqXS1BhyIiEjMlYiJZyDnHE9uOcPas8YTydPywaGfU11AYMh7f1hh0KCIiMVMiJpKFtjce40BbF+fO0mXJsLElhZw2rYontioRE5HsoURMJAuFk41zZ6ujfqRzZk9g3d5WWjt7gw5FRCQmSsREstCjWxqZWj2G6TVlQYeSUc6dNZ4BB0/6A92KiGQ6JWIiWaa7r58ntjVywdxazNQ/LNLi6dWMKSrQ5UkRyRpKxESyzIodzXT09HPh3IlBh5JxigtDnHFiDY9vU4uYiGQHJWIiWeaRzYcoLghxtgZyHdS5s8az9VA7B9u6gg5FRGRESsREsszDmw9x5swayooLgw4lI4UHuH1Cw1iISBZQIiaSRfY0dbDt8DEu0GXJIZ08uYKqsiKWP6/LkyKS+ZSIiWSRR7YcBuCCubUBR5K5QiHjZbMn8NjzhxkYcEGHIyIyLCViIlnkkU2HmFYzhpkTxgYdSka7cO5EDh/tZuP+tqBDEREZlhIxkSzR0dPH8q2NXDxvkoatGMHL59ZiBg9vOhR0KCIiw1IiJpIlHt18mO6+AV5xyqSgQ8l4E8pLWDS1ioc3KxETkcymREwkS/xtwwGqy4pYVl8TdChZ4cK5tazZ00LTsZ6gQxERGZISMZEs0NM3wN83HeLi+ZMoLNDbNhYXzp2Ic/CYf4ODiEgm0hldJAs8uf0IR7v6eOUpJwQdStZYWFfJ+LHFujwpIhlNiZhIFvjbhgOUFRdw3pwJQYeSNUIh4+Vza3l0y2H6+geCDkdEZFBKxEQy3MCA48GNB3n5SbWUFhUEHU5WecXJk2jp6OXpHU1BhyIiMiglYiIZ7umdTRw62s1lCycHHUrWOf+kWkqLQty/4UDQoYiIDEqJmEiGu+uZfZQVF3DJfP2sUbzKigu54KSJ3L/+gEbZF5GMpEQsj5jZbDP7kZmtNbN+M3sk6JhkeD19A9y7bj+vOHmSfuQ7QZcuOIFDR7tZs6cl6FBERF5CiVh+OQW4HNgMbAk4FonBY1sO09rZyxWn1QUdSta6aP5EigqM+9fvDzoUEZGXUCKWX+52zk1zzl0FbAg6GBnZXc/uo7qsiJfpbsmEVZQWce7sCdy/4QDO6fKkiGQWJWJ5xDmne/izyLHuPh7ceIDLF06mSIO4jsplC05gT1Mn6/fqR8BFJLPo7C6Sof66dj9dvQO8frEuS47WpadMprggxJ/W7A06FBGRF1EiJkMys3eb2UozW3n4sH4mJt1+s2I3syeWc/qM6qBDyXqVZUVcOK+Wvzy7T4O7ikhGUSImQ3LO3eKcW+qcW1pbWxt0OHlly8GjrN7dwpvPmIaZBR1OTnj94qk0tnezfGtj0KGIiBynREwkA/12xR6KCkyXJZPownm1VJQW8mddnhSRDKJETCTDdPf1c+fqBl5x8gmMLy8JOpycUVJYwKsWTeFvGw5yrLsv6HBERAAlYiIZ5951+2nu6OXNy6YFHUrOecOSOjp7+7l3ncYUE5HMoEQsj5hZmZldaWZXAnVAbfh/MysLOj4B5xy3Lt/B7InlvGy2xg5LtqUzqplVO5Y7nt4ddCgiIoASsXwzEfi9/zgLODnif/2QYQZYuauZ9XvbeOe59eqknwJmxtVnzmDN7hY27GsNOhwRESVi+cQ5t9M5Z0M8dgYdn8BPl++gqqyINyyeGnQoOevfl0ylpDDEHU+pVUxEgqdETCRD7Gnq4G8bDvDWZdMZU1wQdDg5q7KsiNecOoU/r9lLuzrti0jAlIiJZIibH91GYSjENWfXBx1Kzrv6zOkc6/HuThURCZISMZEMsK+lk9+t3MNVS6dyQmVp0OHkvNOmVbF4ehW3Lt9B/4B+CFxEgqNETCQD/OjRbTgH771gVtCh5AUz4/87fya7jniXg0VEgqJETCRgB9u6+PWKPVx5+lSmVmsUkXT5t5NPoH58mZ8Eq1VMRIKhREwkYN9+aAsDA473XTA76FDySkHIuP68mTzb0MqT25uCDkdE8