From f60614cf5fa47095a5ed4de78a5e8734c3d2e039 Mon Sep 17 00:00:00 2001 From: Kazi Shudipto Amin Date: Sat, 6 Nov 2021 09:50:24 -0600 Subject: [PATCH 01/76] Add new chapter: metropolis_hastings; in python --- .../metropolis_hastings-checkpoint.md | 127 +++++++++ .../metropolis-checkpoint.ipynb | 251 ++++++++++++++++++ .../metropolis-checkpoint.py | 54 ++++ .../monte_carlo-checkpoint.py | 35 +++ 4 files changed, 467 insertions(+) create mode 100644 contents/metropolis_hastings/.ipynb_checkpoints/metropolis_hastings-checkpoint.md create mode 100644 contents/metropolis_hastings/code/python/.ipynb_checkpoints/metropolis-checkpoint.ipynb create mode 100644 contents/metropolis_hastings/code/python/.ipynb_checkpoints/metropolis-checkpoint.py create mode 100644 contents/metropolis_hastings/code/python/.ipynb_checkpoints/monte_carlo-checkpoint.py diff --git a/contents/metropolis_hastings/.ipynb_checkpoints/metropolis_hastings-checkpoint.md b/contents/metropolis_hastings/.ipynb_checkpoints/metropolis_hastings-checkpoint.md new file mode 100644 index 000000000..e9739eab7 --- /dev/null +++ b/contents/metropolis_hastings/.ipynb_checkpoints/metropolis_hastings-checkpoint.md @@ -0,0 +1,127 @@ +# Metropolis-Hastings Algorithm + +We saw how [Monte Carlo Integration](../monte_carlo_integration/monte_carlo_integration.html) uses random numbers to approximate the area of pretty much any shape we choose. +The Metropolis-Hastings algorithm is a slightly more advanced Monte Carlo method which uses random numbers to approximate a probability distribution. +What's really powerful about this approach is that you don't need to know the probability function itself - you just need a function which is _proportional_ to it. + +Why is this helpful? Well, we often have probability functions of the following form: + +$$ +P(\mathbf{x}) = \frac{f(\mathbf{x})}{\int_D f(\mathbf{x})d\mathbf{x}} +$$ +where $$D$$ is the domain, i.e., all possible values of the coordinates $$\mathbf{x}$$. +It's often easy for us to know $$f(x)$$ (eg. for a Gaussian distribution, it is $$e^{-x^2}$$). +But the integral at the bottom can be quite difficult to calculate, even numerically. +This is especially true when the coordinates ($$\mathbf{x}$$) are multidimensional, and $$f(\mathbf{x})$$ is an expensive calculation. + +## Random walk in 1D + +The Metropolis-Hastings Algorithm is very similar to a random walk, so let's first see how we can get a distribution from a random walk. + +

+ <FIG> Random Walk in 1D +

+ +The dot above is a "walker", whose initial position is randomly chosen. We also divide the domain into discrete locations or "bins" and set the visit counter to be zero for each bin. Then at each iteration, the walker randomly choses to go either to the right ($$x \rightarrow x+1$$) or left ($$x \rightarrow x-1$$). Each time it visits a bin, the visit count for that bin goes up by one. Over time, we get a distribution of visits, in this case a random one. + +## Random walk, but with an acceptance criteria + +The Metropolis-Hastings algorithm works in a similar way, but differs crucially in one way - after choosing a random step for the walker (left or right), a decision is made about whether to __reject__ or __accept__ the step. This decision is guided by $$f(x)$$, or any function that is proportional to the target probability function. + +

+ <FIG> Metropolis Walk in 1D +

+ +## The function for generating a random step + +So far we used a very simple function for generating the next step: it will be either +1 or -1 to the current location. For the simple version of the algorithm to work, this can actually be any symmetric function. For example, it can be any real number between $$-a$$ and $$+a$$, or it can be sampled from some symmetric distribution, $$g$$, such as a Gaussian. + +## The full algorithm for a 1D example function + +### Initialize + +Let our target distribution be: +$$ +P(x) = \frac{\exp\left[ -x^4 + x^3 - 2x^2 - x \right]}{\int_{-10}^{10} \exp\left[ -x^4 + x^3 - 2x^2 - x \right]} +$$ + +and the function which is proportional to it is +$$ +f(x) = \exp\left[ -x^4 + x^3 - 2x^2 - x \right] +$$ + +{% method %} +{% sample lang="py" %} +[import:4-8, lang:"python"](code/python/metropolis.py) +{% endmethod %} + +Next, we choose some symmetric step generating function. Here we will use a random number in the interval $$(-1,1)$$ +{% method %} +{% sample lang="py" %} +[import:10-14, lang:"python"](code/python/metropolis.py) +{% endmethod %} + +Choose the domain of $$x$$, and an initial point for $$ x_0 $$ ($$x_t$$ at $$t = 0$$) chosen randomly from the domain of $$x$$. +{% method %} +{% sample lang="py" %} +[import:30-31, lang:"python"](code/python/metropolis.py) +{% endmethod %} + +Then iterate: + +1. Generate new position $$x' = x_t + g()$$ +2. Calculate the acceptance probability, $$A = \min\left(1, \frac{f(x_{t+1})}{f(x)}\right)$$ +3. Choose a random real number, $$u$$, between $$0$$ and $$1$$ +4. Accept or reject: + * If $$ u \leq A $$, then __accept__ move, and set new position, $$x_{t+1} = x' $$ + * Otherwise, __reject__ move, and set new position to current, $$x_{t+1} = x_t $$ +5. Increment $$t \rightarrow t + 1$$ and repeat from step 1. + +The code for steps 1 to 4 is: +{% method %} +{% sample lang="py" %} +[import:19-31, lang:"python"](code/python/metropolis.py) +{% endmethod %} + +The following plot shows the result of running the algorithm for different numbers of iterations ($$N$$), with the same initial position. The histograms are normalized so that they integrate to 1. We can see the convergence toward $$P(x)$$ as we increase $$N$$. + +

+ <FIG> multiple histograms +

+ +## Full Example Code +The following code puts everything discussed together, and runs Metropolis-Hastings algorithm for $$N$$ steps. All the positions visited by the algorithm are then written to a file, which can be later read and fed into a histogram or other density calculating scheme. +{% method %} +{% sample lang="py" %} +[import, lang:"python"](code/python/metropolis.py) +{% endmethod %} + + +# === Monte Carlo === + + + + +## License + +##### Code Examples + +The code examples are licensed under the MIT license (found in [LICENSE.md](https://github.com/algorithm-archivists/algorithm-archive/blob/master/LICENSE.md)). + +##### Text + +The text of this chapter was written by [K. Shudipto Amin](https://github.com/shudipto-amin) and is licensed under the [Creative Commons Attribution-ShareAlike 4.0 International License](https://creativecommons.org/licenses/by-sa/4.0/legalcode). + +[

](https://creativecommons.org/licenses/by-sa/4.0/) + +##### Images/Graphics +- The image "[squarecircle](res/square_circle.png)" was created by [James Schloss](https://github.com/leios) and is licensed under the [Creative Commons Attribution-ShareAlike 4.0 International License](https://creativecommons.org/licenses/by-sa/4.0/legalcode). +- The animation "[simplemontecarlo](res/monte_carlo.gif)" was created by [James Schloss](https://github.com/leios) and is licensed under the [Creative Commons Attribution-ShareAlike 4.0 International License](https://creativecommons.org/licenses/by-sa/4.0/legalcode). + + +##### Pull Requests + +After initial licensing ([#560](https://github.com/algorithm-archivists/algorithm-archive/pull/560)), the following pull requests have modified the text or graphics of this chapter: +- none diff --git a/contents/metropolis_hastings/code/python/.ipynb_checkpoints/metropolis-checkpoint.ipynb b/contents/metropolis_hastings/code/python/.ipynb_checkpoints/metropolis-checkpoint.ipynb new file mode 100644 index 000000000..0c281b0db --- /dev/null +++ b/contents/metropolis_hastings/code/python/.ipynb_checkpoints/metropolis-checkpoint.ipynb @@ -0,0 +1,251 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as pp\n", + "import importlib\n", + "import metropolis as met\n", + "%matplotlib widget\n", + "\n", + "pp.rcParams.update({\n", + " \"text.usetex\": True,\n", + "})\n" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "importlib.reload(met)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "xmin, xmax = -10, 10\n", + "\n", + "x_dat1 = [np.random.uniform(xmin, xmax)]\n", + "x_dat2 = [np.random.uniform(xmin, xmax)]\n", + "x_dat3 = [np.random.uniform(xmin, xmax)]\n", + "\n", + "Ns = [5_00, 5_000, 50_000]\n", + "for n,x_dat in enumerate((x_dat1, x_dat2, x_dat3)):\n", + " N = Ns[n]\n", + " x = x_dat[0]\n", + " for n in range(N):\n", + " x = met.iterate(x)\n", + " x_dat.append(x)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(array([0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6]),\n", + " [Text(0, 0, ''),\n", + " Text(0, 0, ''),\n", + " Text(0, 0, ''),\n", + " Text(0, 0, ''),\n", + " Text(0, 0, ''),\n", + " Text(0, 0, ''),\n", + " Text(0, 0, '')])" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "620e8924da414fcc982f420a8ec77d87", + "version_major": 2, + "version_minor": 0 + }, + "image/png": 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", + "text/plain": [ + "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "fig, ax = pp.subplots()\n", + "\n", + "xx = np.linspace(-7,7,1000)\n", + "ax.plot(xx, met.f(xx)/np.trapz(met.f(xx),x=xx), \n", + " color='k', linewidth=2, alpha=0.5,\n", + " label=\"$P(x)$\"\n", + "\n", + " )\n", + "\n", + "\n", + "for n,x_dat in enumerate((x_dat1, x_dat2, x_dat3)):\n", + " x_dat = np.array(x_dat)\n", + " #ax2 = ax.twinx(sharey=True)\n", + " bins = np.arange(-7,7.1, 0.25)\n", + " ax.hist(x_dat, bins=bins, \n", + " density=True,\n", + " histtype='step',\n", + " alpha=1,\n", + " linewidth = 2,\n", + " label=f\"N = {Ns[n]}\"\n", + " )\n", + " \n", + "ax.legend(fontsize=12)\n", + "ax.set_xlabel(\"$x$\", fontsize=16)\n", + "ax.set_ylabel(\"Density\", fontsize=16)\n", + "pp.xticks(fontsize=12)\n", + "pp.yticks(fontsize=12)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "fig.savefig(\"../../res/multiple_histograms.png\", dpi=600)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Test output of `metropolis.py`" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(array([3.99992000e-04, 9.59980800e-04, 3.19993600e-04, 1.75996480e-03,\n", + " 1.11997760e-03, 2.23995520e-03, 2.39995200e-03, 6.55986880e-03,\n", + " 3.07993840e-02, 1.10157797e-01, 2.59594808e-01, 4.28231435e-01,\n", + " 4.51030979e-01, 2.77514450e-01, 1.37597248e-01, 7.15985680e-02,\n", + " 6.95186096e-02, 7.94384112e-02, 9.27181456e-02, 1.03517930e-01,\n", + " 1.10717786e-01, 1.23037539e-01, 1.29517410e-01, 1.35197296e-01,\n", + " 1.39917202e-01, 1.29917402e-01, 1.23437531e-01, 1.14557709e-01,\n", + " 1.06797864e-01, 9.70380592e-02, 8.11983760e-02, 6.93586128e-02,\n", + " 5.41589168e-02, 4.34391312e-02, 3.65592688e-02, 2.57594848e-02,\n", + " 2.20795584e-02, 9.59980800e-03, 1.19197616e-02, 7.43985120e-03,\n", + " 3.51992960e-03, 4.39991200e-03, 3.19993600e-03, 5.59988800e-03,\n", + " 1.14397712e-02, 2.64794704e-02, 4.27191456e-02, 5.37589248e-02,\n", + " 5.33589328e-02, 5.09589808e-02, 2.52794944e-02, 1.44797104e-02,\n", + " 4.39991200e-03, 1.27997440e-03, 0.00000000e+00, 0.00000000e+00]),\n", + " array([-7. , -6.75, -6.5 , -6.25, -6. , -5.75, -5.5 , -5.25, -5. ,\n", + " -4.75, -4.5 , -4.25, -4. , -3.75, -3.5 , -3.25, -3. , -2.75,\n", + " -2.5 , -2.25, -2. , -1.75, -1.5 , -1.25, -1. , -0.75, -0.5 ,\n", + " -0.25, 0. , 0.25, 0.5 , 0.75, 1. , 1.25, 1.5 , 1.75,\n", + " 2. , 2.25, 2.5 , 2.75, 3. , 3.25, 3.5 , 3.75, 4. ,\n", + " 4.25, 4.5 , 4.75, 5. , 5.25, 5.5 , 5.75, 6. , 6.25,\n", + " 6.5 , 6.75, 7. ]),\n", + " [])" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "560d140d17b6451e9790069a145f86b0", + "version_major": 2, + "version_minor": 0 + }, + "image/png": 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+ "text/plain": [ + "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x_dat = np.loadtxt('output.dat')\n", + "fig, ax = pp.subplots()\n", + "\n", + "xx = np.linspace(-7,7,1000)\n", + "ax.plot(xx, met.f(xx)/np.trapz(met.f(xx),x=xx), \n", + " color='k', linewidth=2, alpha=0.5,\n", + " label=\"$P(x)$\"\n", + "\n", + " )\n", + "\n", + "x_dat = np.array(x_dat)\n", + "#ax2 = ax.twinx(sharey=True)\n", + "bins = np.arange(-7,7.1, 0.25)\n", + "ax.hist(x_dat, bins=bins, \n", + " density=True,\n", + " histtype='step',\n", + " alpha=1,\n", + " linewidth = 2,\n", + " label=f\"N = {Ns[n]}\"\n", + " )" + ] + }, + { + "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": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/contents/metropolis_hastings/code/python/.ipynb_checkpoints/metropolis-checkpoint.py b/contents/metropolis_hastings/code/python/.ipynb_checkpoints/metropolis-checkpoint.py new file mode 100644 index 000000000..36fc65f59 --- /dev/null +++ b/contents/metropolis_hastings/code/python/.ipynb_checkpoints/metropolis-checkpoint.py @@ -0,0 +1,54 @@ +import numpy as np +import matplotlib.pyplot as pp + +def f(x): + '''Function proportional to target distribution, a sum of Gaussians''' + # Gaussian heights, width parameters, and mean positions respectively: + a1, b1, x1 = 10, 4, -4 + a2, b2, x2 = 3, 0.2, -1 + a3, b3, x3 = 1, 2, 5 + + return a1*np.exp( -b1*(x-x1)**2 ) + \ + a2*np.exp( -b2*(x-x2)**2 ) + \ + a3*np.exp( -b3*(x-x3)**2 ) + +def g(): + '''Random step vector''' + return np.random.uniform(-1,1) + +def iterate(x, f=f, g=g): + '''Perform one full iteration and return new position''' + + x_proposed = x + g() + A = min(1, f(x_proposed)/f(x) ) + + u = np.random.uniform(0,1) + if u <= A: + x_new = x_proposed + else: + x_new = x + + return x_new + +if __name__ == "__main__": + xmin, xmax = -10, 10 + x0 = np.random.uniform(xmin, xmax) + + x_dat = [x0] # for storing values + N = 50_000 # no. of iterations + + x = x0 + for n in range(N): + x = iterate(x) + x_dat.append(x) + + # Write data to file + output_string = "\n".join(str(x) for x in x_dat) + + with open("output.dat", "w") as out: + out.write(output_string) + out.write("\n") + + + + diff --git a/contents/metropolis_hastings/code/python/.ipynb_checkpoints/monte_carlo-checkpoint.py b/contents/metropolis_hastings/code/python/.ipynb_checkpoints/monte_carlo-checkpoint.py new file mode 100644 index 000000000..c21bb054e --- /dev/null +++ b/contents/metropolis_hastings/code/python/.ipynb_checkpoints/monte_carlo-checkpoint.py @@ -0,0 +1,35 @@ +import math +import random + + +def in_circle(x, y, radius = 1): + """Return True if the point is in the circle and False otherwise.""" + return (x*x + y*y) < radius*radius + +def monte_carlo(n_samples, radius = 1): + """Return the estimate of pi using the monte carlo algorithm.""" + in_circle_count = 0 + for i in range(n_samples): + + # Sample x, y from the uniform distribution + x = random.uniform(0, radius) + y = random.uniform(0, radius) + + # Count the number of points inside the circle + if(in_circle(x, y, radius)): + in_circle_count += 1 + + # Since we've generated points in upper right quadrant ([0,radius], [0, radius]) + # We need to multiply the number of points by 4 + pi_estimate = 4 * in_circle_count / (n_samples) + + return pi_estimate + +if __name__ == '__main__': + + pi_estimate = monte_carlo(100000) + percent_error = 100*abs(math.pi - pi_estimate)/math.pi + + print("The estimate of pi is: {:.3f}".format(pi_estimate)) + print("The percent error is: {:.3f}".format(percent_error)) + From dcd5e13dd2c703dc93f0298cdcceaac1e5c0878e Mon Sep 17 00:00:00 2001 From: Kazi Shudipto Amin Date: Sat, 6 Nov 2021 09:57:02 -0600 Subject: [PATCH 02/76] Add markdown and python files for metropolis --- .../code/python/metropolis.py | 54 ++++++++ .../metropolis_hastings.md | 127 ++++++++++++++++++ 2 files changed, 181 insertions(+) create mode 100644 contents/metropolis_hastings/code/python/metropolis.py create mode 100644 contents/metropolis_hastings/metropolis_hastings.md diff --git a/contents/metropolis_hastings/code/python/metropolis.py b/contents/metropolis_hastings/code/python/metropolis.py new file mode 100644 index 000000000..36fc65f59 --- /dev/null +++ b/contents/metropolis_hastings/code/python/metropolis.py @@ -0,0 +1,54 @@ +import numpy as np +import matplotlib.pyplot as pp + +def f(x): + '''Function proportional to target distribution, a sum of Gaussians''' + # Gaussian heights, width parameters, and mean positions respectively: + a1, b1, x1 = 10, 4, -4 + a2, b2, x2 = 3, 0.2, -1 + a3, b3, x3 = 1, 2, 5 + + return a1*np.exp( -b1*(x-x1)**2 ) + \ + a2*np.exp( -b2*(x-x2)**2 ) + \ + a3*np.exp( -b3*(x-x3)**2 ) + +def g(): + '''Random step vector''' + return np.random.uniform(-1,1) + +def iterate(x, f=f, g=g): + '''Perform one full iteration and return new position''' + + x_proposed = x + g() + A = min(1, f(x_proposed)/f(x) ) + + u = np.random.uniform(0,1) + if u <= A: + x_new = x_proposed + else: + x_new = x + + return x_new + +if __name__ == "__main__": + xmin, xmax = -10, 10 + x0 = np.random.uniform(xmin, xmax) + + x_dat = [x0] # for storing values + N = 50_000 # no. of iterations + + x = x0 + for n in range(N): + x = iterate(x) + x_dat.append(x) + + # Write data to file + output_string = "\n".join(str(x) for x in x_dat) + + with open("output.dat", "w") as out: + out.write(output_string) + out.write("\n") + + + + diff --git a/contents/metropolis_hastings/metropolis_hastings.md b/contents/metropolis_hastings/metropolis_hastings.md new file mode 100644 index 000000000..e9739eab7 --- /dev/null +++ b/contents/metropolis_hastings/metropolis_hastings.md @@ -0,0 +1,127 @@ +# Metropolis-Hastings Algorithm + +We saw how [Monte Carlo Integration](../monte_carlo_integration/monte_carlo_integration.html) uses random numbers to approximate the area of pretty much any shape we choose. +The Metropolis-Hastings algorithm is a slightly more advanced Monte Carlo method which uses random numbers to approximate a probability distribution. +What's really powerful about this approach is that you don't need to know the probability function itself - you just need a function which is _proportional_ to it. + +Why is this helpful? Well, we often have probability functions of the following form: + +$$ +P(\mathbf{x}) = \frac{f(\mathbf{x})}{\int_D f(\mathbf{x})d\mathbf{x}} +$$ +where $$D$$ is the domain, i.e., all possible values of the coordinates $$\mathbf{x}$$. +It's often easy for us to know $$f(x)$$ (eg. for a Gaussian distribution, it is $$e^{-x^2}$$). +But the integral at the bottom can be quite difficult to calculate, even numerically. +This is especially true when the coordinates ($$\mathbf{x}$$) are multidimensional, and $$f(\mathbf{x})$$ is an expensive calculation. + +## Random walk in 1D + +The Metropolis-Hastings Algorithm is very similar to a random walk, so let's first see how we can get a distribution from a random walk. + +

+ <FIG> Random Walk in 1D +

+ +The dot above is a "walker", whose initial position is randomly chosen. We also divide the domain into discrete locations or "bins" and set the visit counter to be zero for each bin. Then at each iteration, the walker randomly choses to go either to the right ($$x \rightarrow x+1$$) or left ($$x \rightarrow x-1$$). Each time it visits a bin, the visit count for that bin goes up by one. Over time, we get a distribution of visits, in this case a random one. + +## Random walk, but with an acceptance criteria + +The Metropolis-Hastings algorithm works in a similar way, but differs crucially in one way - after choosing a random step for the walker (left or right), a decision is made about whether to __reject__ or __accept__ the step. This decision is guided by $$f(x)$$, or any function that is proportional to the target probability function. + +

+ <FIG> Metropolis Walk in 1D +

+ +## The function for generating a random step + +So far we used a very simple function for generating the next step: it will be either +1 or -1 to the current location. For the simple version of the algorithm to work, this can actually be any symmetric function. For example, it can be any real number between $$-a$$ and $$+a$$, or it can be sampled from some symmetric distribution, $$g$$, such as a Gaussian. + +## The full algorithm for a 1D example function + +### Initialize + +Let our target distribution be: +$$ +P(x) = \frac{\exp\left[ -x^4 + x^3 - 2x^2 - x \right]}{\int_{-10}^{10} \exp\left[ -x^4 + x^3 - 2x^2 - x \right]} +$$ + +and the function which is proportional to it is +$$ +f(x) = \exp\left[ -x^4 + x^3 - 2x^2 - x \right] +$$ + +{% method %} +{% sample lang="py" %} +[import:4-8, lang:"python"](code/python/metropolis.py) +{% endmethod %} + +Next, we choose some symmetric step generating function. Here we will use a random number in the interval $$(-1,1)$$ +{% method %} +{% sample lang="py" %} +[import:10-14, lang:"python"](code/python/metropolis.py) +{% endmethod %} + +Choose the domain of $$x$$, and an initial point for $$ x_0 $$ ($$x_t$$ at $$t = 0$$) chosen randomly from the domain of $$x$$. +{% method %} +{% sample lang="py" %} +[import:30-31, lang:"python"](code/python/metropolis.py) +{% endmethod %} + +Then iterate: + +1. Generate new position $$x' = x_t + g()$$ +2. Calculate the acceptance probability, $$A = \min\left(1, \frac{f(x_{t+1})}{f(x)}\right)$$ +3. Choose a random real number, $$u$$, between $$0$$ and $$1$$ +4. Accept or reject: + * If $$ u \leq A $$, then __accept__ move, and set new position, $$x_{t+1} = x' $$ + * Otherwise, __reject__ move, and set new position to current, $$x_{t+1} = x_t $$ +5. Increment $$t \rightarrow t + 1$$ and repeat from step 1. + +The code for steps 1 to 4 is: +{% method %} +{% sample lang="py" %} +[import:19-31, lang:"python"](code/python/metropolis.py) +{% endmethod %} + +The following plot shows the result of running the algorithm for different numbers of iterations ($$N$$), with the same initial position. The histograms are normalized so that they integrate to 1. We can see the convergence toward $$P(x)$$ as we increase $$N$$. + +

+ <FIG> multiple histograms +

+ +## Full Example Code +The following code puts everything discussed together, and runs Metropolis-Hastings algorithm for $$N$$ steps. All the positions visited by the algorithm are then written to a file, which can be later read and fed into a histogram or other density calculating scheme. +{% method %} +{% sample lang="py" %} +[import, lang:"python"](code/python/metropolis.py) +{% endmethod %} + + +# === Monte Carlo === + + + + +## License + +##### Code Examples + +The code examples are licensed under the MIT license (found in [LICENSE.md](https://github.com/algorithm-archivists/algorithm-archive/blob/master/LICENSE.md)). + +##### Text + +The text of this chapter was written by [K. Shudipto Amin](https://github.com/shudipto-amin) and is licensed under the [Creative Commons Attribution-ShareAlike 4.0 International License](https://creativecommons.org/licenses/by-sa/4.0/legalcode). + +[

](https://creativecommons.org/licenses/by-sa/4.0/) + +##### Images/Graphics +- The image "[squarecircle](res/square_circle.png)" was created by [James Schloss](https://github.com/leios) and is licensed under the [Creative Commons Attribution-ShareAlike 4.0 International License](https://creativecommons.org/licenses/by-sa/4.0/legalcode). +- The animation "[simplemontecarlo](res/monte_carlo.gif)" was created by [James Schloss](https://github.com/leios) and is licensed under the [Creative Commons Attribution-ShareAlike 4.0 International License](https://creativecommons.org/licenses/by-sa/4.0/legalcode). + + +##### Pull Requests + +After initial licensing ([#560](https://github.com/algorithm-archivists/algorithm-archive/pull/560)), the following pull requests have modified the text or graphics of this chapter: +- none From 7af56cb53b7654a9cb8537bc45c5a6f1cc41e74f Mon Sep 17 00:00:00 2001 From: Kazi Shudipto Amin Date: Sat, 6 Nov 2021 10:18:46 -0600 Subject: [PATCH 03/76] Add image for 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HcmV?d00001 From 701cbbc3155fd10eecd288dd4201441553d398e1 Mon Sep 17 00:00:00 2001 From: Kazi Shudipto Amin Date: Sat, 6 Nov 2021 14:13:53 -0600 Subject: [PATCH 04/76] Update .gitignore, SUMMARY.md, and metropolis --- .gitignore | 2 +- SUMMARY.md | 1 + .../metropolis_hastings/metropolis_hastings.md | 14 +++++++++----- 3 files changed, 11 insertions(+), 6 deletions(-) diff --git a/.gitignore b/.gitignore index 231da8ea1..909c069ae 100644 --- a/.gitignore +++ b/.gitignore @@ -478,7 +478,7 @@ paket-files/ # Python Tools for Visual Studio (PTVS) __pycache__/ *.pyc - +*.ipynb_checkpoints* # Cake - Uncomment if you are using it # tools/** # !tools/packages.config diff --git a/SUMMARY.md b/SUMMARY.md index d76af219d..4819e329f 100644 --- a/SUMMARY.md +++ b/SUMMARY.md @@ -22,6 +22,7 @@ * [Tree Traversal](contents/tree_traversal/tree_traversal.md) * [Euclidean Algorithm](contents/euclidean_algorithm/euclidean_algorithm.md) * [Monte Carlo](contents/monte_carlo_integration/monte_carlo_integration.md) +* [Metropolis Hastings](contents/metropolis_hastings/metropolis_hastings.md) * [Matrix Methods](contents/matrix_methods/matrix_methods.md) * [Gaussian Elimination](contents/gaussian_elimination/gaussian_elimination.md) * [Thomas Algorithm](contents/thomas_algorithm/thomas_algorithm.md) diff --git a/contents/metropolis_hastings/metropolis_hastings.md b/contents/metropolis_hastings/metropolis_hastings.md index e9739eab7..acf0d099a 100644 --- a/contents/metropolis_hastings/metropolis_hastings.md +++ b/contents/metropolis_hastings/metropolis_hastings.md @@ -42,23 +42,27 @@ So far we used a very simple function for generating the next step: it will be e Let our target distribution be: $$ -P(x) = \frac{\exp\left[ -x^4 + x^3 - 2x^2 - x \right]}{\int_{-10}^{10} \exp\left[ -x^4 + x^3 - 2x^2 - x \right]} +P(x) = \frac{f(x)}{\int_{-10}^{10} f(x)} $$ -and the function which is proportional to it is +where $$f(x)$$ is the function proportional to it, $$ -f(x) = \exp\left[ -x^4 + x^3 - 2x^2 - x \right] +f(x) = 10e^{-4(x+4)^2} + 3e^{-0.2(x+1)^2} + e^{-2(x-5)^2} $$ {% method %} {% sample lang="py" %} -[import:4-8, lang:"python"](code/python/metropolis.py) +[import:4-13, lang:"python"](code/python/metropolis.py) {% endmethod %} +We chose a sum of three Guassians because it is easy to verify - we know what the integral of it will be. The plot of $$P(x)$$ in the figure below shows three different peaks of varying width and height, with some overlap as well. +

