{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "866b8631", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "id": "01b45a9d", "metadata": {}, "source": [ "Let's combine what we have learned about monto carlo methods with markov chain processes. The following is a classic MCMC use on data.\n", "\n", "https://astro-330.github.io/Lab4/Lab4_solutions.html" ] }, { "cell_type": "code", "execution_count": 11, "id": "ef2fe684", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from astropy.io import fits, ascii\n", "\n", "# LOAD DATA FROM HOGG et al 2010, Table 1\n", "data = ascii.read('data/hogg_2010_data.csv',format='csv')\n", "\n", "# SKIP THE FIRST FEW DATA POINTS\n", "m=data['ID'] > 4\n", "data=data[m]\n", "print(data.columns)\n", "\n", "plt.errorbar(data['x'],data['y'],yerr = data['sigma_y'],fmt='.',label='Data',ms=15);\n" ] }, { "cell_type": "markdown", "id": "24501a59", "metadata": {}, "source": [ "If you are using np.polyfit, set the cov='unscaled' keyword in polyfit to have it return not only the fit coefficients, but also the full covariance matrix. The parameter uncertainties, assuming no off-axis covariance, are the square roots of the diagonal terms (of which for a linear fit there will be 2. You can pull the diagonal terms of a square array using ```np.diag()```." ] }, { "cell_type": "code", "execution_count": 13, "id": "2d655c34", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Best fit slope: 2.24 +/- 0.11 \n", "Best fit intercept: 34.0 +/- 18.2 \n" ] } ], "source": [ "p,pcov = np.polyfit(data['x'],data['y'],1,w=1./data['sigma_y'],cov='unscaled')\n", "perr = np.sqrt(np.diag(pcov))\n", "\n", "print('Best fit slope: {:0.2f} +/- {:0.2f} '.format(p[0],perr[0]))\n", "print('Best fit intercept: {:0.1f} +/- {:0.1f} '.format(p[1],perr[1]))\n" ] }, { "cell_type": "markdown", "id": "097a4441", "metadata": {}, "source": [ "Now, let’s plot the results. I will use the coefficients of the fit to create an object called pfit from which I can generate the best-fitting line. Since this is a linear fit, this is overkill, but leaves open the option of using polynomicals." ] }, { "cell_type": "code", "execution_count": 15, "id": "b51802bf", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig,ax = plt.subplots(figsize=(10,8))\n", "plt.rcParams.update({'font.size': 16})\n", "plt.errorbar(data['x'],data['y'],yerr = data['sigma_y'],fmt='.',label='Data',ms=15)\n", "pfit = np.poly1d(p)\n", "x=np.arange(0,300)\n", "plt.plot(x,pfit(x),label='Fit using np.polyfit')\n", "plt.xlabel('x')\n", "plt.ylabel('y')\n", "plt.legend();\n", "plt.text(150,100,'Best fit m: {:0.2f} +/- {:0.2f} '.format(p[0],perr[0]))\n", "plt.text(150,50,'Best fit b: {:0.1f} +/- {:0.1f} '.format(p[1],perr[1]));" ] }, { "cell_type": "markdown", "id": "33b2e894", "metadata": {}, "source": [ "Another way to turn np.polyfit fit (coefficient arrays) into actual curves is via np.polyval, which takes in the p above along with the array of values where you want to evaluate the polynomial.\n", "\n", "Repeat the question above, however, this time write your own script to solve this problem by evaluating $\\chi^2$ on a grid of m and b values. You should write a chi2() function that reads in 4 arguments m,b,data_x,data_y,unc_y (though you can call them what you want). You should then write a fit_line() or minimize_chi2() function that will, across your grid of 𝑚 and 𝑏 values, evaluate $\\chi^2$ using your chi2() function. You may use the values above to guide your grid, making sure the grid spans at least 2-sigma in both directions.\n", "\n", "Plot the $\\chi^2$ values for all grid points. We suggest creating an array, chi2_image, which is a shape characterized by the lengthd of your m_grid and b_grids. Then, as you double-for-loop over m and b values and calculate $\\chi^2$, you can set chi2_image[i,j] to the output $\\chi^2$ value.\n", "\n", "Tip: Remember, 𝑚 and 𝑏 values won’t index your array directly. So you’ll want to loop via something like for i,m in enumerate(m_grid): and for j,b in enumerate(b_grid): if you’re going to do that.\n", "\n", "While $\\chi^2$ fitting is reliable for determining the best-fit values, it is not always easy to estimate errors on these parameters. For example, in the above example, we had to explicitly initialize a grid of parameters to fit on, and as soon as this grid has to get finely spaced, or moves into any number of dimensions > 2, everything gets much more computationally expensive to calculate, and understanding the chi-squared “surface” in multi-D becomes difficult. Additionally, we had to narrow in our range of 𝑚 and 𝑏 values to get it to work, but there may actually be a better solution elsewhere in parameter space that we’re not accessing." ] }, { "cell_type": "code", "execution_count": 18, "id": "0fcd2995", "metadata": {}, "outputs": [], "source": [ "def calc_chi2(m, b ,x ,y, yerr):\n", " '''\n", " Calculate chi2 value for a linear model.\n", " \n", " Parameters\n", " ----------\n", " m: float\n", " slope of the line\n", " b: float\n", " y-intercept of the line\n", " x, y: float\n", " data points to be fit\n", " yerr: float\n", " one sigma errors on the y-values\n", " Returns\n", " -------\n", " chi2 \n", " The value of chi2 \n", " '''\n", " \n", " f = m*x + b\n", " chi2 = np.sum((y - f)**2/yerr**2)\n", " \n", " return chi2\n" ] }, { "cell_type": "markdown", "id": "c0890822", "metadata": {}, "source": [ "Next we need to set-up a grid of parameters to search through. With two free parameters (m and b), this isn’t too difficult, but quickly gets complicated with more parameters." ] }, { "cell_type": "code", "execution_count": 19, "id": "e3ebebcd", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Best fit slope: 2.24 \n", "Best fit intercept: 34.0 \n", "Minimum chi2: 18.7 \n" ] } ], "source": [ "m_grid = np.arange(1.8,2.7,0.01)\n", "b_grid = 1.*np.arange(-20,80,1)\n", "\n", "m_arr,b_arr,chi2 = [],[],[]\n", "chi2_min = 1e8 \n", "m_min, b_min = 0,0\n", "\n", "image = np.zeros(shape=(len(m_grid),len(b_grid)))\n", "chi2 = []\n", "for i,m in enumerate(m_grid):\n", " for j,b in enumerate(b_grid):\n", " \n", " c = calc_chi2(m,b,data['x'],data['y'],data['sigma_y'])\n", " \n", " chi2.append(c)\n", " m_arr.append(m)\n", " b_arr.append(b)\n", " image[i,j] = c\n", " if c < chi2_min:\n", " chi2_min = c\n", " m_min = m\n", " b_min = b\n", " \n", "chi2 = np.array(chi2)\n", "b_arr = np.array(b_arr)\n", "m_arr = np.array(m_arr)\n", "\n", "print('Best fit slope: {:0.2f} '.format(m_min))\n", "print('Best fit intercept: {:0.1f} '.format(b_min))\n", "print('Minimum chi2: {:0.1f} '.format(chi2_min))" ] }, { "cell_type": "markdown", "id": "9755c18f", "metadata": {}, "source": [ "In the above, we store the output 𝜒2\n", " values in two ways: in an array (chi2), and and in an “image” array in 2D at each m,b position. See how to plot the results from these two methods of storing the 𝜒2\n", " values below." ] }, { "cell_type": "code", "execution_count": 20, "id": "f13a2f56", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# using imshow on the 2D grid. This version makes contouring easier. \n", "\n", "extent = [np.min(m_grid),np.max(m_grid),np.min(b_grid),np.max(b_grid)]\n", "\n", "fig, ax = plt.subplots(figsize=(12,10))\n", "im = ax.imshow(image,origin='lower',extent=extent,vmin=18,vmax=25,aspect=0.01)\n", "cb = plt.colorbar(im,ax=ax,shrink=0.945,label = '$\\chi^2$')\n", "ax.set_xlabel('slope (m)')\n", "ax.set_ylabel('intercept (b)')\n", "ax.contour(image,levels=[chi2_min+1,chi2_min+2.3,chi2_min+6.17],colors='k',extent=extent);" ] }, { "cell_type": "markdown", "id": "16413e83", "metadata": {}, "source": [ "Now determine the best fit parameters and one-sigma errors. The best-fit value can either be the minimum $\\chi^2$ value or (bonus) by fitting a function to your $\\chi^2$ values and interpolating the best fit.\n", "\n", "You can determine the 1-sigma errors on your best-fit parameters by noting where chi2 = chi2 + 1" ] }, { "cell_type": "code", "execution_count": 21, "id": "5e321f97", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Best fit slope: 2.24 +/- 0.10 \n", "Best fit intercept: 34.0 +/- 18.0 \n" ] } ], "source": [ "msk = chi2 < (np.min(chi2) + 1.)\n", "\n", "m_err = (np.max(m_arr[msk]) - np.min(m_arr[msk]))/2.\n", "b_err = (np.max(b_arr[msk]) - np.min(b_arr[msk]))/2.\n", "\n", "print('Best fit slope: {:0.2f} +/- {:0.2f} '.format(m_min,m_err))\n", "print('Best fit intercept: {:0.1f} +/- {:0.1f} '.format(b_min,b_err))" ] }, { "cell_type": "markdown", "id": "76efa744", "metadata": {}, "source": [ "#### MCMC Fitting\n", "\n", "While $\\chi^2$ is a good method for determining best-fitting values, it less reliable in determining errors on those parameters. If your science question requires good error estimates and/or if your model contains more than a few parameters, Monte Carlo (MCMC) is a popular tool.\n", "\n", "https://ui.adsabs.harvard.edu/abs/2018ApJS..236…11H/abstract\n", "\n", "You will need to install two packages for this to work:" ] }, { "cell_type": "code", "execution_count": 22, "id": "76decb14", "metadata": {}, "outputs": [], "source": [ "import emcee\n", "import corner" ] }, { "cell_type": "markdown", "id": "8200c75e-9e13-4b43-a60d-4562c5461e51", "metadata": {}, "source": [ "Look up (or choose) definitions for the mean, variance, skewness,and kurtosis of a distribution. Also lookup or compute the analytic values of these four statistics for a top-hat (uniform) distribution. Write a computer program that uses some standard package (such as numpy) to generate K random numbers $x$ from a uniform distribution in the interval 0 < x < 1. Now use those K numbers to compute a sampling estimate of the mean, variance, skewness, and kurtosis (four estimates; lookup definitions as needed). Make four plots of these four estimates as a function of 1/K for K = 4$^n$ for n=1 up to n=10 (that is, K=4, K=16, and so up to K=1,048,576)." ] }, { "cell_type": "code", "execution_count": 24, "id": "3dc880a4", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sample_mean = []\n", "sample_var = []\n", "\n", "# INCREASE NUMBER OF SAMPLES IN EACH LOOP\n", "for i in range(10):\n", " K=4**i\n", " \n", " # random samples from a uniform distribution between 0-1\n", " x = np.random.rand(K) \n", " \n", " mean = (1./K) * np.sum(x) # DEF OF SAMPLE MEAN\n", " var = (1./K) * np.sum((x-mean)**2) # DEF OF SAMPLE VARIANCE\n", "\n", " sample_mean.append(mean)\n", " sample_var.append(var)\n", "\n", " \n", "# PLOT RESULTS ON SAME PLOT\n", "fig,ax = plt.subplots(figsize=(8,6))\n", "plt.rcParams.update({'font.size': 14})\n", "\n", "ax.plot(np.arange(10),sample_mean,'ro',label='Sampled Mean')\n", "ax.set_title('Question 4, Hogg 1')\n", "plt.axhline(y=0.5,color='r',label='True Mean')\n", "\n", "ax.plot(np.arange(10),sample_var,'bo',label='Sampled Variance')\n", "ax.set_xlabel('Number of samples 4**K')\n", "ax.axhline(y=0.1,color='b',label='True Variance')\n", "\n", "#ax.set_scale('log')\n", "ax.legend();" ] }, { "cell_type": "markdown", "id": "d37e54b4-3a4a-4763-b6c7-6f4b5a82344f", "metadata": {}, "source": [ "Write a very simple M–HMCMC sampler. Sample in a single parameter x and give the sampler as its density function p(x) a Gaussian density wit hmean 2 and variance 2. (Note that variance is the square of the standard deviation.) Make the proposal distribution q(x) a Gaussian pdf for a mean x and variancea of 1. Initialize the sampler with x=0 and run the sampler for more than $10^4$ steps. Plot the results as a histogram, with the true density over plotted sensibly." ] }, { "cell_type": "code", "execution_count": 25, "id": "5836fc29", "metadata": {}, "outputs": [ { "data": { "image/png": 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4Jq18iNg0ZQr062feNYvvi4qC++/XyHWRS1DxIWLL99/DBx/AI4/YTiKuNGyYmflx7JjtJCJeS8WHiC0vvAAPPABlythOIq5UvTrUrKmR6yIXoeJDxIYjR2DRIvMuWfzP8OHw0kuQnm47iYhXUsOpiA1xcVC3rjmU7B+0jdYPNGsG4eGwfDl07247jYjX0cqHiKedOgUvv6xVD38WFGT+fadO1dAxkfNQ8SHiaStWQKlS0Lix7STiTl27wqFD8PHHtpOIeB0VHyKe5HTCiy/CwIHmQDLxX5ddZrZRT59uO4mI11HPh4gnff65GSrWrZvtJOIJ/frBDTeYf/MbbrCdRsRraOVDxJOmT4devaBoUdtJxBOuuQZatzY9PiKSTcWHiKccOADvvAMPP2w7iXjSoEEwbx6cPGk7iYjXUPEh4ilxcWYL5vXX204inlSrljnvZfFi20lEvIaKDxFPSEuD2bPNu2AJLA6H+Xd/6SVtuxX5i4oPEU9YtgyuugoaNLCdRGzo0MFMtdW2WxFAxYeI+zmdptF00CBtrw1UYWHQt6+23Yr8RVttRdzts89g3z7o0sV2ErGpf39tuxX5i1Y+RNxt+nTo3RuKFLGdRGy65hpo1UrbbkVQ8SHiXvv2werVMGCA7STiDbTtVgRQ8SHiXjNnQosWULas7STiDe64w1xy0bZbCXAqPkTcJT0d5s7VUDH5f9p2KwKo+BBxnzffhMsvh4YNbScRb/LAA/D777Bhg+0kItao+BBxl7g4s8NB22vl78LC4KGHzCU5kQClrbYi7pCQYG7x8dl3lYuNv+DTJcD07QsVK8KhQ1CmjO00Ih6nlQ8Rd5g5Ezp1gpIlbScRb1S+vLkcN3eu7SQiVqj4EHG1pCRYssRcchG5kAEDzHk/p0/bTiLicSo+RFxt0SKoUgVuucV2EvFmzZtDoUJmDoxIgFHPh4grOZ2m0XTUKNtJxIud7f8ZUK4+tw97mm5bCp/znD0TW3g6lojHaOVDxJU2bDCnl7ZvbzuJ+IDXq9xNzf07KXfsoO0oIh6l4kPEleLioGdPs51S5BKOFo3g/RvvoHPCe7ajiHiUig8RVzl0CFatMtsoRXJpcfXmtN/5EWGZp2xHEfEYFR8irjJnDtx1l45LlzzZGnUzh4tdzj27PrMdRcRjVHyIuEJmptk2qdNrJa8cDpZUb07nhLW2k4h4jIoPEVdYtQpCQqBZM9tJxAe9c3MDov84QOVff7QdRcQjVHyIuMLMmdCvn5nbIJJHJ0OL8PbNDejyjVY/JDCo+BApqB9+gE2bzGFhIvm0pHpz7t21kRKnTtqOIuJ2Kj5ECmr2bGjTBkqXtp1EfNgPV5Rj51XlabfzY9tRRNxOxYdIQZw6BQsXanutuER246nTaTuKiFup+BApiLffhssvh7p1bScRP7DuxtpEpJ3g9v07bUcRcSud7SJSELNnQ+/e4HDYTiJ+ICM4hDcr3UXHhPcpF1vlks/X+S/iq7TyIZJfu3fD559D9+62k4gfWV61CU13f05EapLtKCJuo+JDJL/mzIHWreGKK2wnET/y8+VRfH3NTWo8Fb+myy4i+ZGeDgsWwIoVtpOIFykXG++Sr7OsalOGbHqNObe11iU98Uta+RDJj3fegZIloX59y0HEH6278Q5KnjpJrX1qPBX/pOJDJD/ONpoG6UdIXC+78XT7OttRRNxCvzlF8urHH81E0wcftJ1E/Niyak1psvtzItV4Kn5IxYdIXs2dC/fdp4mm4la/RF7D19dUoK0aT8UPqfgQyYuMDJg/H/r0sZ1EAsDSqk3NpRdNPBU/o+JDJC/efReKF4eGDW0nkQDw/o13EH7qJLX27bAdRcSlVHyI5IUaTcWDMoJDeLNyIzolqPFU/It+g4rk1k8/waefqtFUPGp51SY0/vELLk/503YUEZdR8SGSW3Pnwr33wlVX2U4iAeSXyGvYdk1F2n6rxlPxHyo+RHIjIwNefVWNpmLFsqpN6Lh9HQ5nlu0oIi6h4kMkN1avhiJFoFEj20kkAL1/4x2UOJXC7Zp4Kn4i18XHkSNHaNmyJcWLF6dGjRps3749+7HU1FR69+7NoEGD6NKlC3v37s3xuVu2bKFjx44MGDCAUaNG4dS2MfE1ajQVi842nnZW46n4iVz/Jn322WcZNGgQq1atIjU1lS5dumQ/1q1bN+68806mT5/OyJEjueeee8jMzATg4MGDdOzYkbi4OOLi4sjIyGDSpEmufyUi7vLLL7B+PfToYTuJBLDlVZtwtxpPxU/kqvg4deoUw4cPp3HjxjRo0IBx48axf/9+ALZt20Z8fDwdOnQAoHLlyjgcDpYtWwbAxIkTqVevHhEREQB07tyZ8ePHk5KS4o7XI+J6c+dCy5Zw9dW2k0gAO9t42u7bj2xHESmw4Nw8KSwsjKioqOyPMzMz6d+/PwCrVq0iOjqa0NDQ7MerVq3K6tWr6datG6tWrWLQoEHZj1WuXJnU1FQ2bNhAixYtXPU6RNwjM9M0ms6ff9GnueoodZGLWVqtKSM2Lmb2bW1wOnQJUHxXroqPvztw4ABLlizh9ddfByAxMZFSpUrleE5ERATbt28nJSWFffv25Xg8ODiYYsWKsXv37vMWHxUqVMDhcAAwbNgwhg0blteIIq6zZg0HUrOo+0kGWRtUYIhdH/yrFuM+nMUde3ewuVw123FE8i1PxUdCQgKjR4/mvffeo0GDBmzatImkpCQiIyNzPC80NJTU1FSSksxpjBd6/Hx27dpFiRIl8hJLxH1mz2Z51cZkBRWynUSEjOAQ3qjciI7b31fxIT4tT+t21apVY82aNaxcuZJt27bx1ltvERkZSXp6eo7npaWlERERkV10XOhxEa+2dy98/DFvVNb2WvEeK9R4Kn4gXxcNW7duTb169Th06BDly5fn6NGjOR4/cuQIMTExhIWFUaZMmRyPp6WlcfLkSWJiYgqWXMTd5s2D5s35rXipSz9XxEM08VT8Qb47lkqWLEmVKlVo164dO3bsyLG6kZiYmN3P0a5dO7Zu3Zr92K5duwgPD6d27doFiC3iZqdPm+JDE03FC52deIpmJomPylXxkZyczMKFC0lOTgZgx44dZGRk0LhxY6pXr06dOnVYt84Mv0lISCAoKIj27dsDMHDgQNavX8+pU6cAWLx4MaNHjyYsLMwdr0fENdauhUKFoEkT20lEzvH+jXcQfioFNmywHUUkX3LVcPrbb7/x1FNP8eijj1K/fn3Kly/P8uXLsx9funQpQ4cOZfPmzRw9epS1a9dSqJBp0IuOjiYuLo5evXoRGRlJ6dKlGTFihHtejYirzJ4NvXqZAkTEy2QEh/BmpbvoM3s2NGhgO45InjmcXjLrPDk5mfDwcJKSkrTbRezatw+io+HnnyEqSjM8xCvd8McBPlk0CA4cgCuusB1HAlh+/n5rSo3IP736KjRtCn8brCfibX6+PApq1YJFi2xHEckzFR8if6dGU/ElffqYS4TesYAtkmsqPkT+7q/GaZo2tZtDJDfatIGjR2HjRttJRPJExYfI382eDT17QnCeTx4Q8bywMOje3fx3K+JDVHyInHXggFn5eOgh20lEcq93b3jrLfjjD9tJRHJNxYfIWa++Co0bw3XX2U4iknsVKsBtt6nxVHyKig8RgDNnYO5cNZqKb1LjqfgYFR8iAO+/bwqQ5s1tJxHJu7Zt4bffYNMm20lEckXFhwio0VR822WXQbduajwVn6HiQ+TgQXOWS8+etpOI5F/v3vDGG2o8FZ+g4kNk/nxo1AjKlrWdRCT/br4ZatSAxYttJxG5JBUfEtjUaCr+RI2n4iNUfEhg+/BDyMiAFi1sJxEpuPbt4ddfYfNm20lELkrFhwS22bPNULGQENtJRApOjafiI1R8SOD69VdYs0aNpuJfzjaeHjtmO4nIBan4kMA1fz40bAjXX287iYjrVKoEt9wCS5bYTiJyQSo+JDBlZZlG0969bScRcT01noqXU/EhgemjjyA1Fe6913YSEddr394clPjFF7aTiJyXig8JTK+8okZT8V9FikDXrmo8Fa+l4kMCz6+/wurV0KuX7SQi7tOnD7z+Ohw/bjuJyDlUfEjgWbAAGjSAG26wnUTEfSpXhqpV4bXXbCcROYeKDwksWVkwZ44mmkpgUOOpeCkVHxJY1GgqgeT++2HvXtiyxXYSkRxUfEhg0URTCSRFi0KXLmo8Fa+j4kMCx+HDajSVwNOnDyxfDklJtpOIZFPxIYFj/nyoV0+NphJYqlY1zadqPBUvouJDAoMaTSWQ9eljZtuo8VS8hIoPCQxnG03vu892EhHP69ABfvkFtm61nUQEUPEhgWL2bOjRQ42mEpiKFYPOndV4Kl5DxYf4PzWaiphLL8uWQXKy7SQiKj4kAJxtNC1f3nYSEXuqV4eKFWHpUttJRFR8iJ9To6nI/1PjqXiJYNsBRNzq448hJUUTTcUvlYuNz9Xz9kxsYf7HAw/AsGGwbRvUqOHGZCIXp5UP8W+vvGImmhYubDuJiH3Fi0OnTmo8FetUfIj/OnwYVq1So6nI3/XpY/o+TpywnUQCmIoP8V8LFqjRVOSf/v1viIkxO19ELFHxIf7pbKNp3762k4h4nz59dOlFrFLxIf7p44/h5Ek1moqcT8eO8P33pvFUxAIVH+Kfzk40VaOpyLlKlDAFyJw5tpNIgNJWW/E/ZxtNExMv+rTcblMU8Ut9+kDDhjB5shm/LuJBWvkQ/7NgAdStq0ZTkYupUQOio2H5cttJJACp+BD/kpVlLrlooqnIxTkcajwVa1R8iH95/31IS4NWrWwnEfF+nTrBd9/BN9/YTiIBRsWH+JeZM81QsZAQ20lEvF94uBm5rsZT8TAVH+I/9u2Ddet0yUUkL/r0gSVLzBlIIh6i4kP8x+zZ0Lw5XHut7SQivuO22+D669V4Kh6l4kP8Q0YGzJ0L/fvbTiLiWxwO6NcPZs2ynUQCiIoP8Q9vv21mFdx9t+0kIr6nSxcz8XTrVttJJECo+BD/MHOmOcclSP9Ji+RZ8eLQrRvExdlOIgFCv6nF9yUmwpYtZpy6iORP//6m7+OPP2wnkQCg8eric/45Fn3sR69Qonwthk/ekn3fnoktPB1LxGvl5iiBPRNbmObTBQtg+HD3h5KAppUP8WmXZZyi7c6Pea16c9tRRHzfgAHmEmZWlu0k4udUfIhPuy9xAwdKXsnXZW6yHUXE97VuDSdPwocf2k4ifk6XXcR3OZ10SXiPxdVbmO2Cf6MTa0XyoXBh6N3bNJ42aWI7jfgxFR/is6r9upuyxw/xbsV6tqOI+I8+fcxpt3v3QtmyttOIn9JlF/FZXb5Zy8pKDUktfJntKCL+49proUULeOUV20nEj6n4EJ9UMi2Zlt9/xpJqajQVcbkBA8zE4PR020nET6n4EJ/UbudHbL/6Rn68QsvCIi7XsCFERMBbb9lOIn5KxYf4HIczi84J77GkWjPbUUT8U1CQGTqmiafiJio+xOfU2ZNAsfQ01sXcYTuKiP/q3h2+/hq2b7edRPyQig/xOd23rWZZ1SZkFgqxHUXEf0VEQKdOZuiYiIup+BDf8vPP3LnnG16rrksuIm43YAAsWQJJSbaTiJ9R8SG+JS6OD/9Vi9+Kl7KdRMT/3XILVKoEixfbTiJ+RsWH+I6UFJg3j4W36NA4EY95+GHTeOp02k4ifkTFh/iO116DsmXZGnWz7SQigaN9ezhyBD75xHYS8SMqPsQ3OJ3w0kswcOA557iIiBuFhUHfvjB9uu0k4kdUfIhv+PRTOHTIdN+LiGf17w/r1sHPP9tOIn4iV8XH3r17adKkCcWLF6d69eqsX78++7HU1FR69+7NoEGD6NKlC3v37s3xuVu2bKFjx44MGDCAUaNG4dR1Q8mPGTOgVy+4TOe4iHjcNddA69bw8su2k4ifuGTx4XQ66d27N40aNSIuLg6n00nLli356aefAOjWrRt33nkn06dPZ+TIkdxzzz1kZmYCcPDgQTp27EhcXBxxcXFkZGQwadIk974i8T/798Pq1ebdl4jYMWgQzJsHJ0/aTiJ+4JLFx7fffsvIkSN59NFH6dq1Kx988AEOh4M1a9awbds24uPj6dChAwCVK1fG4XCwbNkyACZOnEi9evWIiIgAoHPnzowfP56UlBQ3viTxOzNnQrNmUK6c7SQigatWLYiO1rZbcYlLFh8xMTHcdddd2R+XLl2aihUrEhoayqpVq4iOjiY0NDT78apVq7J69WoAVq1aRaVKlbIfq1y5MqmpqWzYsMGFL0H82qlTMGeOaTQVEXscDrP6MX26tt1KgV2y+ChcuPA59x0/fpyWLVuSmJhIqVI5hz1FRESwe/duUlJS2LdvX47Hg4ODKVasGLt3777g96tQoQJRUVFERUUxderUvLwW8UfLl0Pp0uaUTRGxq0MHOHYMPvrIdhLxccF5/YSNGzfSpk0boqKiSEpKIjIyMsfjoaGhpKamkvTXON4LPX4hu3btokSJEnmNJf7o7PbaRx7R9loRbxAa+v/bbu++23Ya8WF5Kj4yMzNZtmwZ06ZNA0xhcfIfzUdpaWlERERkFx3p6ennfVzkkr78Ev73P+ja1XYSETmrXz+4/nrzsxkdbTuN+Kg8zfmYMmUKo0aNyu7xKF++PEePHs3xnCNHjhATE0NYWBhlypTJ8XhaWhonT54kJibGBdHF702bBg89BMWK2U4iImeVKQNt22rbrRRIrouPuXPn0rRpU6699lrArGi0adOGHTt25FjdSExMpEULc/ZGu3bt2Lp1a/Zju3btIjw8nNq1a7sqv/irffvgnXdMg5uIeJdBg+DVV+HECdtJxEfl6rJLXFwcBw4cICoqinXr1pGamsrbb7/NwoULqVOnDuvWreO+++4jISGBoKAg2rdvD8DAgQNp3Lgxp06dIiwsjMWLFzN69GjCwsLc+qLED8yYAS1bmuVdEXG7crHxl3zOnol/HepYsybExMCiRebgOZE8umTx8eqrr/LwX/9xTZgwIfv+gQMHEhQUxNKlSxk6dCibN2/m6NGjrF27lkKFCgEQHR1NXFwcvXr1IjIyktKlSzNixAg3vRTxGydPwuzZsGaN7SQicj5nt90+84wZ/hekkzokbxxOL5l3npycTHh4OElJSdrtEuhmzICFC+Grr867yyU379BExPWyVz4A0tOhbFmYP98MAZSAlZ+/3ypXxbtkZcGLL8KQIdpeK+LNQkPNNnjNY5J8UPEh3mXNGkhNhb/6hkTEi/XrB5s3w/bttpOIj1HxId7lhRfMu6nzTNYVES9TqhR062Z+bkXyQMWHeI+EBNPn0bev7SQikltDh5pjEH791XYS8SEqPsR7TJtm3kX9YyS/iHixmBgzan3GDNtJxIeo+BDvcPiwefc0ZIjtJCKSV8OHw6xZkJJiO4n4CBUf4h3i4uCuu8y7KBHxLfXqmW23CxfaTiI+QsWH2JeWBjNnatVDxFc5HDBsmGk8zcqynUZ8gIoPsW/hQnNYVaNGtpOISH7df795I7F6te0k4gNUfIhdZ87A5Mnw2GMaKibiywoXhoEDNXRMckXFh9j19tuQkWHeNYmIb+vTB7Ztg//+13YS8XIqPsQepxOee85cKw4JsZ1GRAoqIgIeegimTLGdRLzcJU+1FXGbjRvhf/+DXr1sJxERVxkyBCpUgF9+geuvt51GvJSKD7HnuefMcdzFigE6rVbEL9xwA7Rta1Y/NHhMLkCXXcSOb7+FTz4xDWoi4l8eewxefRV+/912EvFSKj7EjsmTzSj1q66ynUREXK1aNTN47KWXbCcRL6XiQzzvwAEzSn34cNtJRMRdRo40l11OnLCdRLyQig/xvGnToHlzuPFG20lExF3q1TM/43Pm2E4iXkjFh3jWn3/CK6+Ya8Ii4r8cDoiNNUPHMjJspxEvo+JDPGvWLHM9+PbbbScREXe77z6zm+2112wnES+j4kM8Jy3NHDwVG2s7iYh4QlCQWeWcNEkHzkkOKj7Ec+bONQfINW9uO4mIeErnzqbpdNUq20nEi2jImHjEvx59h09f+Q/PNOzF2sfX2o4jIp4SGmqOUJg40VyG0QGSglY+xENaf7uetJAw1t1Yy3YUEfG0Pn3ghx/g009tJxEvoeJD3O/0afpveYO429uTFVTIdhoR8bTixc0042eesZ1EvISKD3G/N94gOCuLdyvWs51ERGwZMgS2bIEvvrCdRLyAw+l0Om2HAEhOTiY8PJykpCRKlChhO464SlYWVK3K6DJ1WVJdjaYi/m7PxBYXfjA2FnbsgLXq+/In+fn7rZUPca/Vq+GPP3ijciPbSUTEtmHDTN/H1q22k4hlKj7EfZxOGD8eRowgPbiw7TQiYlvp0tCvn3o/RMWHuNFHH8HPP0PfvraTiIi3GDECPvwQtm+3nUQsUvEh7uF0wrhxpsmsaFHbaUTEW1x9NfTsqdWPAKchY+IeH30Eu3apsUxEzjVyJERHw3ffwc03204jFmjlQ1zP6YSxY2H4cNDOJRH5p6goePBB0xMmAUkrH+J6H3wAu3eboUIiIucTGws33WQmn8bE2E4jHqaVD3Gts6seI0aYqYYiIudTrhx06QL/+Y/tJGKBig9xrXXr4Kef4JFHbCcREW83ZgysXGl6PySgqPgQ1zm76vHoo1CsmO00IuLtypaFhx4yvzckoKj4ENdZuxb27IGHH7adRER8xRNPmN8d33xjO4l4kIoPcQ2nE556Ch57THM9RCT3ypSB/v3hySdtJxEPUvEhrrFmDezbZ36JiIjkxciRsH69OfVWAoKKDym4rCwYPRoef1yrHiKSd6VLw6BBpgFVAoKKDym45cvhzz/NgVEiIvkxYoRZ+di40XYS8QAVH1IwGRnm3cq4cRAWZjuNiPiqyEgYNsz8PnE6bacRN1PxIQUzdy6EhkLXrraTiIivGzIEvv3WnHorfk3Fh+RfSoqZTjh+PBQqZDuNiPi68HDTOxYba3rJxG/pbBfJvxdfNEOCWrWynUREvES52PhcPW/PxBbnf+CRR+Cll0wvWadOLkwm3kQrH5I/x47Bc8/BxIngcNhOIyL+IiwMnn7aDB9LT7edRtxExYfkz6RJULMmNGhgO4mI+JvOnc3BlDNn2k4ibqLiQ/Lu4EGzLPrss7aTiIg/KlTIvMF55hlISrKdRtxAxYfk3dix0LIl/PvftpOIiL9q2hQqVzaXd8XvqOFU8mbHDnjtNbMd7i+5bTATEck1h8MUHvXrw4ABcM01thOJC2nlQ3LP6YThw82pteXL204jIv7u1lvNKuu4cbaTiIup+JDce+89+Ppr04UuIuIJ48fD4sWQmGg7ibiQig/JndOnzdkLY8dCRITtNCISKKKjoW9fM3pdY9f9hooPyZ25c00BosPjRMTTnnwStm6FtWttJxEXUfEhl5acbH74n38eChe2nUZEAk1kpDnKYdgwc5il+DwVH3JpEydCxYpw7722k4hIoOrbF0JC4OWXbScRF9BWW7m4n36CadPgs880Rl1E7AkOhhdegPbtoUsXuOIK24mkABxOp3d08CQnJxMeHk5SUhIlSpSwHUfOuu8+uPJKmD37gk/RnA8RcYfzHj53771m5odGr3uN/Pz91sqHXNi6dbBxI+zebTuJiIgxZQpUqWIGj1WubDuN5JN6PuT8MjJg8GBzuqSWN0XEW/zrX6bwGDpUW299mIoPOb9p0yA0VFtrRcT7jBljjnpYudJ2EsknFR9yrkOHzIrHSy+ZJi8REW9SsqQ592XIEDh50nYayQcVH3Kuxx4z5ynUq2c7iYjI+XXrBuXKmfkf4nP0tlZy2rgR3nkHdu2ynURE5MKCgiAuDmrWhO7d4eabbSeSPNDKh/y/jAzT4/HUU3DttbbTiIhcXOXKpvl0wAA1n/qYPK18HD16lEmTJpGSkkJcXFz2/ampqQwePJjLLruMY8eOMX78eMqWLZv9+JYtW5g2bRoRERGULFmS8ePH49DAKu9zdnz64MG2k4iI5M7YsXDTTfDaa2b4mPiEXK98ZGZmsmnTJt59911SU1NzPNatWzfuvPNOpk+fzsiRI7nnnnvIzMwE4ODBg3Ts2JG4uDji4uLIyMhg0qRJrn0VUnD/+x88+yy88ooZYSwi4guKFze784YPhz//tJ1GcinXxUdISAitWrXi1ltvzXH/tm3biI+Pp0OHDgBUrlwZh8PBsmXLAJg4cSL16tUj4q9j2Dt37sz48eNJSUlx1WuQgnI6zbLlgw+a66ciIr6kXTuoVg0ef9x2EsmlPPd8hPzjXfGqVauIjo4mNDQ0+76qVauyevXq7McrVaqU/VjlypVJTU1lw4YN+YwsLrdsGezcaVY+RER8jcNhxq0vXmzOoRKvV+CG08TEREqVKpXjvoiICHbv3k1KSgr79u3L8XhwcDDFihVj9wVGdleoUIGoqCiioqKYOnVqQePJpRw/biYFvvgihIfbTiMikj833ADjxkGvXnDqlO00cgkF3mqblJREZGRkjvtCQ0NJTU0lKSkJ4IKPn8+uXbt0sJwHnD0MbuJ707my2LX02FYEvj73gLjzHuwkIuKNBg+G5cvNkMTx422nkYso8MpHZGQk6enpOe5LS0sjIiIiu+i40ONi152/fE2L7z/jiSYPm2VLERFfFhwM8+bBCy/A9u2208hFFLj4KF++PEePHs1x35EjR4iJiSEsLIwyZcrkeDwtLY2TJ08SExNT0G8tBVAsPZWJ773EhAYPcahEadtxRERco0oVGDYMevaE06dtp5ELKHDx0a5dO3bs2JFjdSMxMZEWLVpkP75169bsx3bt2kV4eDi1a9cu6LeWAnh8w6vsibyapVWb2o4iIuJao0ebM1+mTbOdRC4gz8XHmTNnyMrKyv64evXq1KlTh3Xr1gGQkJBAUFAQ7du3B2DgwIGsX7+eU381AC1evJjRo0cTFhbmivySHx9/zH2JnzKy6SBdbhER/xMWZi6/jB0L339vO42cR54aTlesWMHGjRsJCgrijTfeyC4wli5dytChQ9m8eTNHjx5l7dq1FCpUCIDo6Gji4uLo1asXkZGRlC5dmhEjRrj+lUjunDwJvXoxqV53DpS8ynYaERH3qF0b+vc3B9B9/rlO6PYyDqfTOwbiJycnEx4eTlJSkna7uNMjj8C333J9zeE4HZde+MrNbpezO2dERFypwLvtTp2Cf/8bHngAxoxxTSg5R37+fqsUDCTvvw8LF8I33+Cc+4PtNCIiF5WbNzYXLVDCwszgsTp1oEULuOUWF6aTgtCptoHi6FEzPn3aNIiOtp1GRMQzbrnFjF3v2lXDx7yIio9A4HRC375w++3w0EO204iIeNbjj0PRorr04kV02SUQzJ9vGq527tTuFhEJPMHBsGgR1KhhLr/Ur287UcDTyoe/++knM3J4wQL4xxk8IiIB46ab4PnnoXNncxlarFLx4c9On4YuXaBHD2jSxHYaERG7+vWDmjXN5Wfv2OgZsFR8+LOxY+HECZg0yXYSERH7HA6YOxcSEuCll2ynCWjq+fBX778P06fDli1w2WX5/jKa4SEifiUyEpYuNavBd94J1avbThSQtPLhjw4cMJdbXn4ZKla0nUZExLvUqQOxsWb42MmTttMEJBUf/ub0aejYEe65x4wVFhGRc40aBVdfbUawq//D41R8+Jsnn4Tjx2HGDNtJRES8V6FCsGwZfPQRzJxpO03AUc+HP3nvPdNEtWULFCliO42IiHe7+mp4/XVo2tRMQr39dtuJAoZWPvzF//4HnTqZCl59HiIiuXPnnfDMM9CuHfz+u+00AUPFhz84cQJatTJ717t0sZ1GRMS3DBkCtWubBtTTp22nCQgqPnxdVhZ07w5XXaV5HiIi+eFwwLx5cPiwaUQVt1PPh6979ln45hvYutWcXyAiInlXrBi8/baZgFqlilaR3Ux/rXzZ6tVmtWPTJp3bIiJSUDExsGIFtGkD5ctDrVq2E/ktFR++audOU5nPnQtVq9pOIyJiRW6nMO+Z2CJ3X7BJE/OmrlUr+OorKFs2/+HkgtTz4YsOHYLmzWHECOjQwXYaERH/8vDD0LatGdZ44oTtNH5JxYevOXkSWraERo1g9GjbaURE/I/DAS++CFdeaUYYnDljO5HfUfHhS06fNlvBIiLglVfMD4iIiLheSAi88YaZoTR4sEawu5h6PnyF02n2ov/yC2zeDIUL204kIuLfSpaEdetM4+nVV8MTT9hO5DdUfPiKiRPhzTfhyy/ND8RF5LYBS0RELqFsWVOA1K1r5in17Gk7kV9Q8eELZs2C556DDRsoN+s74DvbiUREAkeVKvDuu9CiBZQubRpRpUBUfHi75cvh0UdN5V21Kiw7YDuRiIhfutSqcdO7BzGrY0f44AO44w4PpfJPajj1ZmvXmiW+N9805w6IiIg162Jqw+TJZtTBf/9rO45P08qHt/rsM7j/fpg/3wy9ERER+/r1g7Q0aNwYPvkEqlWzncgnqfjwRp99Zq4tTptmChAREfEeQ4dCejrcfTesXw+VKtlO5HNUfHibjRtN4fHCC9Crl+00IiJyPrGxpgBp1Ag+/dScCyO5puLDm3z6qZle+uKL8NBDttOIiMjFPPmkKUAaNICPPoKKFW0n8hkqPrzFhg1m+9b06dCjh+00IiJyKQ4HjB9vpqHWqwfvvw+33GI7lU9Q8eEN1qwxY9NnzIAHH7SdRkREcsvhgHHjoHhxaNjQ7FLUNtxLUvFh26JF0L8/LFwI7drZTiMiIhdx4VkgFehcszOPN2hE39ZP8NpyjWK/GBUfNk2dCk89BatXm4pZRETcwhPHTrxWvTkphS9jzsqn4c0YvaG8CBUfNjidMGoUzJ1r9onXqGE7kYiIuMA7NzfgRGgR5vXoAfv2mW25OoH8HCo+PO3UKTO1dPNm2LRJ27NERPzMx9E1IXa9GZvwyy9mZlOhQrZjeRUVH570++/QqpVZ+diyBa68MvshnUQrIuJHatQwp5A3bw5t28LSpVCkiO1UXkNnu3jKt9/CbbdBuXJmIt7fCg8REfFD119vVrmPH4c77zSXYQRQ8eEZa9aYg+Eeegheew3CwmwnEhERT4iMhA8/hFtvNashn35qO5FXUPHhTmfOwJgx0LEjzJljpuGp8UhEJLAULgyzZsEzz5jLMDNmmMvvAUw9H+5y5Ah06gT793P3/ZP48eui8LX6OkREAlafPuYQurZt4b//hZdfhqJFbaeyQisf7vDll2bEbsmSsHUrP15R1nYiERHxBnfcAdu2wU8/mUsxO3faTmSFig9XOnMGnn3WDAwbNgxef92M3BURETmrTBmz8aB9e7j9dnNJJsAuw+iyi6vs2QNdu5rttBs3anCYiIhcWHCwOROmfn3o3Nmcijt7tmlQDQBa+SgopxOWLIGqVc21vK+/VuEhIiK506ABbN8OGRnmb8iaNbYTeYSKj4I4dAhatzbjc5csgZkzA7Z5SERE8umKK+Ddd2HCBOjSxZxu/ueftlO5lYqP/MjKMstjFStCsWKQmAj33GM7lYiI+CqHA7p3h+++M5fv/XwVRD0fefXjj2a71E8/wbJl0KyZ7UQiIuIvrrkG4uNh/nzo1g3q1YMXX4TrrrOdzKW08pFbJ05AbKzp7ahc2VSnKjxERMTVHA4zEfuHHyAiwqyyT5pk+kL8hFY+LsXpNCPRH3sM/vUv+OILU4D8RQfCiYiIW1xxBbz6qilE+veHBQtg8mQzJdXHp2Wr+LiYzz4zRceBA/DCC3D//T7/Dy4iIu6Xmzemeya2yN0Xq1PH7KScNcv0hVStCs8/b4ZZ+ihddjmf7duhRQtza9YMvv8eOnRQ4SEiInaEhMDAgfC//5nJqHXqmJ6QX36xnSxfVHz83fffm2EvtWrBTTfBzz+bw+C0fVZERLxByZIwcSLs2mU+rlABevc2gy59iIoPMHP227WDatWgSBFThEyZAqVK2U4mIiJyrrJlYdEiSEiAtDTzhrlPH59ZCQnc4sPpNGPQmzaFunUhKspso50zx++2NImIiJ+66SYz5DIhAVJTzcf33w9btthOdlGB13CalgbLl8OMGWZWx8CBsHix6SoWERHxIrndUblnYgtThDzzDEyfDnffDVWqmENO77sPChVyc9K8cTid3nGUXnJyMuHh4SQlJVGiRAnXf4M9e8z487lz4eqr4ZFHzBjbYsUK9GW11VZERGw7Z+dMUpJZyX/xRVN49OoFPXqYIWYulp+/3/698pGWBu+8Y/ZGr19vRqC/+aY5RfASO1dUVIiIiM8KD4cRI2DwYDMxdfZs+M9/zA7OPn1My4HF1RD/Kz6cTvj8c1i4EFasgDJlzL7oefNMXwcqLEREJECEhECrVua2d6/5W9i3rzmjrEMH6NTJnMTu4VES/tFwmpUFmzbBkCGmWbRlS1PRffCBOfQtNja78BAREQlIZcua1Y89e8xOmaQkaNQIbrzRjJXYudO8gfcA3+35SE83E0jffhtWroTMTGjViu7J1/F52SpkFgpxf2gREREfcd6JqqdOwdq1sHQpvPceXHkl3Huvud15p1k5uQT/7/n46SdYt87cPvnEHLhzzz2mw7dePQgO5lNdUhEREcmdsDBo08bc0tJ4qOtEGm3YQqO5iwg9ncGGG2rw2fXV2Vy2Kr+WMLtCcz0W/iK8u/jYv9/M4ti40RQbe/eamRxNm8KECXDzzRp5LiIi4gqXXcYn0bfxSfRtPOHMosqvP3LX/76iU8J7THxvOnsjrubzslXp+8PnbLmuEn9eZlY5stJT8/ytvK/4WLAA/vtfc0ll/35zcE7dujB1KjRoUOCtsSIiInJxTkcQ28vEsL1MDFPpSvH0FGru+5baexMY/tkSov/Yzy+R1/B1mZv4/MobmJbHr+99xccbb5itsF27mjNWVGyIiIhYdSK0KB/9qyYf/asmABGpSVQ/9AP/PriLFj9s8oPiIz4e3DFkTERERFzieJHw7Es0WempMO3+PH2+1xUflca+T1BokXPud0WDi4iISKDyphlXHis+JkyYwM8//0xqaio9e/akYcOGefp8b/p/mqslf/U2JW5rbTuGx+l1Bxa97sCi1y0X45EhYzNmzODHH39kzpw5zJs3jwEDBvDTTz954lv7hOSt79iOYIVed2DR6w4set1yMW4vPjIyMnjqqafo3r07AGFhYTRp0oTx48e7+1uLiIiIF3L7ZZfNmzfzxx9/UKlSpez7qlatSmxsbI7nnR20mp/9wr7PqdcdUPS6A4ted2AJvNd99vXmaWC6081mzJjhDAoKcp45cyb7vpUrVzoB57Fjx7Lv279/vxPQTTfddNNNN9188LZ///5c1wZuX/lISkqiZMmSBAX9/xWe0NBQAFJTU4mIiACgTJky7N+/n+LFi+PQ1FIRERGf4HQ6OXHiBGXKlMn157i9+IiMjCQ9PT3HfWlpaQDZhQdAUFAQUTp5VkRExOeEh4fn6flubzgtX748KSkpnDp1Kvu+I0eOEBUVRZEi587zEBEREf/m9uKjfv36lCpViq1bt2bfl5iYSIsWGhomIiISiNxefISEhDB06FBWrlwJQEpKCh9++OE5u11EREQkMHhkyNjIkSMJDg5m8ODBPPzww8ydO5dy5cqd97nr16+nSpUqlChRgmbNmrFnzx5PRPQKiYmJtGvXjkWLFtmO4nYTJkygd+/edO7cmU8++cR2HI85evQojz76KAMGDLAdxWP27t1LkyZNKF68ONWrV2f9+vW2I3nEkSNHaNmyJcWLF6dGjRps377ddiSPW7t2Lddff73tGB6zceNGHA5H9u3555+3HcljkpKSmD59OkuWLMnVz7jD6czLxlz3OnToEG3btqV3796kpKQwbtw4rrzySrZv305wsNcdQ+NShw8f5uOPP+bBBx9kzpw5PPjgg7Yjuc2MGTP4+uuvefXVVzl16hTVqlUjPj6e8uXL247mVpmZmcTHx/PYY49xxx13sGDBAtuR3M7pdNKkSRPuvvturrrqKqZMmcKPP/7Ijh07/P7fe+jQoTRr1oyQkBAefvhhChUqxM6dO23H8pjjx49z6623cvr06YB5E/nQQw9RpUqV7I+7d++eY2OFv/rpp58YPXo0M2bM4PLLL8/dJ7lsoIcLLF682HnkyJHsj+Pj452AMyEhwWIqzypTpoxz/vz5tmO4TXp6uvPyyy93btiwIfu+QYMGOXv06GExlWd16tTJ2b17d9sxPGLHjh3Ojz76KPvj3377zVm0aFHntGnTLKZyv7S0tBwzD15//XVneHi4vUAWDBgwwDlu3Dhn2bJlbUfxiMTEROeYMWNsx/C4Y8eOOe+44w7n4cOH8/R5Hrnsklv3338/pUqVyv64fv36wP/PBQkEISEhtiO41YUm3q5Zs8ZiKs/y93/jv4uJieGuu+7K/rh06dJUrFjR73+mw8LCcowOyMzMpH///hYTedY777zDrbfeynXXXWc7isdMnjyZZ599lrp167J27VrbcTxm7Nix3HDDDUyYMIHbb7+dxx57jNOnT1/y87yq+ChcuHCOjw8fPszNN9/MTTfdZCmRuFpiYiJBQUE5liIjIiI4cuQIx48ft5hM3OGfP9NgluNbtmxpIY0dBw4cYMmSJTzxxBO2o3jE0aNHiY+P9+tLx+fTrl07Jk+eTHp6Oi1atGDChAm2I7ldamoqc+fO5ZZbbuGFF15gwYIFzJw5k5EjR17ycz3aSDF8+PCLNl0NGTIkxy+lJUuW+EXDTl5ftz/L7cRb8U8bN26kTZs2ATNQMCEhgdGjR/Pee+/RoEEDNm3a5PerPmPGjOHpp5+2HcPjmjVrRrNmzRg8eDBjxozhySefpHXr1n795nnLli2kpaXRuXNnHA4HN910Ex06dGDmzJk8//zzOX7P/5NHi48pU6bk+rn79u0jPT2dZs2auTGRZ+Tldfu73E68Ff+TmZnJsmXLmDZtmu0oHlOtWjXWrFnD22+/Tdu2bXnrrbfo1KmT7Vhus2LFCurXr89VV11lO4o1DoeDp59+mvj4eNavX+/Xxcfhw4cBKFq0aPZ99evXZ968eRw8eJBrr732gp/rVZddzkpLS2PmzJk89dRTtqOIi2nibeCaMmUKo0aN8vt3/ufTunVr6tWrx6FDh2xHcatZs2bxwAMPZG817dGjB3v37sXhcLBhwwbb8TzG4XDQsGHDc95o+ZvixYsD5LhkXrp0aeDSbya9rvg4c+YMEydOJDY2NrsxLyUlxXIqcRVNvA1Mc+fOpWnTptnvhNLT0zlz5ozlVJ5VsmTJHNsw/dGcOXP45ptvsm/jxo3j6quv5ptvvqFGjRq243nUr7/+StOmTW3HcKtatWoREhLCV199lX3fsWPHqF69OsWKFbvo53pV8XHmzBn69OlDuXLl+OKLL1i3bh2LFi1i/PjxtqN5zJkzZ8jKyrIdw2008db//43/KS4ujp9//pnDhw+zbt06Vq5cSa9evfz69Ork5GQWLlxIcnIyADt27CAjI4PGjRtbTuZe0dHRVKtWLft23XXXUbhwYapVq3bJP0a+bN++fQwcOJB9+/YB5vJTIGyWuPzyyxk8eDAzZ87Mvu/tt9/OXXO1m7b+5ku3bt2cwDm3t956y3Y0t/vzzz+dL730krNQoULOxo0bOzdt2mQ7ktucPn3aOWLECOegQYOc3bt39+vX+k/Lly93Xnfddc5y5co5X3/9ddtx3G7evHnn/ZkeOHCg7WhutXv3bme5cuWcV1xxhbN9+/bO2NhYZ3Jysu1YHjd//vyAmPNx8OBBZ+XKlZ1FixZ11q1b17lkyRLbkTwmMzPTOXToUGffvn2djz76qHPGjBm5+jyvmnAqIiIi/s+rLruIiIiI/1PxISIiIh6l4kNEREQ8SsWHiIiIeJSKDxEREfEoFR8iIiLiUSo+RERExKNUfIiIiIhHqfgQERERj1LxISIiIh6l4kNEREQ8SsWHiIiIeJSKDxFxm5UrV3L55ZcTGhrKzp07+fLLLylSpAjz5s2zHU1ELNKptiLiVitXrqRt27Zs2rSJw4cPc+zYMXr37m07lohYpOJDRNyuefPm/PHHH1SsWJH58+fbjiMilumyi4i43fTp00lISKB27dq2o4iIF1DxISJud/z4cSpUqMB//vMfUlJSbMcREctUfIiIW2VmZjJz5kw+++wzAJ555hnLiUTENhUfIuJWEyZMYNCgQRQvXpznnnuOqVOnkpiYaDuWiFik4kNE3GbJkiVMnTqVzMxMAAoVKkRGRgb3338/X3zxheV0ImKLdruIiIiIR2nlQ0RERDxKxYeIiIh4lIoPERER8SgVHyIiIuJRKj5ERETEo1R8iIiIiEep+BARERGPUvEhIiIiHqXiQ0RERDxKxYeIiIh41P8BlGvnATwdYeUAAAAASUVORK5CYII=\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def gaussian(x,mu,sig) :\n", " '''\n", " Gaussian distribution\n", " \n", " Parameters\n", " ----------\n", " x: float array\n", " Values where Gaussian will be evaluated\n", " mu, sig: float\n", " Mean and sigma of the Gaussian\n", " Returns\n", " -------\n", " gaussian \n", " The value of the Gaussian evaluated at x \n", " '''\n", " return np.exp(-0.5*((x-mu)/sig)**2)\n", "\n", "mn = 2\n", "sg = np.sqrt(2.) \n", "xk = 0 # INITIALIZE SAMPLER\n", "\n", "samples = []\n", "for i in range(10**4):\n", " xp = np.random.normal(xk,1) # PROPOSAL DISTRIBUTION\n", " # GAUSSAIAN SIGMA = 1\n", " r = np.random.rand()\n", " \n", " f1 = gaussian(xp, mn, sg) # NEW SAMPLE\n", " f2 = gaussian(xk, mn, sg) # OLD SAMPLE\n", " ratio = f1/f2\n", "\n", " if (ratio > r): # ACCEPT OR REJECT?\n", " samples.append(xp)\n", " xk=xp\n", " else:\n", " samples.append(xk)\n", " \n", " \n", "# PLOT SAMPLES\n", "samples_prob2 = samples # SAVE FOR LATER\n", "n, bins, patches = plt.hist(samples,bins=75)\n", "mx = np.max(n)\n", "\n", "# PLOT TRUTH\n", "a=np.arange(1000)/100. - 3.\n", "true_dist = gaussian(a, mn, sg)\n", "plt.plot(a,mx*true_dist,'r')\n", "plt.xlim(-2,6)\n", "plt.xlabel('x');" ] }, { "cell_type": "markdown", "id": "fd387ba5-32d8-407b-8c94-df66a52bf794", "metadata": {}, "source": [ "Redo the previous problem, but now with an input density that is uniformon 3" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def pdf3(x):\n", " '''\n", " Top Hat between 3 to 7 distribution\n", " \n", " Parameters\n", " ----------\n", " x: float array\n", " Values where Top Hat will be evaluated\n", " Returns\n", " -------\n", " p \n", " returns 1 if inside tophat, 0 if outside \n", " ''' \n", " if (x >= 3) & (x<=7):\n", " p = 1.\n", " else:\n", " p=0.\n", " return p\n", "xk = 6. # NEED TO START INSIDE DISTRIBUTION\\\n", "\n", "samples = []\n", "for i in range(10**5):\n", " xp = np.random.normal(xk,1) # PROPOSAL DISTRIBUTION\n", " r = np.random.rand()\n", " \n", " f1 = pdf3(xp) # SAMPLE NEW\n", " f2 = pdf3(xk) # SAMPLE NEW\n", " ratio = f1/f2\n", " \n", " if (ratio > r): # COMPARE\n", " samples.append(xp)\n", " xk=xp\n", " else:\n", " samples.append(xk)\n", "\n", "\n", "# PLOT SAMPLES\n", "n, bins, patches = plt.hist(samples,bins=20)\n", "mx = np.max(n)\n", "\n", "# PLOT TRUTH\n", "a=np.arange(1000)/100.\n", "true_dist= (a >=3) & (a<=7)\n", "plt.plot(a,mx*true_dist,'r')\n", "plt.xlabel('x');" ] }, { "cell_type": "markdown", "id": "c9785f98-a6de-418b-a279-c960a6118ae2", "metadata": {}, "source": [ "Redo the same problem, but now with an input density that is a function of two variables (x,y). For the density function use two different functions. The first density function is a covariant two-dimensional Gaussian density with variance tensor\n", "\n", "$$ V = \\begin{bmatrix}\n", "2.0 & 1.2\\\\\n", "1.2 & 2.0\n", "\\end{bmatrix} $$" ] }, { "cell_type": "code", "execution_count": 27, "id": "58229ce3", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy import stats\n", "\n", "def pdf4a(x,y) :\n", " '''\n", " Two dimensional Gaussian distribution, \n", " \n", " Parameters\n", " ----------\n", " x,y: float array\n", " Values where 2D Gaussian will be evaluated\n", " \n", " mu, sig: float\n", " Mean and sigma of the Gaussian\n", " Returns\n", " -------\n", " gaussian \n", " The value of the Gaussian evaluated at x, y \n", " '''\n", " \n", " mean = [0,0]\n", " cov = [[2.0,1.2],[1.2,2.0]]\n", " gauss = stats.multivariate_normal(mean, cov)\n", " \n", " return gauss.pdf([x,y]) \n", "xk = 6. # NEED TO START INSIDE DISTRIBUTION\n", "yk = 5.\n", "\n", "xsamples, ysamples = [], []\n", "\n", "for i in range(10**4):\n", "\n", " ind = [[1.0,0],[0,1]]\n", " xp,yp = np.random.multivariate_normal([xk,yk],ind) \n", "\n", " r = np.random.rand()\n", " \n", " f1 = pdf4a(xp,yp)\n", " f2 = pdf4a(xk,yk)\n", " ratio = f1/f2\n", "\n", " if (ratio > r):\n", " xsamples.append(xp)\n", " xk=xp\n", " ysamples.append(yp)\n", " yk=yp\n", " else:\n", " xsamples.append(xk)\n", " ysamples.append(yk)\n", " \n", "data = np.column_stack((ysamples,xsamples))\n", "figure = corner.corner(data, truths=[0,0],labels=[\"x\", \"y\"],\n", " quantiles=[0.16, 0.5, 0.84],show_titles=True, \n", " title_kwargs={\"fontsize\": 12})" ] }, { "cell_type": "markdown", "id": "1ab4ff04-6cb3-4b59-b5a9-32918a401a47", "metadata": {}, "source": [ "Now do it the MCMC way." ] }, { "cell_type": "code", "execution_count": 29, "id": "5e7f15b7", "metadata": {}, "outputs": [], "source": [ "def lnprob(theta,x,y,sigma):\n", " '''\n", " Evaluate whether to accept or \n", " \n", " Parameters\n", " ----------\n", " x,y: float array\n", " Values where Top Hat will be evaluated\n", " Returns\n", " -------\n", " p \n", " returns 1 if inside tophat, 0 if outside \n", " ''' \n", " lp = lnprior(theta)\n", "\n", " if not np.isfinite(lp):\n", " return -np.inf\n", "\n", " return lp + lnlike(theta, x, y, sigma)\n", "\n", "\n", "\n", "def lnprior(theta):\n", " '''\n", " Evaluate whether sample falls inside of priors\n", " \n", " Parameters\n", " ----------\n", " theta: float array\n", " Current values of fitted parameters\n", " \n", " Returns\n", " -------\n", " returns 0 if inside prior, -inf if outside \n", " ''' \n", " if (0 < theta[0] < 5) & (-30 < theta[1] < 200):\n", " return 0.0\n", " \n", " return -np.inf\n", "\n", "\n", "def lnlike(theta,x,y,sigma):\n", " '''\n", " Evaluate the log-likelihood\n", " \n", " Parameters\n", " ----------\n", " theta: float array\n", " Current values of fitted parameters\n", " \n", " x,y, sigma: float arrays\n", " Data points and one sigma errors\n", "\n", " Returns\n", " -------\n", " lnl\n", " log-likelihood value \n", " ''' \n", " # MAKE MODEL\n", " model = theta[0]*x + theta[1]\n", "\n", " # EVALUATE LIKELIHOOD\n", " chi2 = ((y - model)**2)/(sigma**2)\n", " lnl = -0.5 * np.sum(chi2)\n", " \n", " return lnl\n", "\n", "\n", "def initialize_walkers(mguess,bguess):\n", " '''\n", " Initialize the walkers using an initial guess\n", " \n", " Parameters\n", " ----------\n", " mguess, bguess: float value\n", " Rough initial guess of parameters\n", " Returns\n", " -------\n", " ndim, nwalkers, p0\n", "\n", " ''' \n", " \n", " # Two free parameters (m,b) and 20 walkers\n", " ndim, nwalkers = 2, 20\n", " p0 = np.random.rand(ndim * nwalkers).reshape((nwalkers, ndim))\n", "\n", " # initialize slope \n", " p0[:,0] = (p0[:,0]*4. - 2) + mguess\n", " \n", " # initialize intercept\n", " p0[:,1] = (p0[:,1] * 60 - 30) + bguess\n", " \n", " return ndim,nwalkers,p0" ] }, { "cell_type": "code", "execution_count": 30, "id": "8368f85e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of initial burnin samples: 56\n", "Did the chains converge? True\n" ] } ], "source": [ "# LOAD DATA FROM HOGG et al 2010, Table 1\n", "data = ascii.read('data/hogg_2010_data.csv',format='csv')\n", "\n", "# SKIP THE FIRST FEW DATA POINTS\n", "m=data['ID'] > 4\n", "data=data[m]\n", "\n", "mguess = 2\n", "bguess = 30\n", "\n", "max_n=3000\n", "ndim, nwalkers, p0 = initialize_walkers(mguess,bguess)\n", "\n", "# INITIALIZE SAMPLER\n", "sampler = emcee.EnsembleSampler(nwalkers, ndim, lnprob, args=(data['x'],data['y'],data['sigma_y']))\n", "\n", "# RUN MCMC\n", "pos, prob, state = sampler.run_mcmc(p0, max_n)\n", "# As a bonus, we can determine the number of burnin samples and whether the chains converged.\n", "\n", "tau = sampler.get_autocorr_time(tol=0)\n", "burnin = int(2 * np.max(tau))\n", "converged = np.all(tau * 100 < sampler.iteration)\n", "print('Number of initial burnin samples:',burnin)\n", "print('Did the chains converge?',converged)" ] }, { "cell_type": "code", "execution_count": 31, "id": "f6359c9a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, (ax1, ax2) = plt.subplots(1, 2,figsize=(20,5))\n", "\n", "for ii in range(20):\n", " ax1.plot(sampler.chain[ii,:,0], color=\"k\",linewidth=0.5)\n", "\n", "for ii in range(20):\n", " ax2.plot(sampler.chain[ii,:,1], color=\"k\",linewidth=0.5)\n", "\n", "\n", "ax1.set_ylabel('m')\n", "ax2.set_ylabel('b')\n", "ax1.set_xlabel('Step Number')\n", "ax2.set_xlabel('Step Number')\n", "\n", "ax1.set_title('Slope (m) Sample chains')\n", "ax2.set_title('Intercept (b) Sample chains')\n", "\n", "ax1.axvline(burnin,label='Burn-in')\n", "ax2.axvline(burnin)\n", "ax1.legend()" ] }, { "cell_type": "code", "execution_count": 34, "id": "e7ad8fbe", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# PLOT CORNER\n", "labels=['m','b']\n", "burnin = 100\n", "samples = sampler.chain[:, burnin:, :].reshape((-1, ndim))\n", "fig = corner.corner(samples, labels=labels,show_titles=True,quantiles=[0.16, 0.5, 0.84])" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.12.3" } }, "nbformat": 4, "nbformat_minor": 5 }