pQSMZEAbTl4lN+u2MPbz57B9PFqDUu3K0+fSu24Er710Ba1iolIIJSIiQToK/c+x9iSQj500ZygQ8lLpUUFfODC2Ty9o4l/Pt8YdDgikoeUiIkE5LEth3l482E+eNFsqscWBx1O3nrzsmnUVY3hGw9sVquYiKSdEjGRAHT19vPZP69n5oSxvOOc+qDDyWslhQV8+JI5rG1o5f71uoNSRNJLiZhIAL7z9+fZ3dTBl16/kJJCjaIftDcsruOkSeV86d7n6OrtDzocEckjSsRE0uy5/W3c8th2rjx9KmfPGh90OAIUFoS44bWn0NDcyc2Pbgs6HBHJI0rERNKoq7ef//zNM1SVFfPpy+cHHY5EOGfWBF69aDI/fGQbe5o6gg5HRPKEEjGRNPrqfZvYfPAo37hqETXqoJ9xPvOq+RSEjE/duU4d90UkLZSIiaTJgxsPctsTO3nnufVcMHdi0OHIICZXjuHTl89n+dZGbn9qd9DhiEgeUCImkgZbDx3lI799hgV1FXzy0nlBhyPDuPrM6Zw3ZwJf/utz7Gw8FnQ4IpLjlIiJpFhrRy/v+sUqSotC3PL2pZQW6S7JTGZmfO3KRRQVGO/71WrdRSkiKaVETCSFOnv6uf4XK2ho7uDmt53OlKoxQYckMZhcOYZvv/k0Nu5v4zN/Wq/+YiKSMkrERFKkp2+A99y+ilW7mvn2mxaztL4m6JAkDhfNm8SHL57DH1c3cNsTO4MOR0RyVGHQAYjkoq7efj5wxxoe3XKYr75hIa9aNDnokCQBH754Ds/tb+Pz92ykdlwJr140JeiQRCTHqEVMJMnaunp5x0+f5u+bDvKFK07hzcumBx2SJCgUMr7zlsUsnVHNR377DI9tORx0SCKSY5SIiSTRriPHeOPN//IvR57G28+uDzokGaXSogJ+cs0ZzJ44jut/vpIHNx4MOiQRySFKxESS5JHNh3jt9x5nf2sXP732DK44rS7okCRJKsuK+PW7zuTkKRW85/ZV/GFVQ9AhiUiOUCImMkodPX3c8JcNXPuzFUyuLOXuD7yM80+qDTosSbKqsmJuv/5MzppZw8d//yxfvGcjff0DQYclIllOnfVFRmH584189s/r2Hmkg2vPqeeTl85jTLHGCctV5SWF3PbOZXzpr8/xk+U7WLe3lW9cdSrTasqCDk1EspRaxEQSsO1wO9fdtoK33foU/c5xx7vO5IbXnqIkLA8UFYS44bWncNNVp7JhXxuXfvsx7nhqNwMDGmtMROJnGqhQYrF06VK3cuXKoMMI3IZ9rfzwkW3cu24/ZcWFfOCi2Vx7Tr1Gy89TDc0dfOIPa3li2xEW1FXwP686mTNnjg86LMkgZrbKObc06DgkcykRk5jkcyLW1dvP3zYc4Lcr9vDEtiOUlxRy9VnTuf5lM6kdVxJ0eBKwgQHHX57dx433b2J/axfnzZnAe18+i7NnjcfMgg5PAqZETEaiRExikm+JWFdvP8ufb+TBjQe5b/1+2rr6mFo9hrcsm87bzppB5ZiioEOUDNPZ089tT+zk1uU7aGzvZkFdBW9aOo3XnDqFqrLioMOTgCgRk5EoEcsjZnYy8F3gbKAF+AnwOefciL9qnOuJWF//ABv2tfH0jiae2nGEx7ceobO3n3ElhVw0fyJvXDqNs2eOJxRSC4cMr6u3nztX7+WXT+7iuf1tFBeEOP+kWi6ZP5EL501kUkVp0CFKGikRk5Horsk8YWbVwEPARuAKYBZwE94NG58NMLS0O9bdx5aDR9l04Cib9rfx3IGjrN/bSkePl4/OGF/GladP5d9OnsRZM8dTXKh7WiR2pUUFvPXM6bz1zOls2NfKH1Y18MCGgzz0nDcQ7NxJ4zi9vprTp1ezZEY1M2rKlOCL5DG1iOUJM/sU8AlghnOuzZ/2CeAG4ITwtKFkS4vYse4+jrT3cLi9myPt3TS299DQ3MGe5k72NHWwp6mDI8d6js8/triAuSeMY0FdJctOrGFZfQ0T1WIhSeacY8vBdv6+6SBPbm9iza5mjnb3AVBaFGL2xHLmTBzH7InlTK0ew5Qq7zFpXAmFBfoikM3UIiYjUSKWJ8zsMWCfc+7NEdOmA7uA1zrn7h5u+XgSMeccAw76BxwDLvzw/nfO0T/g6HeOnr4B79E/8MLffQN0+4/I6Z29/Rzr7qO9u4+jXX3H/27v8p7buno50t5DZ+9Lr7IWhowpVWOYVjOGadVlTKspY/bEcuafUMHU6jFqjZC0GxhwbD3czjO7W9hy8ChbDrXz/MGj7G/tetF8IYOasSXUjC2iqqyYmrJiqv2/y0sKKSsuoKy4gDHFhZQVeX+XlRRSUhiiqMAoKghRWBCiKBT+23suKghRoHqfFkrEZCS6NJk/5gH/iJzgnNttZh3+a8MmYs/tb2PpFx86nlh5SdVLk60B501PldKiEOUlRZSXFFBeWkh5SSFTqkqZWzqOCeXFjC8vYfzYYiaMK2HC2BLGlxczUa0KkmFCIeOkSeM4adK4F03v6OljX0sX+1o62dfSyd6WThrbu2k+1ktTRw/bG9tp2tVLS0cPfaMct8wMikIhMC/hC5lh+M8GZvbC9Ij/Df/Znx5+fdhtjRjL0HOMmC6OYtsj3dWqVFXSQYlY/qjG66Afrdl/7SXM7N3AuwEqp8zkFadMImRQYIaZURDyT9QhI2RGgb1wgh7sNTP86UYoZJQUhCgu9B+Rf/v/lxaFKC4ooLgw5CdghUqoJKeVFRcye2I5syeWDzufc46e/gE6uvvp6O2ns6ePjp5+jnX309nbR3fvAL0Djr7+AXr7B+jtD//t6B0YoK/fHZ/ucOB/iRpw4I5/oXI4Xjzd+V+6vHnA4UYcyHakdHG4L24jLzuKbY+wcjfi1mPzUFLWIrlMiZgMyTl3C3ALeJcmv/z6hQFHJCLgfdkpKSygpLBg8G9RkjF++LagI5BMp+aF/NEMVA4yvdp/TURERNJMiVj+2ITXF+w4M5sGlPmviYiISJopEcsf9wGvNLPI3sFvAjqBR4MJSUREJL8pEcsfNwPdwJ1mdonfEf8G4JsjjSEmIiIiqaHO+nnCOddsZhcD38MbqqIF+BZeMiYiIiIBUCKWR5xzG4GLgo5DREREPLo0KSIiIhIQJWIiIiIiAdFvTUpMzOwosDnoOFJoAtAYdBApksv7Btq/bJfr+zfXOTdu5NkkX6mPmMRqcy7/cK2ZrczV/cvlfQPtX7bLh/0LOgbJbLo0KSIiIhIQJWIiIiIiAVEiJrG6JegAUiyX9y+X9w20f9lO+yd5TZ31RURERAKiFjERERGRgCgRExEREQmIErE8Z2Ynm9nfzazDzPaZ2efNrCCG5Zaa2QNm1uQ/HjKzM9MRc6zMbLaZ/cjM1ppZv5k9EuNylWb2MzNrNrNWM/uVmY1PcbhxS2T/zOwMf9+2+sd8s5n9r5mVpiHkuCR6/CKWD5nZSjNzZvbqFIWZsNHsn5m9wcxWmFmnmR0xs/vNbGwKw43bKN5/2XBuucrM/mJme82s3cxWmdlbYliuxMxuMrNDZnbMzP5qZvWpj1gymRKxPGZm1cBDgAOuAD4PfAz43AjLTfOXKwTe7j8KgQfNbEYqY47TKcDleAPRboljud8BFwDXA9cCZwB/TnJsyZDI/r0JmAXc6C/7feCjwK9SEeAoJXr8wq4HpiY1ouRKaP/M7HrgDuA+4DK8/XyezBsXMu79y6Jzy0eBduAjwGuBh4E7zOyDIyz3HbxzyseBK/EGs30wE78ISRo55/TI0wfwKaAZqIiY9gmgI3LaIMu9B+gHKiOmVfvT3hv0fkXEFIr4+w/AIzEsczZeYnp+xLRl/rRLgt6nJOzfhEGmvdvfvxlB79No9y9i/mrgMHCdv2+vDnp/knX8gKPAu4KOP0X7ly3nlsHeR3cAO4ZZZirQB1wTMa0O6AGuD3qf9AjuoRax/HYZ8DfnXFvEtN8AY4CXD7NcEd4J5VjEtHZ/miU7yEQ55wYSWOwy4KBz7rGI9TwN7PBfyxiJ7J9zbrCfklnjP08ZXUTJleDxC/sC8Djw9ySFk3QJ7t8b/eefJzOWVEhw/7Ll3DLU+2i499Ar/Oc7I9azF1hOhp1bJL2UiOW3ecCmyAnOud14LWLzhlnuj/48N5nZRDObCHwLr3Xt9ymKNV1eUia+5xi+TLLZ2cAAsC3oQJLBzBYB/4F3+SfXnIl3qe86M2sws14ze8rMzgk6sCTJ5nPL2Qx/CXYe0OCca4+ansvnFomBErH8Vg20DDK92X9tUM65fcCFwL8DB/3HG4BXOucOpyDOdEqoTLKVmZ0AfBb4pXPuUNDxJMl3ge8557YGHUgKnADMxTtmnwReg9d6dL+ZTQoysGTI1nOLmV0MvA64aZjZ8urcIrFTIiZxM7PJeN9OV+E1qV/m//1XM5seZGwSOzMrxrsxIdzpOOuZ2ZvxEpUvBh1LihhQDlznnPuVc+5+vASgH/hAoJElQTaeW/y7Hu8A7nLO3RZoMJKVMu0uG0mvZqBykOnV/mtD+S+8vhxXOud6AczsH3h3bn0c+FCS40ynZqB2kOkjlUlWMTMDfoF3Z9u5zrms3zczKwK+jndHaMjMqoAK/+WxZjbOOXc0sACToxnv5oNHwhOcc21mtgo4Oaigkiirzi1mVoN39+ou4OoRZk/0fCs5Ti1i+W0TUX0T/NvHyxi8n1TYPGBD+EQJ4JzrATbgDY2QzV5SJr6h+o5lq2/jDVlyhXMuV/ZrLN6dad/E+2BrBp71X/sNL9yUkM2ew2sVi+64bnj9/LJd1pxbzKwMuAcoxrsrt2OERTYB0wYZ7y3Xzi0SJyVi+e0+4JVmNi5i2puATuDRYZbbBSzwL20B3kCFwAJgZwriTKf7gBPM7GXhCWa2FJjpv5b1zOxTeJex3uacWx50PEnUjte/KPIRHmTz04zcYpEN7vGfLwxPMLNK4HReSDqzWVacW8ysEO8S6hzg0hj7Vz7gP78+Yj1TgPPIkXOLJEaXJvPbzXhN/Xea2Y14ycYNwDcjh7Qws63Ao8656/xJP8EbRPJPZvYDvG/j7wcmA7ekL/zh+d9YL/f/rQMqzOxK//97nXMd0fvmnPuXmT0A/MLMPo7XynAjsNw591Cad2FYieyfmb0V+DJwG7DXzM6KWOW2TOoQHe/+Oef6iLhk56+j3v9znXPuqdRHHbsE6+dKM7sLuNXM/htoxBv7rxdvcN6Mkcj+kSXnFuAHePv2YWC8vfiXN9Y457rN7O8AzrmL/ecGM7sV+LbfNeAw3vl2F3B7OoOXDBP0QGZ6BPvA61fyD7xWsP144y8VRM2zE7gtatrFwGNAk/94FLgg6P2JirEerz/NYI/6YfatCvgZ3h1ObXgdcV8ygGPQj0T2Dy8BG2qZa4Pep2QcvyHWkYkDuiZaP8uBHwJH/PftQ8DCoPcnifuXDeeWnTHs2yNEDWILlOBdOj+Md7frvcCJQe+PHsE+zDmHiIiIiKSf+oiJiIiIBESJmIiIiEhAlIiJiIiIBESJmIiIiEhAlIiJiIiIBESJmIiIiEhAlIiJiIiIBESJmIiIiEhA/h+IKtBK9Hv65AAAAABJRU5ErkJggg==\n", - "text/plain": [ - "<Figure size 432x288 with 1 Axes>" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "postPredDist(models.singleGaussianList, models.singleGaussianList, hyp2Posterior)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 2 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython2", - "version": "2.7.12" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -}