GalacticDNSMass

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inferenceDemo.ipynb (190586B)


      1 {
      2  "cells": [
      3   {
      4    "cell_type": "markdown",
      5    "metadata": {},
      6    "source": [
      7     "# Inference on the Mass Distribution of Galactic Double Neutron Stars\n",
      8     "In this demo we investigate mass distribution models under *Hypothesis B*: that Recycled and Non-recycled neutron stars have differing mass distributions. Under this assumption 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",
      9     "\n",
     10     "* **Hypothesis 1 $Z_{tu}^{B}$**: Recycled NS distribution is two-Gaussian (bimodal) and non-recycled is uniform. (Most favoured hypothesis in our findings)\n",
     11     "* **Hypothesis 2 $Z_{ss}^{B}$**: Recycled & non-recycled are both single-Gaussian distributions. (Conventional)\n",
     12     "\n",
     13     "However this code can easily be altered to compare any other two sub-hypotheses by changing the models investigated through replacing occurences of:\n",
     14     "> models.uniformList\n",
     15     ">\n",
     16     "> models.___________List\n",
     17     "\n",
     18     "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",
     19     "\n",
     20     "### Requirements (Imports)"
     21    ]
     22   },
     23   {
     24    "cell_type": "code",
     25    "execution_count": 1,
     26    "metadata": {},
     27    "outputs": [],
     28    "source": [
     29     "# We require functions for uniform, truncated gaussian, and truncated two-gaussian models.\n",
     30     "# models.py contains functions like models.evalSingleGaussian(parameters, values)\n",
     31     "import models\n",
     32     "\n",
     33     "# We sample using pymultinest (nested sampling)\n",
     34     "# This can be rather difficult to install, see https://johannesbuchner.github.io/PyMultiNest/install.html\n",
     35     "# UNCOMMENT IF YOU WANT TO SAMPLE YOURSELF!\n",
     36     "#import pymultinest\n",
     37     "\n",
     38     "# Useful librarys for mathematical operations\n",
     39     "import numpy as np\n",
     40     "from scipy import stats\n",
     41     "from scipy.special import erf\n",
     42     "import random\n",
     43     "\n",
     44     "# Filesystem operations\n",
     45     "import os\n",
     46     "import sys"
     47    ]
     48   },
     49   {
     50    "cell_type": "markdown",
     51    "metadata": {},
     52    "source": [
     53     "# Data\n",
     54     "Here we load an array which describes the masses for each star in all 17 DNS systems:\n",
     55     "<img src=\"demoFiles/fig_pcSamples.png\" width=80%>\n",
     56     "Here we see 12 systems for which we have precise mass measurements of each component star; as well as another 5 systems which only have total mass and the component mass distributions are derived as per *Section 2*."
     57    ]
     58   },
     59   {
     60    "cell_type": "code",
     61    "execution_count": 2,
     62    "metadata": {},
     63    "outputs": [],
     64    "source": [
     65     "# Load DNS mass samples\n",
     66     "bothMassSamples = np.load('demoFiles/Samples/bothMassSamples.npy')\n",
     67     "# For each DNS, pulsar & companion samples are grouped in pairs.\n",
     68     "# Creates array of shape like (17x10000x2) (17 DNSs x 10000 observation samples x 2 (pulsar + companion))\n",
     69     "\n",
     70     "# Only use 200 samples for faster sampling\n",
     71     "massSamples = bothMassSamples[:,:200,:]\n",
     72     "\n",
     73     "# Define the number of samples drawn from each star mass distribution, and the total number of DNS systems.\n",
     74     "nSamples, nMeasurements = len(massSamples[0]), len(massSamples)"
     75    ]
     76   },
     77   {
     78    "cell_type": "markdown",
     79    "metadata": {},
     80    "source": [
     81     "# Prior\n",
     82     "Here we define prior used in **Hypothesis B**. 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."
     83    ]
     84   },
     85   {
     86    "cell_type": "code",
     87    "execution_count": 3,
     88    "metadata": {},
     89    "outputs": [],
     90    "source": [
     91     "def prior(cube, ndim, nparams):\n",
     92     "    # cube is initially a unit hypercube which is to be mapped onto the relevant prior space.\n",
     93     "    \n",
     94     "    # j is the hyperparameter index. We map the priors beginning with the parameters of model1,\n",
     95     "    # and then incriment j by the number of parameters in that model1. Then mapping\n",
     96     "    # the parameters of the next model2.\n",
     97     "    j = 0\n",
     98     "    \n",
     99     "    # Loop over both models in the sub-hypothesis.\n",
    100     "    for modelBeingMapped in [modelName1, modelName2]:\n",
    101     "        if modelBeingMapped == 'singleGaussian':\n",
    102     "            cube[j] = 0.8 + cube[j] * (2 - 0.8)\n",
    103     "            cube[j+1] = 0.005 + cube[j+1] * (0.5 - 0.005)\n",
    104     "            j += 2\n",
    105     "        if modelBeingMapped == 'twoGaussian':\n",
    106     "            cube[j] = 0.8 + cube[j] * (2 - 0.8)\n",
    107     "            cube[j+1] = cube[j] + cube[j+1] * (2 - cube[j])\n",
    108     "            cube[j+2] = 0.005 + cube[j+2] * (0.5 - 0.005)\n",
    109     "            cube[j+3] = 0.005 + cube[j+3] * (0.5 - 0.005)\n",
    110     "            cube[j+4] = cube[j+4] * 1\n",
    111     "            j += 5\n",
    112     "        if modelBeingMapped == 'uniform':\n",
    113     "            cube[j] = 0.8 + cube[j] * (2 - 0.8)\n",
    114     "            cube[j+1] = cube[j] + cube[j+1] * (2 - cube[j])\n",
    115     "            j += 2\n",
    116     "\n",
    117     "    return"
    118    ]
    119   },
    120   {
    121    "cell_type": "markdown",
    122    "metadata": {},
    123    "source": [
    124     "# Likelihood Function\n",
    125     "\n",
    126     "Here we impliment the likelihood function given by *Equation 11*.\n"
    127    ]
    128   },
    129   {
    130    "cell_type": "code",
    131    "execution_count": 4,
    132    "metadata": {},
    133    "outputs": [],
    134    "source": [
    135     "def likelihood(cube, ndim, nparams):\n",
    136     "    \n",
    137     "    # 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",
    138     "    paramList1 = [cube[i] for i in range(ndim1)]\n",
    139     "    paramList2 = [cube[i] for i in range(ndim1, ndim)]\n",
    140     "    \n",
    141     "    # 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",
    142     "    pdfProductSumList = []\n",
    143     "    \n",
    144     "    # For the m_r and m_s pairs in each BNS system. (eg. 1000x2)\n",
    145     "    for massSample in massSamples:\n",
    146     "        \n",
    147     "        # Evaluate the PDF function down the m_r and m_s samples of the BNS\n",
    148     "        mrProbabilities = modelEval1(paramList1, massSample[:,0])\n",
    149     "        msProbabilities = modelEval2(paramList2, massSample[:,1])\n",
    150     "        \n",
    151     "        # Evaluate the product of the m_r and m_s probability for each pair.\n",
    152     "        probabilityProduct = mrProbabilities*msProbabilities\n",
    153     "        \n",
    154     "        # Append the sum over all the probability products of each pair.\n",
    155     "        pdfProductSumList.append(np.sum(probabilityProduct))\n",
    156     "    \n",
    157     "    # If either the m_r or the m_s samples are completely outside their model then return a log-likelihood of -inf.\n",
    158     "    if 0 in pdfProductSumList:\n",
    159     "        #print(\"Zero probability value - Parameters: {}, {}\".format(paramList1,paramList2))\n",
    160     "        return -np.inf\n",
    161     " \n",
    162     "    # The log-likelihood is the log of the normalised sum over the log of each pdfProductSum\n",
    163     "    loglikelihood = nMeasurements * np.log(1.0/nSamples) + np.sum(np.log(pdfProductSumList))\n",
    164     "    return loglikelihood"
    165    ]
    166   },
    167   {
    168    "cell_type": "markdown",
    169    "metadata": {},
    170    "source": [
    171     "# Inference\n",
    172     "\n",
    173     "## **Hypothesis 1 $Z_{tu}^{B}$**: recycled NS distribution is two-Gaussian (bimodal) and non-recycled is uniform.\n",
    174     "\n",
    175     "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, as well as a larger uncertainty in the model Bayes Evidence.\n",
    176     "\n",
    177     "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 provided below:"
    178    ]
    179   },
    180   {
    181    "cell_type": "code",
    182    "execution_count": 5,
    183    "metadata": {},
    184    "outputs": [],
    185    "source": [
    186     "modelName1, modelEval1, ndim1, paramNames1 = models.twoGaussianList\n",
    187     "modelName2, modelEval2, ndim2, paramNames2 = models.uniformList\n",
    188     "\n",
    189     "# Define the total number of hyperparameters\n",
    190     "ndimHyp1 = ndim1 + ndim2\n",
    191     "\n",
    192     "### Inference\n",
    193     "# Directory to send output to. Create it if it does not exist.\n",
    194     "directoryNameHyp1 = 'demoFiles/hypo1/' + modelName1[:4] + \"/\" + modelName2[:4]\n",
    195     "if not os.path.exists(directoryNameHyp1):\n",
    196     "    os.makedirs(directoryNameHyp1)"
    197    ]
    198   },
    199   {
    200    "cell_type": "markdown",
    201    "metadata": {},
    202    "source": [
    203     "**Uncomment this cell if you wish to run the sampling. \n",
    204     "NOTE: This may take a while!**"
    205    ]
    206   },
    207   {
    208    "cell_type": "code",
    209    "execution_count": 6,
    210    "metadata": {},
    211    "outputs": [],
    212    "source": [
    213     "#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)"
    214    ]
    215   },
    216   {
    217    "cell_type": "code",
    218    "execution_count": 7,
    219    "metadata": {},
    220    "outputs": [],
    221    "source": [
    222     "egOutput = '''\n",
    223     "*****************************************************\n",
    224     "MultiNest v3.10\n",
    225     "Copyright Farhan Feroz & Mike Hobson\n",
    226     "Release Jul 2015\n",
    227     "\n",
    228     "no. of live points =  100\n",
    229     "dimensionality =    7\n",
    230     "resuming from previous job\n",
    231     "*****************************************************\n",
    232     "Starting MultiNest\n",
    233     "generating live points\n",
    234     "live points generated, starting sampling\n",
    235     "Acceptance Rate:                        0.955414\n",
    236     "Replacements:                                150\n",
    237     "Total Samples:                               157\n",
    238     "Nested Sampling ln(Z):                 -6.272028\n",
    239     "Acceptance Rate:                        0.271370\n",
    240     "Replacements:                                400\n",
    241     "Total Samples:                              1474\n",
    242     "Nested Sampling ln(Z):                 10.303706\n",
    243     "'''"
    244    ]
    245   },
    246   {
    247    "cell_type": "markdown",
    248    "metadata": {},
    249    "source": [
    250     "## **Hypothesis 2 $Z_{ss}^{B}$**: recycled & non-recycled are both single-Gaussian distributions. "
    251    ]
    252   },
    253   {
    254    "cell_type": "code",
    255    "execution_count": 8,
    256    "metadata": {},
    257    "outputs": [],
    258    "source": [
    259     "modelName1, modelEval1, ndim1, paramNames1 = models.singleGaussianList\n",
    260     "modelName2, modelEval2, ndim2, paramNames2 = models.singleGaussianList\n",
    261     "\n",
    262     "# Define the total number of hyperparameters\n",
    263     "ndimHyp2 = ndim1 + ndim2\n",
    264     "\n",
    265     "### Inference\n",
    266     "# Directory to send output to. Create it if it does not exist.\n",
    267     "directoryNameHyp2 = 'demoFiles/hypo2/' + modelName1[:4] + \"/\" + modelName2[:4]\n",
    268     "if not os.path.exists(directoryNameHyp2):\n",
    269     "    os.makedirs(directoryNameHyp2)"
    270    ]
    271   },
    272   {
    273    "cell_type": "markdown",
    274    "metadata": {},
    275    "source": [
    276     "**Uncomment this cell if you wish to run the sampling. NOTE: This may take a while!**"
    277    ]
    278   },
    279   {
    280    "cell_type": "code",
    281    "execution_count": 9,
    282    "metadata": {},
    283    "outputs": [],
    284    "source": [
    285     "#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)"
    286    ]
    287   },
    288   {
    289    "cell_type": "markdown",
    290    "metadata": {},
    291    "source": [
    292     "# Analysis"
    293    ]
    294   },
    295   {
    296    "cell_type": "code",
    297    "execution_count": 10,
    298    "metadata": {},
    299    "outputs": [
    300     {
    301      "name": "stdout",
    302      "output_type": "stream",
    303      "text": [
    304       "  analysing data from demoFiles/hypo1/twoG/unif/.txt\n",
    305       "  analysing data from demoFiles/hypo2/sing/sing/.txt\n",
    306       "For Hypothesis 1 we find a log-Bayes Evidence: 24.2533062226\n",
    307       "For Hypothesis 2 we find a log-Bayes Evidence: 19.4291942354\n",
    308       "\n",
    309       "Here we have shown that Hypothesis 1 (two-Gaussian recycled, uniform non-recycled) is strongly favoured\n",
    310       "over the alternative hypothesis (single-gaussian distributions) with a Bayes Factor of 121.5, (log-BF: 4.8)\n",
    311       "\n"
    312      ]
    313     }
    314    ],
    315    "source": [
    316     "# We load the results for each hypothesis which were created by pymultinest\n",
    317     "hyp1Res = pymultinest.analyse.Analyzer(ndimHyp1, outputfiles_basename=directoryNameHyp1 + '/')\n",
    318     "hyp1Stats = hyp1Res.get_stats()\n",
    319     "hyp2Res = pymultinest.analyse.Analyzer(ndimHyp2, outputfiles_basename=directoryNameHyp2 + '/')\n",
    320     "hyp2Stats = hyp2Res.get_stats()\n",
    321     "\n",
    322     "print(\"For Hypothesis 1 we find a log-Bayes Evidence: {}\".format(hyp1Stats['global evidence']))\n",
    323     "print(\"For Hypothesis 2 we find a log-Bayes Evidence: {}\".format(hyp2Stats['global evidence']))\n",
    324     "\n",
    325     "logBF = np.round(hyp1Stats['global evidence'] - hyp2Stats['global evidence'], 1)\n",
    326     "\n",
    327     "print(\n",
    328     "\"\"\"\n",
    329     "Here we have shown that Hypothesis 1 (two-Gaussian recycled, uniform non-recycled) is strongly favoured\n",
    330     "over the alternative hypothesis (single-gaussian distributions) with a Bayes Factor of {}, (log-BF: {})\n",
    331     "\"\"\".format(np.round(np.exp(logBF), 1), logBF))"
    332    ]
    333   },
    334   {
    335    "cell_type": "markdown",
    336    "metadata": {},
    337    "source": [
    338     "## We can also explore the parameter posteriors to view their distributions:\n",
    339     "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."
    340    ]
    341   },
    342   {
    343    "cell_type": "code",
    344    "execution_count": 11,
    345    "metadata": {},
    346    "outputs": [],
    347    "source": [
    348     "# We import plotting tools\n",
    349     "%matplotlib inline\n",
    350     "import matplotlib.pyplot as plt\n",
    351     "\n",
    352     "# Corner module provides great visualisations for our purpose.\n",
    353     "import corner\n",
    354     "\n",
    355     "\n",
    356     "def cornerPlot(samples, bounds, parameterNames):\n",
    357     "    plt.rcParams.update({'font.size': 15})\n",
    358     "    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",
    359     "\n",
    360     "hyp1Posterior = np.asarray([param for param in hyp1Res.get_equal_weighted_posterior()])\n",
    361     "hyp2Posterior = np.asarray([param for param in hyp2Res.get_equal_weighted_posterior()])"
    362    ]
    363   },
    364   {
    365    "cell_type": "markdown",
    366    "metadata": {},
    367    "source": [
    368     "## **Hypothesis 2 $Z_{ss}^{B}$** Posterior"
    369    ]
    370   },
    371   {
    372    "cell_type": "code",
    373    "execution_count": 12,
    374    "metadata": {
    375     "scrolled": false
    376    },
    377    "outputs": [
    378     {
    379      "data": {
    380       "image/png": 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\n",
    381       "text/plain": [
    382        "<Figure size 698.4x698.4 with 16 Axes>"
    383       ]
    384      },
    385      "metadata": {},
    386      "output_type": "display_data"
    387     }
    388    ],
    389    "source": [
    390     "# We have to reset the model information back to hypothesis 2 information\n",
    391     "modelName1, modelEval1, ndim1, paramNames1 = models.singleGaussianList\n",
    392     "modelName2, modelEval2, ndim2, paramNames2 = models.singleGaussianList\n",
    393     "paramNames1 = [r'$m_r$ ' + pName for pName in paramNames1]\n",
    394     "paramNames2 = [r'$m_s$ ' + pName for pName in paramNames2]\n",
    395     "\n",
    396     "cornerPlt = cornerPlot(hyp2Posterior[:,:ndim1 + ndim2], bounds=[[1.3,1.6],[0,0.5], [1.2,1.4],[0,0.5]], parameterNames=paramNames1+paramNames2)"
    397    ]
    398   },
    399   {
    400    "cell_type": "markdown",
    401    "metadata": {},
    402    "source": [
    403     "## Posterior Predictive Distributions (PPD)\n",
    404     "\n",
    405     "The goal is to now summarise the findings into a mass distributions from our inference sampling.\n",
    406     "\n",
    407     "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",
    408     "\n",
    409     "Instead we take another approach by creating a posterior predictive distibution:\n",
    410     "See paper or https://en.wikipedia.org/wiki/Posterior_predictive_distribution."
    411    ]
    412   },
    413   {
    414    "cell_type": "code",
    415    "execution_count": 13,
    416    "metadata": {},
    417    "outputs": [],
    418    "source": [
    419     "def postPredDist(model1List, model2List, hypPost, plotrange=[0.8, 2], thinningFactor=10):\n",
    420     "    paramList = hypPost[:,:-1].tolist()\n",
    421     "    \n",
    422     "    # Randomly take totalSamples/thinningFactor sets of the hyperparameters from the posterior.\n",
    423     "    drawnParams = [random.choice(paramList) for i in range(len(paramList)/thinningFactor)]\n",
    424     "    \n",
    425     "    # Here we are creating two PPDs, one for recycled NS and one for non recycled NS.\n",
    426     "    # We need to keep track of whether we are looking at reclyed or non-reclyed model parameters.\n",
    427     "    paramsPassed = 0\n",
    428     "    \n",
    429     "    titleList = [r'Recycled NS Posterior Predictive Distribution $m_r$ - {}', r' Non-Recyled Posterior Predictive Distribution $m_s$ - {}']\n",
    430     "    \n",
    431     "    # Loop over each model for recycled and non-recycled\n",
    432     "    for index, (modelName, modelEval, ndim, paramNames) in enumerate([model1List, model2List]):\n",
    433     "        \n",
    434     "        # X-axis plot range\n",
    435     "        xValues = np.linspace(plotrange[0], plotrange[1], 10000)\n",
    436     "        plt.xlim(plotrange[0], plotrange[1])\n",
    437     "        \n",
    438     "        # For each set of hyperparameters we evaluate the function they describe.\n",
    439     "        yValueList = []\n",
    440     "        for params in drawnParams:\n",
    441     "            yValues = modelEval(params[paramsPassed:paramsPassed + ndim], xValues)\n",
    442     "            yValueList.append(yValues)\n",
    443     "        \n",
    444     "        # We incriment paramsPassed by the number of parameters belonging to this model.\n",
    445     "        paramsPassed += ndim\n",
    446     "    \n",
    447     "        # We turn these function values into an array and then take the mean of each function value at each x.\n",
    448     "        yValueArray = np.asarray(yValueList)\n",
    449     "        meanyValues = np.mean(yValueArray, axis=0)\n",
    450     "\n",
    451     "        plt.title(titleList[index].format(modelName))\n",
    452     "        plt.plot(xValues, meanyValues)\n",
    453     "        plt.xlabel(r\"$m$ ($M_\\odot$)\")\n",
    454     "        plt.show()\n",
    455     "    \n",
    456     "    return"
    457    ]
    458   },
    459   {
    460    "cell_type": "markdown",
    461    "metadata": {},
    462    "source": [
    463     "## **Hypothesis 1 $Z_{tu}^{B}$** PPD"
    464    ]
    465   },
    466   {
    467    "cell_type": "code",
    468    "execution_count": 14,
    469    "metadata": {},
    470    "outputs": [
    471     {
    472      "data": {
    473       "image/png": 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WPolwd1jqbdcFcfetFvpwSNfg+qvAPDP7DaG6YZBQHPxmwj+Ly6I2R6XyBeBswm2xxxIO5mMI/7rXsCtwawM2Rfm6n1Cqtz/hzrgeQh1ywr2E21U/bmZdhHY3T7n73RS2D8q1LtPBVB6L+Z4z2fZbNpcSqr2/TGh0ec0k1zebY83srdHn5B6t94vW6805pi/VcVysrcDdZvbj6Ps7CNvg/JQG2zcSjtlPW+jP5ilC0PcS9tznheZzys4TM5tLWL+r0gw+Fuh299R2ZJlKkI4FrnT3b5Yqf0lybcNbo+GHEf68A+Duj5rZc4TSvrt8z64M8t7W7h4zs9cQ7sS72kKfQYmuL9oJfRidQwgmkrfZLwmdAl9vZldH476Z9L1H53tc5XueFHI+pSok36Xh+d2KeBJZbnUlHARx4JaktDrgPYQDaSB6PU74R/qqlOmbCEWBjxAufL3RdO/OsLybovy8LUuec86TNLcAFpH3fQk7ri96/ZbwD2UdRdySnzKshVCk6+x+S/6rCN0hPEA4SMcIDcluIdzlVDOZ5WYYfwHhDrcNhANyQ5SH+UnjNBAO4Hui/AxH2+FHwMFp5vl2QolWonuBSwrdBxR4q3G+65Jr3qXYrvnMvxzHYpbtktd5mGm/ZZpv0rGxLRr+g1Ksb5Ztn3jFCQHYI4Sg7LQc051XyuO40GMzafxTCXcvPh0t+yFSblNPmuYQQt9Og9H+uopQdb7bPi9mv1GC84TokRg59tsp0fRvSjNsE/CHNOmJW7KXpqQ/DZyR7/la6CvTNkwavpI0v03R8evA/2SYb17bOmn8ZsLdZbcQfgNGo/2/ghBEPS9l/FpCSdXa6JhaH413WJSvCws9rsjzPClgvD2Ow0LyPdnjMPGyaIKqYmbXEf4B7+05nhMmIiIzn4VbtbsJgcS2SudHqlMp2hRNKTM7iNCmKOeDU0VEZNY4FlivgEgmoxK3bRbFzF5MKDJ7D6Ho8suVzZGIiEwjx5DSIFukUFVTfWbh4YXnEm5P/LCX+JlfIiIiMrtVTVAkIiIiUk5VU30mkzd//nxftmxZpbMhIlJVVq5cudXdUx8LIjOQgqJZZNmyZaxYsaLS2RARqSpmtr7SeZCpUXV3n4mIiIiUg4IiERERERQUiYiIiAAKikREREQABUUiIiIigIIiEREREUBBkYiIiAigoEhEJuGW1VtYtamv0tkQESkJdd4oIkXZPjDCOy65l/pa4/H/OaPS2RERmTSVFIlIUVZHJUSjcWdoNF7h3IiITJ6CIhEpyobe2MTnp7cPVjAnIiKloaBIRIrybFJQtLlvqII5EREpDQVFIlKU5EBoc99wBXMiIlIaCopEpCh9sTGWdDYDKikSkZlBQZGIFKVvaJRF7Y20NdbR3a+SIhGpfgqKSszMDjKz75vZg2YWN7NbU4bvZWZfNLMHzGynmT1jZpea2d55zPtCM/M0r9PKtkIiGfTFRmlvrqeztZ7ewZFKZ0dEZNLUT1HpHQGcAdwF1KcZfhzweuB/gbuBRcCFwF/M7Eh335lj/juA1CBo1WQyLFKMHbFR9pvXSmdzA72x0UpnR0Rk0hQUld5v3f3XAGb2S2B+yvA7gEPdfSyRYGb3AWuAvwcuzTH/MXe/q4T5FSlK39AY7c11dLbU0zuooEhEqp+qz0rM3cdzDO9NDoiitMeAQSBnFZrIdODuofqsqZ6O5np2qKRIRGYABUXTgJkdDbQAj+UxeqeZbTWzUTO738zeUObsiewhNhpnbNxDm6IWtSkSkZlBQVGFmVkN8HXgceA3OUZfC3wYOJtQ1fYs8KtsgZGZXWBmK8xsRXd3d4lyLbNdXywUdrY11dHZ3MCO2Cjj417hXImITI7aFFXe54DjgRPdPWsdhLtfnvzdzH4L/AX4T+DqDNNcDFwMsHz5cv1qSUkMjISgaE5jaFM07tA/PEZHc7p7C0REqoNKiirIzN4NfAh4u7vfXej07u6EYOhoM6stdf5EMomNhAfANtXX0tnSAMAONbYWkSqnoKhCzOzvgW8CH3b3n09iVh69RKbM0GgIiprraydKh3pjalckItVN1WcVYGYnAVcA33T3L01iPkZoW/SAu8dLlD2RnIZGw02WzQ21NNSF/1b9Q2PZJhERmfYUFJWYmbUQOm8EWAK0m9lZ0ffrgP2Aa4DVwM/N7CVJk3e7+xPRfE4EbgJOcffborTbgF9F07YC/wS8GDizrCslkiIWlRQ11dVSE5U39w+p+kxEqpuCotJbCPwiJS3xfX9CENMBPJ/QSDrZpcB50WcDaqP3hLXA+4C9gHHgPuA17n59ifIukpdEUNTcUENjXWjO1qeSIhGpcgqKSszd17F7IJPqkuiVaz63ps7H3d9ZfM5ESmcoqaH1nMZwGVH1mYhUOzW0FpGCxZIaWu8KilR9JiLVTUGRiBRs4u6zhlrqamtoaahVSZGIVD0FRSJSsOSG1hB6tlZJkYhUOwVFIlKw2GicxroaampCs7e2pnqVFIlI1VNQJCIFGxqJ01S/qxP1UFKkoEhEqpuCIhEpWGw0TvNuQVG9qs9EpOopKBKRgsVGx2luSCkpGlZJkYhUNwVFIlKwodHdq8/aVX0mIjOAgiIRKdjQaJzm+l2XD1WfichMoKBIRAoWG4nvXn3WWMfQ6Dij8fEK5kpEZHIUFIlIwfZsaK1HfYhI9VNQJCIFi43GaUwKiuY01QN61IeIVDcFRSJSsKERlRSJyMyjoEhECjY0Np42KOpTSZGIVDEFRSJSsNSG1u0T1WcqKRKR6qWgSEQK4u7ERvd8zAcoKBKR6qagSEQKMjwWbrtPfcwHqKG1iFQ3BUUiUpDYSBwgpfNGlRSJSPVTUCQiBYmNhqAoufqsvraGpvoalRSJSFVTUCQiBRmKgqLkhtaQeNSHSopEpHopKBKRgqQrKYJQhaagSESqmYIiESnIRElRSlDU3lSvfopEpKopKBKRgsRGorvP9qg+U0mRiFQ3BUUiUpBYlpIiNbQWkWqmoKgMzOwgM/u+mT1oZnEzuzXNOGZmHzOzZ8wsZma3m9kL8pz/68zsITMbMrNHzeyckq+ESAbZ2hT1qaRIRKqYgqLyOAI4A1gDPJZhnI8AnwQuAl4L7ARuNLPF2WZsZi8DfgXcApwO/A74qZm9qjRZF8luaCIo2v3y0d6skiIRqW4Kisrjt+6+1N3PBh5JHWhmTYSg6HPu/i13vxE4G3Dg33LM+5PA7e7+Hne/xd0/BPwe+M/SroJIepkaWrc11jE0Os5ofLwS2RIRmTQFRWXg7rl+FV4KtANXJU0zAPyWUPqTlpk1Aq9Ini7yM+B4M+soKsMiBZjo0TpNQ2tQr9YiUr0UFFXGoUAceDwlfVU0LJMDgXpgdZrpaoBDSpVBkUwm2hTV7dl5I+j5ZyJSvRQUVUYXsNPd4ynpPUCLmTVkmQ6gN810ycMnmNkFZrbCzFZ0d3cXnWGRhNhonMa6GmpqbLf09uYQFPXFVFIkItVJQdEM5+4Xu/tyd1++YMGCSmdHZoChkfgeVWeQXH2mkiIRqU4KiiqjB5hjZqm/LF3AoLuPZJkOILXtUFfKcJGyGRod36ORNewKinRbvohUKwVFlbEaqAUOSkk/lD3bCyV7Ahhlz3ZHhwLjZL79X6RkYqPxPfoogtB5I6ikSESql4KiyvgL0Ee4DR8AM2sh9Fd0faaJ3H2Y0D/R2SmDzgHudPcdpc+qyO5yBUUqKRKRalVX6QzMRFGAc0b0dQnQbmZnRd+vc/dBM/s88Ekz6yGUDn2AEKR+M2k+5wI/Ag509/VR8meAW83sa8A10XLOAE4r82qJAKGfotSOGwHmqE2RiFQ5BUXlsRD4RUpa4vv+wDrg84Qg6KPAPGAF8Ep335w0TQ2hmm3iNh93vyMKsP4beBfwFPBmd7+h9KshsqfYSJyWNA2ta2uM1oZa9VMkIlVLQVEZuPs6kgKZDOM48D/RK9M4lwCXpEm/hlBKJDLlYqNxOlvq0w5r00NhRaSKqU2RiBQkU5siiB4Kq36KRKRKKSgSkYIMZ7glH6KHwg6rpEhEqpOCIhEpSGw0feeNEEqK1KZIRKqVgiIRKUhsJJ6xpCi0KVJQJCLVSUGRiOTN3cOzz7K2KVL1mYhUJwVFIpK34bFxgMxtilRSJCJVTEGRiOQtNhIHoDlN540QSopG4uMMjcanMlsiIiWhoEhE8haLgp1MDa3bJ3q1VmmRiFQfBUUikrdEUJS5n6LE88/UrkhEqo+CIhHJ267qs0z9FKmkSESql4IiEcnb8Fj26rNESZEe9SEi1UhBkYjkLTaS/e6zNrUpEpEqpqBIRPKWb5silRSJSDVSUCQiecsVFCXuPtNDYUWkGikoEpG8DY1kb1PU2lCHmUqKRKQ6KSgSkbxN9FOUoaSopsaY01hHn9oUiUgVUlAkInnLFRSBHvUhItVLQZGI5C3RT1FjXeZLR1tTnTpvFJGqpKBIRPI2NBqnqb6GmhrLOE4oKVJQJCLVR0GRiORtaDSeteoMQkmRqs9EpBopKBKRvMUUFInIDKagSETyFhsdz9hHUUJbU73aFIlIVVJQJCJ5i43EcwZF7c2hpMjdpyhXIiKloaBIRPI2NBrP2HFjQltTPfFxn7h9X0SkWigoqhAzu9XMPMPr+AzTLMsw/s+mOv8yOw2MjNGSMyjSQ2FFpDrVVToDs9i7gfaUtE8DxwD35pj2g8Cfk75vLWG+RDIaHI6zqK0p6ziJh8L2xUZZ1J59XBGR6URBUYW4+6PJ382sAVgO/Nzdc/3FXuPud5UtcyIZ7Bweo7Ux+2Vj4qGwKikSkSqj6rPp4zSgC/hppTMiksngyBitjbnbFIEeCisi1UdB0fTxRmAD8Kc8xv2xmcXNbJOZfcXMmsucNxEABkbitDTkV1KkNkUiUm1UfTYNmFkL8HfA9z37fczDwLeBG4A+4CTgP4ADgdeVOZsyy43GxxkZG6c1j7vPAPVVJCJVR0HR9PBaoJUcVWfuvgn4t6SkW81sM/AdM3u+uz+QOo2ZXQBcALDvvvuWLscy6wwOh1vsc7YpalZJkYhUJ1WfTQ9vBNa6+4oipv1l9H5cuoHufrG7L3f35QsWLCg6gyIDIyHIydWmqLm+lroaoy+mkiIRqS4KiirMzDqA0ym+gbWnvIuUxWAUFOVqU2RmdDTXs0NBkYhUGQVFlfd6oJHig6KzoveVpcmOSHo7J6rPspcUAXS01NOroEhEqozaFFXeG4EH3H1V6gAzWwvc5u7vjL5fCLQROm7sA04APgRc7e4PTlmOZVYaHI6qz3KUFAF0Nter+kxEqo5KiirIzOYDpwCZHtNRByT/LV8NnAj8GLgOeDPwxehdpKwGRvJraA3Q0VxP76CCIhGpLiopqiB33wrUZxm+LOX7z8gcQImU1cBwok1R7uqzzpYG1nbvLHeWRERKSiVFIpKXxN1nc1RSJCIzlIIiEclLop+iljyCos6WevqHxoiP66ZIEakeCopEJC+JkqLm+jzuPmuOerVWY2sRqSIKikQkLwPDYzTX11JbYznH7WwJQZFuyxeRaqKgSETyMjASz6uPIoDO5gYAdeAoIlVFQZGI5KV/aGziYa+5dCRKigZHypklEZGSUlAkInnpHxqlvSm/XjwSbYpUUiQi1URBkYjkpS82mndJUWdzoqRIQZGIVA8FRSKSl/6hMdqbVVIkIjOXgiIRyUvf0ChtjfmVFNXV1tDWWKeSIhGpKgqKRCQvhZQUAbQ319MbU0NrEakeCopEJKfR+DiDI/G82xRB6Ktoh0qKRKSKKCgSkZz6h0Jv1vnefQZRUKQ2RSJSRRQUiUhO/UMhuCmopKi5QT1ai0hVUVAkIjn1xaKSoub8g6L25no1tBaRqqKgSERy2lVSVGj12QjuXq5siYiUlIIiEcmpLwqK2guoPpvb0sBo3OkfHitXtkRESkpBkYjk1Bc1tC6kpGjenPBQ2O07dVu+iFQHBUUiklNf1GC6kDZFc1tDULRtQEGRiFQHBUUiklPilvw5jQWUFLU2ArBt53BZ8iQiUmoKikQkp97BETqa66mtsbynmag+U0mRiFQJBUUiktP2wdGJ6rB8qfpMRKqNgiIRyalnYITOlvzbEwE01dfS2lDLNjW0FpGGQeWGAAAepUlEQVQqoaBIRHLqGRxhbkthJUUA8+Y0sn1AbYpEpDooKBKRnHoGRugqsPoMQhWaqs9EpFooKKoQMzvPzDzN619yTNdhZj82sx4z22FmV5jZvKnKt8xOPYOjdBVYfQYwr7VB1WciUjXyv79WyuVkIJb0/ckc418FHAKcD4wDFwHXAC8vS+5k1ouNxImNxosqKZo3p4FHnu0rQ65EREpPQVHl3evuO/MZ0cyOB14FnOjut0dpG4G7zexUd7+xjPmUWapnMJT0dBXRpmhuayPbB8Lzz8zyv51fRKQSVH1WXU4HNicCIgB3vwd4KhomUnKTCYrmtTYwEh/X889EpCooKKq8J8xszMzWmNk/5xj3UGB1mvRV0TCRkusZCI/4KLSfouRp9PwzEakGCooqZxPwSeBtwGuBu4Dvmdn7s0zTBfSmSe+Jhu3BzC4wsxVmtqK7u3uSWZbZaFdJURENraNerbfqUR8iUgXUpqhC3P0PwB+Skq43sybgE2b2dXcfL9FyLgYuBli+fLmXYp4yuySCos4iqs8WtTcBsKVfQZGITH8qKZpefgnMBZZlGN4DdKRJ74qGiZTc1p0j1Fhx1WeJoGhz31CpsyUiUnIKiqYXT3lPtZr0bYcytTUSmbTu/iHmtjYW9DDYhK6Weuprjc19KikSkelPQdH0chawFVifYfj1wGIze1kiwcyWAwdEw0RKrrt/mAVtjUVNa2YsbGtii0qKRKQKqE1RhZjZr4B7gAeBWuCc6PWeRHsiM1sL3Obu7wRw9zvN7AbgMjP7ILs6b7xDfRRJuXT3D7OwyKAIYFF7I5v7FRSJyPSnoKhy1gD/CCwFDHgUONfdf5I0Th0hYEp2DvBV4EeEkr5rgfeUPbcya23pH+bgRW1FT7+ovYnHNveXMEciIuWhoKhC3P1jwMdyjLMsTVov8I7oJVJW4+PO1p3FV59BCIrueHxrCXMlIlIealMkIhntiI0yGncWzJlcUNQ/PMaAerUWkWlOQZGIZNQddbq4sH1ybYpAfRWJyPSnoEhEMtoS3Uo/2ZIiUF9FIjL9KSgSkYy6d4ZAZnJtisK0CopEZLpTUCQiGU2UFE0iKFrc0QzAxt5YSfIkIlIuCopEJKNNO4Zoa6yjranwh8EmzGmso6ulng09CopEZHpTUCQiGW3sjbF3Z/Ok57N0bgvPbB8sQY5ERMpHQZGIZPRsb4y9O5smPZ99uprZqJIiEZnmFBSJSEbPlqikaJ+uFjb0xhgfz/SsYxGRylNQJCJpxUbi9AyOlqb6rKuZkbHxiX6PRESmIwVFIpLWsztCdVdpqs9aANjQo3ZFIjJ9KSgSkbSejW6h37ujFA2twzye2a52RSIyfSkoEpG0JoKiElSfLekMJUW6A01EpjMFRSKS1saeGDUGizsmX33W3FDLovZGnto2UIKciYiUh4IiEUnrqW2DLOlqpr62NJeJAxfM4YluBUUiMn0pKBKRtNZvG2DZvNaSze/ABXN4cstO3HVbvohMTwqKRGQP7s5TW0sdFLXSPzxGd79uyxeR6UlBkYjsoWdwlP6hMZbNL11QdNDCNgDWdu8s2TxFREpJQZGI7OGpraHtz7J5LSWb54ELQ4CldkUiMl0pKBKRPayP7hIrZUnR4vYmWhpqeWKLSopEZHpSUCQie1i3dYAaCw9yLRUz45BFbaza1FeyeYqIlJKCIhHZw2Obd7JsXiuNdbUlne+RS9p59Nk+PRhWRKYlBUUisoc1m/t53uK2ks/3iL076B8e42n1bC0i05CCIhHZzdBonHXbBjhkUemDoiP37gDgkWdVhSYi04+Cogows7PN7DdmttHMdprZSjN7Ux7TeZrXXVORZ5k91m7ZiTtlKSk6ZPEc6mqMh5/dUfJ5i4hMVl2lMzBLfQB4Cng/sBU4A7jSzOa7+zdzTPtl4JdJ3/vLk0WZrVY/Fw6pcgRFjXW1HLKojYc3KigSkelHQVFlvNbdtyZ9v9nM9iYES7mConXurtIhKZs1z/XRUFfDfnNL10dRsmP27eTXf32W+LhTW2NlWYaISDFUfVYBKQFRwv3A3lOdF5FUD23cwWGL26gr0YNgU71o/7nsHB7TrfkiMu0oKJo+jgcey2O8C81szMy2mtmPzGxuuTMms0d83Hloww5esLSzbMt44bJwyN7z1PayLUNEpBgKiqYBMzsFOJPQXiibS4F/Bk4GPgu8HvijmWXsTMbMLjCzFWa2oru7u1RZlhlq7ZadDIzEeX4Zg6K9O5tZOrdZQZGITDtqU1RhZrYMuBL4tbtfkm1cdz8v6evtZrYKuA54LXBNhmkuBi4GWL58uXrMk6weeKYXoKxBEcCLls3j5tWb1a5IRKYVlRRVUFT1dT2wHnhLEbP4PbATOLaU+ZLZ668bemlrqmP/eaV75lk6Jz5vAT2DozywobesyxERKYSCogoxsxbgWqAB+Ft3L7iLX3dPlPyoBEhK4t6ntnPMvl3UlLn05sSDF1BbY9y8aktZlyMiUggFRRVgZnXAL4CDgdPcvahfBjM7DZgDrCxh9mSW2tI/xONbdvLSA+eVfVkdLfUct18XN61WUCQi04faFFXGdwgdNr4XmGdmyb9C97v7sJndBODup0BoMA0sB24kdPh4LPAJ4B7gd1OYd5mh7nxiGwDHH1D+oAjglEMX8rnrV/P0tkH2nVeePpFERAqhkqLKeFX0/nXgzpTXXtGw2uiV8ARwBPBd4A+EgOoy4FXuHp+CPMsMd9eT22hrquOIvdunZHl/+/zQLdc1f904JcsTEclFJUUV4O7L8hjnpJTvNwE3lSlLMsu5O396fCsv3n9e2TptTLWks5mXHDCXq+/bwL+ffBBmugtNRCpLJUUiwqpN/WzoiXHqYQundLlvOHYf1m0bZOX6nildrohIOgqKRIQ/ProZMzjlsEVTutzXHLUXbU11/PjP66Z0uSIi6SgoEhFuePQ5jt23iwVtjVO63NbGOt784n25/uFNPLO94F4pRERKSkGRyCz3RPdOHnm2j1cfMbWlRAnnvXQZNWb84E9PVmT5IiIJCopEZrlfrtxAbY1x5guWVGT5e3U0c84Ll3Ll3U+zbutARfIgIgIKikRmtfi4c/V9GzjxkAUsbG+qWD7ee+rBNNTV8PnrV1csDyIiCopEZrGbVm1mc98wZx+3T0XzsbCtiX99xUH8/pHn+P3Dz1U0LyIyeykoEpnFLr79SZZ0NvPKwyvTnijZBSccwJFL2vnENQ+xdedwpbMjIrOQgiKRWWrl+h5WrO/h/JfvP2UdNmZTX1vDl85+Pv1DY7z78vsYGRuvdJZEZJap/JVQRKacu/OVP66hq6Wef1i+tNLZmXDo4na+cNbR3LNuOx/7v4cYH/dKZ0lEZhE95kNkFrr1sW7+vHYbn3rt4bQ2Tq/LwOtesIQnuwf4+k2PU1djfPb1R1FTo0eAiEj5Ta+roYiU3dBonP++9lH2m9fCW168X6Wzk9b7Tj2YcXe+efNatu4c5qvnvIC2pvpKZ0tEZjhVn4nMMl+/6XGe6B7g0687koa66XkJMDM+8MpD+PTrjuCWNd383bf+zMr12yudLRGZ4abnFVFEyuLuJ7fx/due4JzlSznxkAWVzk5WZsa5xy/jivNfzMjYOGd9704+/n8PsblvqNJZE5EZSkGRyCzxbG+Md19xH8vmtfLxvz2s0tnJ20sOmMcf3n8Cbz9+GT+/9xlO+MItXPibR1i7pb/SWRORGcbcdXfHbLF8+XJfsWJFpbMhFdA7OMIbL76LDT0xrvnXv+GghXMqnaWirN82wDduWstvHtjIaNxZvl8Xpx25mFcevoj95rVWOnsyQ5nZSndfXul8SPkpKJpFFBTNTjsGR3nrD+9mzeZ+fvT2F/Kyg+dXOkuTtnXnML9YsYFf/3Ujq58LJUb7zm1h+X5dLF82l6P36eCghXNoqq+tcE5lJlBQNHsoKJpFFBTNPuu2DvCPl97LM9sH+f7bjuPkQyvfc3WpPb1tkBtXbebup7axcn0PW3eOAGAG+81t4eBFbew/v5V9uppZ2tXCPl3NLOlqpqVBN99KfhQUzR4KimYRBUWzy+8f3sRHrn4IA77/tuW8aP+5lc5S2bk767YNsmpTH2ue6+fxLf2sea6fZ3pie/SQPa+1gcUdTezV0cTijiYWtzexuKOZvTqaWNQe0qdbH05SGQqKZg+d8SIzzNadw3zuutX86r4NHLmknW+96ViWzZ8d7W3MjP3nt7L//FbOOGqvifTxcWfrwDDPbI+xoWeQDT0xNvTEeG5HjI29Q6xc30PP4Oge82trqouCpSh4ShM4dbbUY6bOJUVmAgVFIjPEwPAYl925nm/fspah0Tj/9oqDeM8pB0/bvoimUk2NsbCtiYVtTRy3X1facYZG42zuG2LTjiGe2zHEc33hfdOOGM/1DfPY5m629A+TWrjeUFfDgjmN7NXRxBF7t3PMvl0cs28n+85tUbAkUmUUFIlUuY29Ma64az2X37WevqExTj1sIR894zAOXFCdd5hVSlN9LfvNa816F9tofJzu/uGkgGmILX1DbOkfZmNPjKtWbODSO9cDoXruBUs7OXqfTg5c2DpRgqW2TCLTl85OkSq0uW+Im1Zt4Zq/buSep7ZTY3DakYs5/+UHcOy+6UtCZPLqa2vYu7OZvTub0w4fi4+zZnM/f32ml/uf7uX+p3u4afWW3cZZ1N64W4PvfbpaWNLZzD5dYb66Y06kctTQehZRQ+vqtblviAee6eXeddu5/bGtrNkcbkM/YEErr3/BEs48ZglL57ZUOJeSTmwkzrptAzy1Nbye7B5gQ88gG3tjbNoxRHx892vwgrbGiSBpSWczi9qbolcji9qbWNjeSGOdAqeppIbWs4dKiirEzA4HvgkcD/QC/wv8l7vHc0zXAXwNOJPQI/m1wHvcfVt5cyxToWdghCe37uTJ7vAD+tjmnTy4oZct/cMANNTWsHxZFx859lBOOHgBh+3VpnYr01xzQy2H7dXOYXu17zFsLD7Oc31DbIwafm/sjU0ETA9t3MENj2xmJD6+x3RzWxtY2BaCpMVRoDSvtYGu1gbmtTbS1Vo/8a4ASiR/CooqwMy6gBuBR4HXAQcCXyYEOZ/IMflVwCHA+cA4cBFwDfDycuVXJsfdGRiJ0zMwwo7YKN07h9kcNeTd3Jdo1DvMs70xdsR23QFVV2Msm9/K3xw0n6P36eDofTo4fK8Omhv0IzdT1NXWsE9XC/t0tfDiNMPdnd7B0YljZUvf8MTnzX3DbOkfYtWmPrbuHGY8Q6H/nMY65kYB09yWejqa62lrqqetqY725ug96Xv7xPd6muprFHTLrKKgqDL+BWgG3uDufcAfzawduNDMvhCl7cHMjgdeBZzo7rdHaRuBu83sVHe/cYryPyvEx53hsTiDI3EGhscYGI4zODLGwMT3sTBsZGxi+MDwGL2xUXoHR+gZHKV3cJQdsRFG4+l/sebPaWBRexN7dzRx7L6d7D+/lQMWtLL//Dks7WqmrlZ3js1mZkZXFNCkK2lKiI87O2KjbB8YZvtAeN82MELPwMhu7907h3mie4D+oVH6hsb2qLpLVWPQ0lBHc0MtLQ21NNeH9+S0kF4X3qPvjXW1NNbV0FBXk/ReO/G9qb6GhtpaGutraKitmXjX8S6VpqCoMk4H/pAS/PyMUOpzIvDbLNNtTgREAO5+j5k9FQ2b0qDI3Rl3GHcnPu549Hk8Sk8ePj6e9Nl3jRsfD6+x6H00Ph69J9LHGYuH4WPjycPGQ1piWHx8Yh6Jz2PR/IbHxhkZC+/Do3FG4uMMj44zPLbr825p0bhjOX4wktXWGC0NtcxprKOjuZ6ulgYOXjiHzpYGOlvq6Wqpp7O5gY6W+olAaGFbk26Xl5KorTHmtjYwt7Uh72ncndhonP6hMfpiIUjqGxqlf2gsBE2xMQZHQuC/6z1OLPq+decwsdHd0wo4ZTKuR0NtCKLqa426mhrqao362hrqaoy62kT6rmF1tTXU11jK5zBebTRefcqw2powrNZs1+fkl4X51VhYlsweCooq41Dg5uQEd3/azAajYZmCokOB1WnSV0XDsnpscz8nf+nWiaAlNTjZFcikH54a9ExniQtifU34F5r6z7WxLvzb7arb9S+1sW73f66Jf7atDbW0NtbR0lBHa2PtxHtrQ12UHuatagapJmZGS0M4rhe1N016fu7O8Ng4sZHkPxtxhjL86Zj4o7JHWnziT8lYPPwpGo0+j8aT/yiF8QdG4knjRcPi44wm/dFKjJ+pxFYkQUFRZXQRGlen6omGFTPdAekmMLMLgAsA2vc+gCOWdFBjUGOGRe+J7zU1SZ9zDLfkdAsX2No8h1s0/8Tw8G8u/IOri/7x1daEf4cTwxL/CqPPtbVGffSvLjFdYprEMkRk6pgZTfW107pLAU+UTrszPg5j4+MT7/GkkuvdXu4cdlGlcy5TRUHRDOfuFwMXQ7gl/5tvOqbCORIRqQyLqsV2/fBN3wBOKkMNGiqjB+hIk94VDSv1dCIiIpKDgqLKWE1KGyAzWwq0kL7NUMbpIpnaGomIiEieFBRVxvXAq82sLSntHCAG3JZjusVm9rJEgpktJ7Qnur4cGRUREZktFBRVxveAYeBqMzs1agx9IfCV5Nv0zWytmf0w8d3d7wRuAC4zszeY2ZnAFcAd6qNIRERkchQUVYC79wCnEFr5/Rb4L+CrwKdSRq1jz5aA5xBKk34EXAasBF5fzvyKiIjMBrr7rELc/VHg5BzjLEuT1gu8I3qJiIhIiaikSERERAQFRSIiIiIAmLu6PZ8tzKwfWFPpfJTRfGBrpTNRRlq/6jWT1w1m/vo9z93bco8m1U5timaXNe6+vNKZKBczW6H1q14zef1m8rrB7Fi/SudBpoaqz0RERERQUCQiIiICKCiabS6udAbKTOtX3Wby+s3kdQOtn8wQamgtIiIigkqKRERERAAFRSIiIiKAgqIZwcwON7ObzGzQzJ41s0+bWeoz09JNt9zMbjCz7dHrRjN78VTkuRBmdpCZfd/MHjSzuJndmud0HWb2YzPrMbMdZnaFmc0rc3YLUsy6mdkLo/VaG+3zNWb2KTNrmoIsF6TYfZc0fY2ZrTAzN7O/LVM2izaZ9Yse6nyvmcXMbJuZ/d7MWsuY3YJN4tyb9tcWMzvbzH5jZhvNbKeZrTSzN+UxXaOZfdnMtpjZgJn9zsyWlT/HMhUUFFU5M+sCbgQceB3waeD/ER4ym226pdF0dcDbolcd8Ecz26+ceS7CEcAZhI4nHytguquAk4DzgfOAFwLXlDhvk1XMup0DHAhcFE37beADwBXlyOAkFbvvEs4H9ilpjkqrqPUzs/OBK4HrgdMJ6/k406/vuILXr4quLR8AdgLvB/4OuAW40sz+Pcd03yBcTz4InEXouPKP0/FPiRTB3fWq4hfwUaAHaE9K+zAwmJyWZrp/AeJAR1JaV5T2rkqvV0pea5I+/xK4NY9pjicEiickpb0oSju10us0yXWbnybtgmjd9qv0Ok12/ZLG7wK6gXdG6/a3lV6fUu0/oB/4p0rnv0zrVxXXlgzn0ZXAU1mm2QcYA85NSlsCjADnV3qd9Jr8SyVF1e904A/u3peU9jOgGTgxy3T1hJN7ICltZ5Rmpc7kZLj7eBGTnQ5sdvfbk+ZzD/BUNGxaKGbd3D3d4xTuj973nlyOSqvIfZfwGeDPwE0lyk7JFbl+/xC9X1rKvJRDketXFdeWLOdRtnPoVdH71Unz2QjcwTS6rkjxFBRVv0OB1ckJ7v40oaTo0CzT/Soa58tmttDMFgJfJZQ6/aJMeZ1Ke2yXyCqyb5dqdTwwDjxR6YyUgpkdDfwjoYpipnkxoTrqnWa2wcxGzexuM3tppTNWItV8bTme7NWEhwIb3H1nSvpMva7MOgqKql8X0JsmvScalpa7Pwu8Avh7YHP0egPwanfvLkM+p1pR26Uamdli4BPAT9x9S6XzUyLfBL7l7msrnZEyWAw8j7DP/gN4LaFU5fdmtqiSGSuFar22mNkpwJnAl7OMNmuuK7OVgqJZysz2IvxrW0ko9j09+vw7M9u3knmT/JlZA6FBeaLBaNUzszcSgob/rnReysSAOcA73f0Kd/894cc4DvxbRXNWAtV4bYnuHrsS+LW7X1LRzEhFTbc7HaRwPUBHmvSuaFgmHyLU/Z/l7qMAZnYz4Q6YDwLvKXE+p1oPsCBNeq7tUjXMzIDLCHcI/Y27V/16mVk98EXCnXU1ZtYJtEeDW82szd37K5bB0ughNBy/NZHg7n1mthI4vFKZKqGquraY2VzCXYDrgbfkGL3Y661UCZUUVb/VpNRlR7fEtpC+TU3CocAjiYsWgLuPAI8Qbveudntsl0imtkbV6GuEbhhe5+4zZZ1aCXf4fIXwI9MDPBAN+xm7GpRXs1WE0qLURsdGaBdW7arm2mJmLcC1QAPh7sbBHJOsBpam6U9qJl1XZjUFRdXveuDVZtaWlHYOEANuyzLdeuDIqPoFCJ2SAUcC68qQz6l2PbDYzF6WSDCz5cAB0bCqZmYfJVS1vNXd76h0fkpoJ6E9SvIr0aHex8j9T74aXBu9vyKRYGYdwHHsCgCrWVVcW8ysjlDNdzBwWp7t8W6I3l+fNJ+9gZczA64rouqzmeB7hOLoq83sIsKP/oXAV5Jv0zeztcBt7v7OKOl/CR3G/Z+ZfYfwL/Vfgb2YZk+Ejv7NnRF9XQK0m9lZ0ffr3H0wdf3c/U4zuwG4zMw+SPgHfhFwh7vfOMWrkFEx62ZmbwY+C1wCbDSzlyTN8onp1Ji10PVz9zGSqpWieSyLPj7k7neXP9f5K/LYXGFmvwZ+aGYfAbYS+hYbJXTEOW0Us35Uz7XlO4R1ey8wz3bv7f5+dx82s5sA3P2U6H2Dmf0Q+FpUfd1NuN6uBy6fysxLmVS6oyS9Jv8itEO4mVA6tInQv0ttyjjrgEtS0k4Bbge2R6/bgJMqvT5p1m8ZoQ1GuteyLOvXCfyYcLdIH6Eh5R4dtlXbuhGCoUzTnFfpdSrFvsswj+nYeWOxx+Yc4LvAtui8vRE4qtLrU8L1m/bXlijfudbtVlI6rAQaCdW73YS7Bq8D9q/0+uhVmpdFO1lERERkVlObIhEREREUFImIiIgACopEREREAAVFIiIiIoCCIhERERFAQZGIiIgIoKBIREREBFBQJCIiIgIoKBKRKWTBX83s7SnpXzUzN7OH00zTaWbbo+EfmsSyvxU9okFEJC0FRSIylf4BmEt45Eqyo4B+4CAzq00Z9mHCU8wBHpzEsr8EvMXMDprEPERkBlNQJCJT6T3AT9x9NCX9KOA3hOdKHZBINLNF0TS/iZKKDorcfR1wB/CuYuchIjObgiIRycjMasxsp5m9z8y+YmZbzKwnUY1lZm8zs0ejca42s+Ys8zoIeCnwy5T0RcBC4FpCadGhSYM/DjxAeAr5VnffNMlV+hWhtEjXPhHZgy4MIpLNAUAr8D5gGHgz8DvgC2b2LeCNwIeAjwBnAu/IMq9TCE8VfyAl/ajo/UHgUeAwADPbF/hnQmB0NPDQ5FeHvwCLkpYpIjKhrtIZEJFpLRE8fMXdvwFgZo8DbyEEL6e6u0fpFwDPyzKv44BV7j6eZhnDwGPAI9F8AS4Ebnf3W83sMuDqya8OjwBx4EXsGZyJyCynoEhEsjka6AW+m5TWGr1/PhEQJaVvzzKvxcDWDMtY5e5jZvYIcLaZHQq8DfgbM+sEllKCkqJoGb1RXkREdqPqMxHJ5ijgjpSG0UcDY8DtiQQzawGWAXvcUp+kiVAilG4ZiYDnEUKbos8Av3P3e4Ajo2FpG1mb2VvN7MGobdM9ZvbKHOs0HOVFRGQ3KikSkWyOAq5KSXs+sNrdh1PGqyH73WHbSSmhiRo8Hw78PEp6GOgE3hAtB0IQNk4ImEiZ/q3AWcAJ7t5rZvsAV5lZzN3vyJCPTrKXaInILKWgSETSiu4kO4g9294cnSFtAHgiyyzXAMenpB0MNBOVFLn7RjO7CnjU3ROlTkcBT7j7YJp5vhc4GYiZ2X7uvj7qGPLrwBlp1mkB0EJovyQishtVn4lIJkcQrhH5BkWPpGlEnezPwL5RYJKQaMg90V7I3c9x9/9KGSdTCdS4u/cD+xCCLtz9cWBBhvGXA064C01EZDcKikQkk6NIKf0xsy5CAJIapBydJi3VrYRqq9NSltHj7huzTHdklnnXmNkcYBOhxAgzOxjozjD+acBt7r4tR15FZBay3W8eEREpHzP7OnCQu7+mRPN7K+HRIedGbYqWAr8APpjapih6fMh64CPufnkpli8iM4vaFInIVPoi8JiZHeLuk27X4+6Xm5kBfzazOmAn8NEMjazPBmLAzya7XBGZmVRSJCJTyszeCGxy99umeLlvAja6++05RxaRWUlBkYiIiAhqaC0iIiICKCgSERERARQUiYiIiAAKikREREQABUUiIiIigIIiEREREQD+P8ufjKq2PnS5AAAAAElFTkSuQmCC\n",
    474       "text/plain": [
    475        "<Figure size 432x288 with 1 Axes>"
    476       ]
    477      },
    478      "metadata": {},
    479      "output_type": "display_data"
    480     },
    481     {
    482      "data": {
    483       "image/png": 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\n",
    484       "text/plain": [
    485        "<Figure size 432x288 with 1 Axes>"
    486       ]
    487      },
    488      "metadata": {},
    489      "output_type": "display_data"
    490     }
    491    ],
    492    "source": [
    493     "postPredDist(models.twoGaussianList, models.uniformList, hyp1Posterior)"
    494    ]
    495   },
    496   {
    497    "cell_type": "markdown",
    498    "metadata": {},
    499    "source": [
    500     "## **Hypothesis 2 $Z_{ss}^{B}$** PPD"
    501    ]
    502   },
    503   {
    504    "cell_type": "code",
    505    "execution_count": 15,
    506    "metadata": {},
    507    "outputs": [
    508     {
    509      "data": {
    510       "image/png": 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\n",
    511       "text/plain": [
    512        "<Figure size 432x288 with 1 Axes>"
    513       ]
    514      },
    515      "metadata": {},
    516      "output_type": "display_data"
    517     },
    518     {
    519      "data": {
    520       "image/png": 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\n",
    521       "text/plain": [
    522        "<Figure size 432x288 with 1 Axes>"
    523       ]
    524      },
    525      "metadata": {},
    526      "output_type": "display_data"
    527     }
    528    ],
    529    "source": [
    530     "postPredDist(models.singleGaussianList, models.singleGaussianList, hyp2Posterior)"
    531    ]
    532   }
    533  ],
    534  "metadata": {
    535   "kernelspec": {
    536    "display_name": "Python 3",
    537    "language": "python",
    538    "name": "python3"
    539   },
    540   "language_info": {
    541    "codemirror_mode": {
    542     "name": "ipython",
    543     "version": 3
    544    },
    545    "file_extension": ".py",
    546    "mimetype": "text/x-python",
    547    "name": "python",
    548    "nbconvert_exporter": "python",
    549    "pygments_lexer": "ipython3",
    550    "version": "3.6.4"
    551   }
    552  },
    553  "nbformat": 4,
    554  "nbformat_minor": 2
    555 }