+ <FIG> Plot of P(x) +

Next, we choose some symmetric step generating function. Here we will use a random number in the interval $$(-1,1)$$ {% method %} {% sample lang="py" %} -[import:10-14, lang:"python"](code/python/metropolis.py) +[import:15-17, lang:"python"](code/python/metropolis.py) {% endmethod %} Choose the domain of $$x$$, and an initial point for $$ x_0 $$ ($$x_t$$ at $$t = 0$$) chosen randomly from the domain of $$x$$. From 32ae4513676608822c170c2047c65c5bdc3b4281 Mon Sep 17 00:00:00 2001 From: Kazi Shudipto Amin Date: Sat, 6 Nov 2021 14:36:59 -0600 Subject: [PATCH 05/76] Untrack .ipynb_checkpoints --- .../metropolis-checkpoint.ipynb | 251 ------------------ .../metropolis-checkpoint.py | 54 ---- .../monte_carlo-checkpoint.py | 35 --- 3 files changed, 340 deletions(-) delete mode 100644 contents/metropolis_hastings/code/python/.ipynb_checkpoints/metropolis-checkpoint.ipynb delete mode 100644 contents/metropolis_hastings/code/python/.ipynb_checkpoints/metropolis-checkpoint.py delete mode 100644 contents/metropolis_hastings/code/python/.ipynb_checkpoints/monte_carlo-checkpoint.py diff --git a/contents/metropolis_hastings/code/python/.ipynb_checkpoints/metropolis-checkpoint.ipynb b/contents/metropolis_hastings/code/python/.ipynb_checkpoints/metropolis-checkpoint.ipynb deleted file mode 100644 index 0c281b0db..000000000 --- a/contents/metropolis_hastings/code/python/.ipynb_checkpoints/metropolis-checkpoint.ipynb +++ /dev/null @@ -1,251 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "import matplotlib.pyplot as pp\n", - "import importlib\n", - "import metropolis as met\n", - "%matplotlib widget\n", - "\n", - "pp.rcParams.update({\n", - " \"text.usetex\": True,\n", - "})\n" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 2, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "importlib.reload(met)" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [], - "source": [ - "\n", - "xmin, xmax = -10, 10\n", - "\n", - "x_dat1 = [np.random.uniform(xmin, xmax)]\n", - "x_dat2 = [np.random.uniform(xmin, xmax)]\n", - "x_dat3 = [np.random.uniform(xmin, xmax)]\n", - "\n", - "Ns = [5_00, 5_000, 50_000]\n", - "for n,x_dat in enumerate((x_dat1, x_dat2, x_dat3)):\n", - " N = Ns[n]\n", - " x = x_dat[0]\n", - " for n in range(N):\n", - " x = met.iterate(x)\n", - " x_dat.append(x)" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(array([0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6]),\n", - " [Text(0, 0, ''),\n", - " Text(0, 0, ''),\n", - " Text(0, 0, ''),\n", - " Text(0, 0, ''),\n", - " Text(0, 0, ''),\n", - " Text(0, 0, ''),\n", - " Text(0, 0, '')])" - ] - }, - "execution_count": 11, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "application/vnd.jupyter.widget-view+json": { - "model_id": "620e8924da414fcc982f420a8ec77d87", - "version_major": 2, - "version_minor": 0 - }, - "image/png": 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PlTUrU7d7Q15IspRxX1YAiYhILRgASdOqpCrcc/k9WLFiBf5b539L3d422IbR4Ci8IS/aBmfW8Dr04SFIMQkVRyrw49ofZ3QRExERlQsGQNIsOSZDiiWqfLkmgEiyhNHgaOp6UAgiHo0jHAhn3E5ERFROGABJs6ToTBfv2QGwqaop6znRmigi0QhC0RC4iQ5Rieq/CZgqkT/QapuBrleUbgXRLAyApFny9EyASx/fByBnt+7jocfh8Xiw88BOyDEGQKKSNDUK+I8r3Yol6evrg9PpRGtrK/bv359xbGBgAL29vTh48KBCrSM14TqApFnS9EwF8OwAmEv6/dIDJBGVIEEHmFcr8yUs/ePVYrFgeHgYw8PDefzPWLzOzk4IgpDx1d7ennGfvr4+tLS0oKGhAV1dXbMeY7nHqXBYASTNkqMzAS7bZuHZpHcVpwdIIipBtauA+99X5rkfvHTJVUibzQabzQan04mhoaE8N2xxuru70dvbm/XYwMAA+vv7U23s7OyE0+lM3X+5x6mwWAEkzUofA7iUCmD6+URE+dTb2wu32614FbCxsTHnMafTif7+/lRg3bFjB/r6+vJ2nAqLAZA0K70LdykVQDnCLmAiKgybzQa73Y6enh6lm5KVx+OBKIqw2+2p21pbWwEAbrd72cep8BgASbNYASSiUtbb2wuXywWPx6NYG4aGhrKO0cvVJpvNBo/Hs+zjVHiqGwPY19cHi8UCABBFEd3d3Ys6v729XfExF1Qc8rQMAYmt35YUACMMgERUOK2trWhtbUVvby/6+/sXfN5CJ1Ns2LABDodjzvvs27cPe/bsgc1mQ1tbGzo7OzE4OLjgtlDpUlUATI4dSP5Au91udHV1LfiN43K5WHrWECkqQQ89gCV2AUfZBUxEhdXb24v29vZFTYxYTFic77mtVmuqqJJsiyiKc55ntVoLepzyQ1VdwD09PRl/zdjtdgwMDCzoXFEUMT4+XqimUQlKD3CsABJRKbLb7bDZbIqMBbTZbKnwl7wOJLp/k5fPDoMejwcWi2XZx6nwVFMBTA4ozfaD43a7MwaaZrN7925s2bKF6xBpSPoyLiaTaUHnsAJIRMXW29uLzs7OBVcB89UFnB70AKRmJCeDocVigdvtRkdHR8bx5Oftco9TYakqAGZjsVjmLVcvJCACQCQSQSQSSV33+XyLaiOVlmSAq6yshE63sGJ4ZWUlBCExbpDrABJRMXR0dMBisSy4azcfXcAejwcbNmzAjh070NHRAY/HA6fTCYfDkdElnNy1xGq1Ytu2bRnj7pd7nApLNQEwF6vVOm/XriiKsNls8wbFnp4efO9738tj60hJyVm8C+3+BQBBEFLVQlYAiUrc1MnEgsxKPXce9fb2oqurK6MiV0g2mw2Dg4NwOp3o7OyEzWZDV1dXRkBzOBwQRTG1O0hHR0dGlXK5x6mwBFklO9q73W60t7fj7JfT0NCA3t7enGXugYGB1DFRFNHQ0DDrMZKyVQDXrl2LyclJ1NXV5emVUDF8YfcXcOCZA6jWV+M79u8squv/3//93/Efv/sPhHQhXN5xOfZ07ilgS4kom3A4jJGREaxbt272JK5l7MKRd+bVyu1GomFz/nwg8fldX1+v6c9v1VQAc/1VlKzuZTM8PIyNGzcu+DlMJtOCx4pRaZNjMmRJBvSLqwACM/eXo3LOPxaISEG1zUq3YEYptYUojaoCoMVimTVoFcg9oHR8fBzDw8OppV8OHjwIILGcjM1mSw1MJfWJT8dTlxe6BMzZ95clGXKcAZCo5HS9onQLiEqeagIgAGzfvh1utzvVpetyuTK6fj0eD1wuV2oMg91uzwiHw8PDGBgY4CBUDVjKLiBJ6YGRE0GIiKgcqWodwO7uboiiCJfLBZfLhb1792bMhnK73TlnR7lcrtQ6S06nkwtCq1x6cFtqBRDgdnBERFSeVFUBBJBRvTu7C9fhcOScDNLR0cEuXw1JD4BLHQMIZHYlExERlQtVVQCJFmo5AZAVQCIiKncMgKRJ+ZgEAnAMIBERlScGQNIkKbb0MYAZ+wEzABIRURliACRNSt/FY7FrO7ILmIiIyh0DIGlSenDjLGAiItIa1c0CJlqI9OC2rAogu4CJSs7Wn2+FN+RVuhkAgKaqJuy6dZfSzSCahQGQNGk5AZDLwBCVNm/Ii9HgqNLNWJK+vj44nU60trZi//79GccGBgbQ29ub2rWKaDnYBUyalJwEIugEGI3GRZ3LLmCi8qATdGiublbkSycs/ePVYrFgeHgYw8PDefzfWLzOzk4IgpDx1d7ennGfvr4+tLS0oKGhAV1dXbMeo9DHaelYASRNkqZ8AABdPADhf16W+461zbP2FTUYDBD0AhBlACQqZU1VTdjTuUeR524bbFtyFdJms8Fms8HpdGJoaCjPLVuc7u5u9Pb2Zj02MDCA/v7+VBs7OzvhdDpT9y/0cVoeBkDSpGRw0xkA+I8v+ny9UQ+EOQaQiAqjt7cXLS0tGB4eRmtrq2LtaGxszHnM6XRicHAQNpsNALBjxw5s2LAhFdAKfZyWh13ApEnSmWVgBIMAmFfP/pqn+0ZXkTjOAEhEhWCz2WC321N71Jcaj8cDURRht9tTtyWDqtvtLvhxWj5WAElzYrEYZEkGBEBn1AP3vz/7Tg9eOmdlMBUAYxLi8Tj0en2hmktEGtXb24sNGzbA4/GkqmDFNjQ0hP7+foyPj2PLli3o7+8HkAiA2dhstpzHinGcFo4BkDQnEomkLuuMwpIeQ2ecqRBGIhFUV1cvu11EROlaW1vR2tqK3t7eVPBaiIVOltiwYQMcDsec99m3bx/27NkDm82GtrY2dHZ2YnBwcMFtodLFAEiakxEADUsbBZGsAAJAKBRiACSigujt7UV7e/uixr0tJizO99xWqxUWiyWjLaIoznme1WpV9DgtDMcAkubkuwIYDoeX3SYiomzsdjtsNpsiYwFtNlsq/CWvA8jokj47DHo8HlgsloIfp+VjBZA0J7MCOE8AnDqZGA94Fl0slLgQDTIAElFB9fb2orOzc8FVwHx1AZ899jC5LmEyGFosFrjdbnR0dGQcT07cKPRxWh4GQNKcRVUAZSnrZBC9wXLmuIxQKJTH1hERZero6IDFYllw124+uoA9Hg82bNiAHTt2oKOjAx6PB06nEw6HI6NLOLlridVqxbZt29Dd3Z16jEIfp+VhACTNSa/Y5awA1jbP+Rg6eeYxWAEkKk3ekBdtg22KPXc+9fb2oqurq2izgW02GwYHB+F0OtHZ2QmbzYaurq6MAOZwOCCKYmp3kI6OjowqZaGP0/IIsizLSjeiXPl8PtTX12NychJ1dXVKN4cW6M0338TW/3ErAgJwwbV1ePNfPln0Y2z+7xfCs28SNTLwxD8/ixtvvLEALSWiXMLhMEZGRrBu3bqM7RmB5e3CkW/N1c2K7UaiZXP9fAD8/AZYASQNWtQYwBzSu47ZBUxUWpqqmpRuQkoptYUoHQMgaU6+A2D64xGR8nbdukvpJhCVPC4DQ5qTMQaQy8AQEZEGMQCS5uSlAph2HgMgERGVGwZA0pzMZWCWuBMIu4CJiKiMMQCS5qQHNmGJFUBBJ6TOZQWQSDlcyIKy4c/F/BgASXOSgU3QC9DplxYAgZl9hFkBJCo+gyExhzEWiyncEipF0WgUAKDX6xVuSeliACTNSQa2pVb/kgQjK4BEStHr9dDr9fD5fEo3hUqMLMuYnJyEyWSC0WhUujkli8vAkOYkA+BSx/8lJQPg9PQ0JEmCTse/p4iKRRAENDc348SJEzCZTKipqYEgLO+POipvsiwjGo1icnISU1NTOPfcc5VuUkljACRNkWU5bxXA9AAZiURQVVW1rMcjosWpr69HKBSC1+vF2NiY0s2hEmEymXDuuedqdoePhWIAJE2JRqOQJAnATAVvqdLPD4fDDIBERSYIAs455xw0NzenxnyRtun1enb7LhADIGlKPmYAZzufE0GIlJMcD0hEC8dBS6Qp+VgDMNv5nAhCRETlhAGQNCWvFUAjdwMhIqLyxABImpIRAPM4BpBdwEREVE4YAElT0it1yw2A7AImIqJyxQBImpIxBtCwzHUAOQmEiIjKFAMgaQrHABIRETEAksbkdQyggQGQiIjKEwMgaUqhxgCyC5iIiMoJAyBpSl7HALILmIiIyhQDIGkKdwIhIiJiACSNyesYQJ0A3ZkQyAogERGVEwZA0pSMMYDLrAACYAAkIqKyxABImpKsAOoMAgRdHgLgmYkg7AImIqJywgBImpIeAPNBd6YbORqNIh6P5+UxiYiICo0BkDSlUAEw/bGJiIhKHQMgaYYsyzMB0JifH/30pWQ4DpCIiMoFAyBpRj6XgEnScS1AIiIqQwyApBkZi0AvcwmYbI/DLmAiIioXDICkGZm7gLACSERE2sUASJpRkABo4H7ARERUfhgASTPSK3R5mwTCCiAREZUhBkDSjMJUABkAiYio/DAAkmZwEggREVECAyBpRmGWgeE6gEREVH4YAEkzCjIG0MAKIBERlR8GQNIMLgNDRESUYFC6AUTFUogxgIJBgCAIkGWZAZCIMtz2w9cw5p+/Z2CF2YSfffvGIrSIaAYDIGlGISqAgiDAZDIhHA6zC5iIMoz5Izjp4x+GVJoYAEkzMscA5icAAkBlZSXC4TArgESUlU4Ams2Vs24f9YchyQo0iAgMgKQhyQqdIAgQ9PkLgCaTKePxiYjSNZsr8cZ322bdvvmBPawQkmI4CYQ0IxnQTCYTBCG/FUAAiMViiMVieXtcIiKiQlFdBbCvrw8WiwUAIIoiuru757y/KIrYvXs3AODgwYPweDzYsWNH6jFIPdIDYD6lP144HEZtbW1eH5+IiCjfVFUB7OvrAwA4HA44HA60traiq6trznOcTifsdjscDgd6e3thtVrR2dlZjOZSkSUDYLJily/pj8duYCIiKgeqCoA9PT1wOByp63a7HQMDA3Oe4/F44HK5UtdbWlqwb9++grWRlBGPxxGNRgHkvwKYHgA5EYSIiMqBarqAPR4PRFHM2nXrdrtht9uznjc0NJRxfe/evTnvS+UrvTJnMpmAPBbq0gMlK4BERFQOVBUAs7FYLBBFcUGP4XK5IIoiBgcHsx6PRCIZH/A+n2/R7SRlFDIAsgJIRETlRlVdwNlYrVaMj4/PeR9RFDEwMACPx4POzs6cE0B6enpQX1+f+lq7dm0BWkyFMCsA5tHZk0CIiIhKneoD4HzhD0hUCR0OR2rGcENDQ9aq4fbt2zE5OZn6OnLkSL6bSwWSHsw4CYSIiLRONQHQZrNlvV0UxTmPOZ3OjLBnt9shiiLcbves+5tMJtTV1WV8UXkoZAWQXcBERFRuVBUALRZL1rGAuSZ1eDwe9PX1ZVQJk2GQ6wCqS7G6gFkBJCKicqCaAAgkumjTK3culytjWZhk4EtqbW1Fd3d3RoVw165daG1t5UxglWEFkIiIaIYis4CfffZZ3H777Xl/3O7ubvT19aXW9du7dy/6+/tTx91uN/r7+zN2B9m+fXtGKBRFEXv27Ml720hZhRwDyEkgRERUbhQJgB0dHRAEAV1dXejs7MTNN9+ct8dOD3cdHR0Zx5I7hKSzWCzzbhdH5a9YFUB2ARMRUTlQpAv4xRdfxO23346HHnoIdrsdjY2N+O53v4tDhw4p0RzSgEIGQKPRCJ0u8VZiBZCIiMqBIhVAu92eGmM3MDCAwcFBfP/730dvb29q/94tW7Zwli3lTSEDoCAIMJlMCIVCrAAS0aKN+sPY/EDuoUcrzCb87Ns3FrFFpAWKTwJxOBwYGhrCxMQEdu/ejQ0bNqC3txcNDQ3YunUrXn75ZaWbSCpQyDGA6Y/JCiARLZYkAyd94ZxfY37+YUn5p3gATJqYmMDIyAj27duHgwcPor6+HhMTE2hra0NjYyMefPBBpZtIZayQFcD0xwyHw5BlOe+PT0Tqs8Jswqq6ypxfOkHpFpKaKb4X8MMPP4z+/n4MDw9DlmXY7XYMDg7ijjvuSN1nYGAA3/nOd7B3714888wzCraWylUyAOr1ehgM+fux9+qAtsE2nHj3BEKjIQDAy8+8DJ0h8bdVU1UTdt26K2/PR0TqMV+37uYH9uCkj70KVBiKBMC3334b/f39GBgYgCzLsFgs+Od//md0dXVh3bp1s+7vcDhgtVqxdetWBkBakmQAzHf1TxIEjAZH4Zf8iEQTz3Fq8hT0Vfq8Pg8REVE+KRIAW1tbASQmgzidTrS1tc17zsTEBOrr6wvdNFKpZADM1/i/JgmAHAMEPWBeCaFWgN/oBwA0GhvhE3yQZCkvz0VERJRvigTA7u5ubN++fVGBzm63Y//+/QVsFamVLMupyRn5qgDumowD/uOAeTVw3x78qvZX+MMf/gAA+NaXvoW/ev2vMBoczctzERER5Zsik0D27NmDkZGRnMfXr18/a9LHunXrsnYPE80nFotBkhLVuEJMADn7cTkTmIiISp0iAXD//v0YHx/PedzhcHCsH+VNoWcAA9wNhIiIyotiy8AIQu757ePj4/B4PEVsDalZsQMgK4BERFTqijYGcNOmTRnXHQ4HLBbLrPuJooiDBw+ipaWlSC0jtSv0ItBAZrBkBZCIiEpd0QKgxWLJqPrJspx1wdx169ahra0NTqezWE0jlWMFkIiIKFPRAuDQ0FDqsk6nw8DAAL7whS8U6+lJw4oRADkJhIiIyokiYwAdDgdsNpsST00axAogERFRJkXWAXzooYeUeFrSqGKMAZw1C1jxTRaJiIhyK/jH1A9+8AMIgoD7778/dduzzz67oHNvv/32QjWLNESRCmBtQZ6GiIgoLwoeALu7u9HQ0JARADs6OiAIQtZJIEmCICAejxe6eaQBxQiABoMBBoMBsViMAZCIiEpewQPgQw89NGvNv/QJIUSFVowACCSqgFNTUxwDSEREJa/gAdDhcMy6ra2trdBPS5SSHgALNQYw+dgMgEREVA4UmQV86NAhvP322xm3vf322/i7v/s7fOlLX8Jzzz2nRLNIpdIDWaErgEAicMpS7uENRERESlNkruL3v/997NmzBx9//DEAYGRkBK2trQASC0a73W64XC785V/+pRLNIxXY+vOt8Ia8AIDjvzuOsDcRAl/96asQdAK8BfjTJ726KMWk/D8BERFRnihSAdy9eze6urpS151OJwRBgMfjwfj4OG6//XY88MADSjSNVMIb8mI0OIrR4CgmA5MIRAMISkGMhccwGhyFNMde1EuVEQCnGQCJiKh0KRIARVHMWAja7XajtbUVF1xwAQDgi1/8IoaHh5VoGqlFYAwAoJNl1ExLqJGBOoOA5ric+IrF0ByLoSmPOS0jAEYZAImIqHQp0gVssVgwMTEBINH9K4oi7HZ76rgoirBYLEo0jdRCkgC9gKZ4HPYxEZG4jKaoDv9wOJR5P/PqvD3lrABYuOGGREREy6JIAGxra8P3v/99NDQ0oL+/H4IgYOvWranje/fu5VZxlBeyLGPaYAb0Mkw1RsBsybxDbXPenotdwEREVC4UCYAPP/wwWltb0dHRASAxBvCaa64BAExOTsLlcqGvr0+JppHKyHEd5Ov/GwDAZLMB995bsOdiFzAREZULRQJgfX09Dh48iJGREVitVtTX12ccHxoa4lqBlBdSbGY5lkIuAQMwABIRUflQdMv6devWzbqtvr6e4Y/yRorOBMBCLgJ99uOzC5iIiEqZogHwpZdegiiKOY/ffvvtxWsMqRIrgERERLMpEgDfeust2O32nOFPlmUIgoB4PF7chpHqpAcxBkAiIqIERQLgtm3bMDExge7ubmzatEmJJpBGKFUBjE/HoVNmmU0iIqJ5KRIAh4eH4XQ60dPTo8TTk4ZIUTm13HlBxgBOnQQevDTx+HEZ+H1i+zlpjQk6WFMLUhMREZUSRQJga2srWlpalHhq0hg5JgMVicsFqQDKEuA/DiDxZjLEIohJMqTpM28tiV3BRERUehTpo3I4HBgcHFTiqUlj4mlj8fJaAaxtTuwictZXZU0dUGHOmH1MRERUahSpAG7atAkDAwO46KKL4HA4YLFYYLVaZ92Ps4BpueRCjQHseiXrzZWm/8SU1wvp3R/l77mIiIjyTJEA2NnZCY/HAwDo7u7Oeh/OAqZ8SK/EFXoSCDBTZZRiMmSJVUAiIipNigTA/v5+JZ6WNKiYC0EDQFVVVeqyHJMBvVDw5yQiIlosRQIgd/qgYinmMjBAZsiUowyARERUmrhQGalackFmnU4Ho9FY8OfjYtBERFQOFAuAPp8PP/jBD7B+/XoYDDOFyLfeegubNm2Cz+dTqmmkIskKoMlkgiAUvho3qwJIRERUghQJgCMjI1i3bh36+/tht9shyzMflNdeey1kWcb3v/99JZpGKpMcA1iM8X9nPw8rgEREVKoUCYBOpxM2mw0ff/xx1lnAW7du5TqBtGyyLEOKJUJYMcb/AawAEhFReVAkALrdbnR1dQFA1m45m82WWiaGaMniiY06AGUqgAyARERUqhQJgFarFZOTkzmP7927F62trUVsEalRsvoHKFMBZBcwERGVKkUCYFtbGx544AF8+umns46NjIygr68PdrtdgZaRmshFXgQaYAWQiIjKgyIBsL+/HxaLBTabDd/5zncAAM899xz+7u/+DuvXr0drayt6enqUaBqpSPo2cOwCJiIimqHIQtAAMDw8jO7ubuzYsQMAcMcddwAAHA4HHnroIaWaRSqidAWQXcBERFSqFAuA9fX16O/vR39/P9566y0AiSVgiPIlPYAVqwKYHjRZASQiolKlWABMx+BHhSAXeRs4ADAYDKkdR1gBJCKiUqVIADx06FBqmRer1YprrrlGiWaQyqVX4IpVAUx/LnmaFUAiIipNRQuAPp8PPT09GBgYgCiKs453dnZix44dMJvNxWoSqVx6Ba5YFUAAqKqqmvX8REREpaQos4AffvhhrFu3Dr29vZBlGddeey22bduGbdu2oa2tDfX19di9ezcsFgsefPDBYjSJNECpCmAyAMoxGVKcVUAiIio9Ba8A/tu//Vtq67eBgYHUbN+zud1uOJ1OdHd3w2Kx4G/+5m8K3TRSOTkmI7nPjBIVQIBVQCIiKk0FDYBvvfUWnE4n2tvb8etf/3rO+9rtduzfvx+dnZ1wOBzYuHEjrr766kI2j1ROiWVggLOXgmEFkIiWZ9QfxuYH9uQ8vsJsws++fWMRW0RqUNAA2NPTg4aGBgwODi74nMHBQaxfvx49PT145plnCtg6UjspJkF/5rISXcAAIE2zAkhEyyPJwElfWOlmkMoUNAC63W50dXWhrq5uUefdcccdePjhhwvUKtKKZAVQEARUVFQU7XnTA2CcFUAiWqIV5rl7Lkb9YUj8FUNLVNAAKIoiNm3atOjzvvjFL+IHP/hBAVpEWpIMgCaTCYIgzHPv/GEFkIjyYb5u3c0P7GFlkJas4LOAbTbbos+xWq0FaAlpTXIh6GKO/wPODoD885yIiEpPUZaBIVJCcgZuMcf/AWd3AbMCSEREpafgAbCYXW9ESbIkQ46zAkhERJRNwdcB/MIXvrDoLt3x8fElP19fXx8sFguAxBjE7u7uBZ0DAAcPHgQA9Pf3L/n5qTRICi0CDXAdQCIiKn0FD4ATExOYmJhY9HlLqRwmg5zD4QAwMwt5rkDndDrR29ubut7V1YX29nYMDQ0t+vmpdCi1DRxwVhcwK4BERFSCCtoFLEnSkr/i8fiin6+npycV/oDE4tIDAwM57y+KIoaHhzP2Ju7q6oLb7YbH41n081PpkBRaBDr5fMk/X1gBJCKiUqSaSSAejweiKKa6f9O53e6c5+3bty8j7CVnLaeHQio/Uky5LmBBEKCrSLy1OAaQiIhKUcG7gIslV8XOYrHkDHMWi2VW93QyLC5l+RoqHekBsNgVQADQVQhAlLOAiYioNKkmAOZitVoXNamkp6cH/f39WSuJkUgEkUgkdd3n8+WjiVQA6V2vxa4AAoDeqAMQhxSVIUkSdDrVFNuJiEgFVP+ptJjw53Q6sXXr1oxxhOl6enpQX1+f+lq7dm2+mkl5VhIVwDPCYa7UT0REpUU1ATBXl60oigvqznW5XGhpaZlz2Zjt27djcnIy9XXkyJElt5cKS8llYABAZ5x5a4VCoaI/PxER0VxUFQAtFkvWsYB2u33Oc5Pj/pKVP1EUsz6OyWRCXV1dxheVJiVnAQOAnhVAIiIqYaoJgECiQpc+49flcmV053o8ntRagUnDw8MYHh5Ga2srPB4PPB4PBgYGuB9xmZNiyq0DCLACSEREpU1VAbC7uxuiKMLlcsHlcmHv3r0Zi0C73e6M66Iooq2tDU6nEy0tLakvp9OZdRIIlY/0CmD6wszFojPOVAAZAImIqNSobhZw+hi+jo6OjGMOhyOjIphtGRhSB8XHAFawAkhU7m774WsY80fmvd8Kswk/+/aNRWgRUf6oLgASATPLwAgAKioqiv78elYAicremD+Ckz6O4SV1YgAkVUruwKEzCkvaV3q5WAEkUg+dADSbZ/ckjPrDkLjZD5UpBkBSpWQFMD2IFRPHABKpR7O5Em98t23W7Zsf2MMKIZUtVU0CIQIAWZZTYwDTg1gx6dOCZzAYVKQNREREuTAAkupMT08j2SuTvhxLMaV3PTMAEhFRqWEAJNVJ73JVqgIo6AQIZxaDDgQCirSBiIgoFwZAUp30nTf0ClUAgZnxh6wAEhFRqWEAJNVJD4BKVQABQGdKvL2mp6cRi8UUawcREdHZGABJdUomAKZNBGE3MBERlRIGQFKdzDGAyv2IJ8cAAuwGJiKi0sIASKpTMhVAE5eCISKi0sQASKpTMgGQXcBERFSiGABJdTIDoIKzgFkBJCKiEsUASKpTCusAAoBg4hhAIiIqTQyApDoZ6wAqtBcwwC5gIiIqXQyApDolMwaQXcBERFSiDEo3gCjfkgFQ0AsQdKUxCYQBkIgKZdQfxuYH9uQ8vsJsws++fWMRW0TlgAGQVCc5BlDJCSBAIoDqDNwPmIgKS5KBk77w/HckSsMASKqTqgBWKFf9S9JzP2AiKpAVZtOcx0f9YUhykRpDZYcBkFQlHo8jGo0CUL4CCAC6MyE0FApBkiTodMq3iYjUYb5u3c0P7GFlkHLipxGpSvoEEEHBCSBJ+jMTQWRZzliehoiISEkMgKQq6SGrJAIgJ4IQEVEJYgAkVclYAkbBNQCztYEBkIiISoXyn5BEeVR6XcAzbeBMYCIiKhUMgKQqpbIPcBK7gImIqBQp/wlJlEelNgYwfTcQVgCJiKhUMACSqqQHwFIYA2hgACQiohKk/CckUR6ld7OWxELQaQHQ7/cr2BIiIqIZXAiaVCWjAriMMYC3/fA1jPkj895vvj0207uAp6amltweIipdufbiHfVzEWYqXQyApCrpFcD08LVYY/5IXlbQ1+kFVFVVIRQKMQASqRT34qVyxABIqjJrEsgy98HUCUCzuXLW7YvZY7O2tjYVAGVZhiAo3zVNRMs33168i70fUTExAJKqJAOgzihA0AlAfHkJsNlciTe+2zbr9sXssVlbW4uxsTFEo1FMT0/DZOKHAZEazLcXL1Ep4yQQUpVkF7C+BNYATDKbzanL7AYmIqJSUDqfkkTLJElSaiFoXQnMAE6qra1NXWYAJCKiUsAuYFKNcDgMWU50+epLYA3AJAbAwsjXTG0iIi1iACTVyNcSMPnGAFgY+ZqpTUSkRQyApBrpAVBvEhBXsC3p0gMgF4NO038TMDU6//1qm4GuV3IezsdMbSIirWEAJNXIWAPQqCvJAMgKYJqpUcB/fNkPk4+Z2kREWsMASKqRUQGsEBBVsC3pGADnIeiA2lWzb586CchS8dtDRKQBDICkGhkVwBKaBFJVVQW9Xo94PM4AmEXI1IyTt/8SJ0+exMTEBPx+P4LBIKQ/fBcIizDVTqL62WdRV1eHFStWYOXKlWhubla62UREZY0BkFQjYxJICQVAQRBQW1uLyclJ+Hw+pZujOFmWceLECXz4SQCfHJ3G8elxyOGds+43GI4jiBogEAOevj/jmK5Ch2itAYaVlQhYVgGY3QWstOXOUuYsZyIqJAZAUo30CqDeWDrrAAJAfX09JicnEQwGEY1GYTQalW5S0QWDQbzzzjt46623MDo6ChwMAtMSUJF9pkZQAALCmSAfDWQejAIIADgFBN4V8Yz1GVx33XVYt25dyWy1t9xZypzlTESFxABIqlGqFUAAqKurS132+/2wWq0Ktqa4/H4/Xn/9dezbtw/T09Ozjq80G3D+dddh1apVWLFiBcxmM2pqavDqzkGM6gUIUQkWfSNigRimJ6cRGY8gPBaGb8oPQAYkGR988AE++OADrFy5EjfccAOuvPLK4r/QHJY7S5mznImoEBgASTXOngRSCrw6oG2wDaffOY3JDycBAC8+/SKqmqsAAE1VTdh16y4lm1gwkUgEr776Kt544w3E45lzsteuXYtrLjfjwspp1DU1AF/5yqzzBV1iP+dmgw577vttxjFZlnHZg9chdGIMkaMz3+tTp07hueeew+9+9zuExqohVzQV5sUtwnJnKXOWMxEVAgMgqUayC1in00EwlEYAlAQBo8FRBIUgAme6MUfHR1FVmwiACIwp2LrCkGUZb731Fr75n9+Ezz8z5lHQCzCvM6NufR0q6irw1JU1gFwJCHpgcHbA8c5RxBUEAUarCYYVZtReDvxK/BV8H/sQ9p4JRAeA4HQchkYT/KvORymOESQiUhIDIKlGsgJYXV2t+DiwJgmAHEtdD1TIkKTEkib1U1HE5EpIggBI6lrmZHx8HD/96U9x6NAh+Pw+BKIBCHoB1bZqVK6vhFQpQYQIBAHoBaR+BQWzLAi9wO+hoAeCjUEYGg2oGKvA1J+mEB2PAgIQHQ/D++rHeKX1Fdx4443Q6/X5eqlERGWNAZBUI1kBrKqqUrglwK54Y8YuF8eiOuw4U5za5JXwP+NxjBrU8/aTZRl79+7F0NAQotGZFRgrz61E3RV1WNm0cvZJ/lOAHE8kOHPu401y9tAmxOsQl2TodQJWmE2JG88H5PNkBI8F8enew4gHY4Ak4+WXX8aHH36IO+64A42NjQt6TZyFS0Rqpp5PINK0WCyWCh7V1dWA0oPjz9q6rM7vBx58EADgu/hiIPQ/lGhVQYRCITz//PP44IMPUrdZLBacc9M58Jv9aK5uxp7OPbNPfPDSxE4g5tXAffMcz+KZ4ydhkSagzzFJ4qabLDj8SQjBT4LYeWAncADofbkXjdc2ovaC2lSVONc4TM7CJSI1YwAkVUifAFJVVZXoYiwhNTU10Ol0kCQJk5OTQIXSLcqPY8eOYXBwEKIopm677rrrYLfb8bOnHoUfSFTyHrx09slTJ5f13I3yBJqF8cSVLFssGyyrUXtFLUxrTPDt9SE2FQOigP/3flQeqUTdNXULGivKWbhEpEYMgKQK6WsAlmIA1Ol0MJvNM4tBKz85ddm+9MMv4ePXPoZ8JgXpK/RYcd0K/DbwWzz4/IPwQgIgJLp587Dnby5x6KA3z95KrikuAYhBqtXjnK9ejNNvn4bfcyYpngTE10TU/VkdUD3343MWLhGpEQMgqUJ6AKyurgZOK9iYHNIXg5Zi8plJEOVHlmXs2bMHH736UWpms9FqRP2mekxVT2EqeGa7u/RJHDm6cQEAtcvb1u00LGi+//1Zt//wX9ehGeMYhRXN//oy8A3gwIEDeP755zE9PY2dB3Zi4jcTaLipYVnPT0RUjhgASRUCgZmdImpqahRsSW7pi0HHw3HAVFqLVS9ENBrFT37yk4zxfjW2Gqz7s3UQdGcF2vRJHPe/V+SWZnf55ZejqakJzzzzDIDE9+HEKyfwwc0f4JJLLlG4dURExcMASKpQDgGwvr4+dTkalID6Oe5cgsLhMJ566ikcPnwYQGItPvPVZlxwxQXzT/IoIStXrsS2bdvQ/1E/AscCkOMydu3aha9+9avYuHHjoh9v1B/G5gdmv/5Rf3l3D3MWNJG6MQCSKpRDAGxomOlqjAXjc9yz9Pj9fvz4xz/GqVOnAAAmkwkrNxgxtaqiYJM8Cqm6uhqrPrcKgd8FgBOJbu2f//zn8Pv9+PznP7+odSQlGaocC8hZ0ETqxgBIqpA+BrAsAmCgfALgxMQEHn/8cUxMTABI/P/efffdcP/qSUwBBZ/kUSiCToC51Yzgn84sEwNg54GdqHuxDo3XNiK4aho1zTJCcj2y7SSSWntwHgu9X6niLGgidWIAJFUotwpgNBhHOUwBGR8fx2OPPZaYuYxEN/a99947ezHlAk7yKCRBEFBzeQ2CpiD87yZmCAfeD0AMizBfbYZOL0COZ/9OaaXbk7OgidSJAZBUIT0AVlfPs66HQurr61NrAcYCcRiVbtA8vvb013DghQOIBRNb2lXUVWDVulX4+Us/B5C2V69QOpM8smmEmLWLuqleD+gA6HTAVRfAX+eHd68XsiwDRwG/NAXztbVlEdSJiBaLAZBUIRkATSYTDCW6xZper0d9fT0mJiYQDcRhkEu3/2x8fBwHXjiQWLQagKHegOo/q8Y4xmfWWFR4v+WF0kPK2kW9K7l4tHk18NeJSRzvvvsunn32WciyjB+99Sgg+1F3dZnN1iEiWoDS/KQkWqRkACx292+uGaBJZ8+QbGhowMTEBKSYDDlammsBTkxMYOfOnanKn7HeiAvtF0JfedaevPPs1au000ID4hJybhWHqZOALGXcdOWVV0Kn0+EnP/kJACB0OARBmIAsy4uaGEJUDjjTW9sYAKnsxeNxhMOJsUjFDoCLnQGaPg4wHogDdaX1FvT5fNi5c+dM5c9swIX2C/Gbe34z+87FWuZl6mTWLtxGiHOe9k3jv+GkL4xVdZV44/7ZY9hS7T/L5ZdfDp1Oh/81/DAAIHRoCm63G3a7nSGQVIUzvbWttD59iJZAiQkg883szDVDspQDYCgUwhNPPJHa17eirgJV11XNrvwVm5y9CzdvrcoSMC8FcN41Rhx+J4JKKYzf/e53MJlM+NznPpevZyUqGZzprU2l8+lDtERKLAEzX3dIrhmSswJgiZiensaTTz6JsbExAIl2rrKtwrg8rlyj5pk9POoPIy4Doq4By5pnnCNg1q1dDbNghv8tH3Ye2ImdB3ai8beNqL8oc0xgU1UTdt26azktIFIUZ3prk+oCYF9fHywWCwBAFEV0d3fPe44oiti9ezcGBwcxNDRU4BZSvpXDEjBJVqs1dTk+VRoBMB6PY/fu3Th69CgAoLa2Fvfccw9+uuenMxM+lND1ypyH//zMh9Oqukq8sZTHX8DyNFUXVEGOyvC/d2aJmL0B1Mv1qFybZUwhEVEZUVUA7OvrAwA4HA4AgNvtRldXF/r7+3OeMzw8jH379kEURYyPK1jtoCUrpwDY1NSUGkcW88cUbg0gSRKee+45fPLJJwCAyspK3H333RlBVbXmCZiWgcsAxCCtq8SkoR4TBxILYcffjcNsMSNQF4B01iQSIqJyoaoA2NPTg5GRkdR1u92O9vb2OQNga2srWltb4XK5itFEKoByCoBGozFVoY75Y4k15xQiyzJeeOEFvPdeYg0/g8GAO++8E6tWrVKsTYWw2JnaST86HkIzxjEKK1b8y3v4xS9+gX379gEATH4TfmH6BSYrJgvW7oVa6usjIm1TTQD0eDwQRTH14ZouOYOP1KkcFoFO19yc6HqUYzJiIeUqSK+//jrefPNNAIBOp8OWLVtw3nnnKdaeQsnHXr2CIOArX/kKpqam8MEHHyASieDUq6dgvN4IKPwjp9a9iImosFQVALOxWCypWY3LFYlEEInMrJmU3B6LlDU1NZW6XFtbq2BLFmbFihWpy1GFuoEPHDiAF198MXX9L/7iL3DRRRcp0pZCWepM7Vx0Oh3uuOMOPP744zhy5Ahi4RgCrwfQ/KUcYwn7bwKmRnM+3k+nw4ibADHaAGB44Q05I9+vj4i0RTUBMBer1Zq3sX09PT343ve+l5fHouXZ+vOt8Ia8AICTr55E8GRitsJvXvwN9Cb9zDZlJSgzABZ/IsiRI0fw3HPPpa7ffPPNuPrqq2ffMTAGCEgs+JxlHT5MnSxcI/NgqTO152I0GvGNb3wDjz76KIBEN/6p351CdGsURuNZm/tNjWadXZzUDAACoF9iSCvE6yMi7VB9AMznxI7t27fjn/7pn1LXfT4f1q5dm7fHp4XzhrwYDSaqKxO+CcSiMQg6Ad6YF0JcKOltytID4HSRK4Dj4+N4+umnEYvFMPjRIPTn6vHqqVchDM7+//JCAiAAcnzOIKM11dXVuPvuu/Eff/gPIAqEvWE8//zzuOOOO7IvFC3ogNrZ4yrj/pOJbeqIiBSgmgBos9my3i6KYs5ji2UymWAyzd3tQsWlE3SolqoRN8ZhqDZgZc3KxIES3qasqakpdbmYFcBgMIgnn3wytW6i3CBDukzCWGgs+wnpYWau3T4WsJxKOWuEOKsCagGw8lodfL8XgGgQ7733HhobG3HzzTfPfoDaVcD978+6+fS/rkMzuPIAESlDVQHQYrHA4/HMCnycAKJejaZG/GXLXwIA1qxZg291fitxYJ5tyubbA3PUX7ius4qKChir9UAojmlfDJIkQacrbJ91LBbDM888g9OnTwNIVCGbL2zG6dhp6AQdmqqaZp+UHqLvf6+g7ctGye9ROj2yLxRtWrsa9RvrEXtdBAC88sorsFqt2bvTqSSVys8YkRJUEwCBRBet2+1OrQPocrlSl4HERBGXy5V1cWiuAVie4uGZCtpiJoAovQemyWIAQnFIcRljY2NYuXJlwZ5LlmX813/9Fw4fPgwg8f9011134dn/6gcEoCkWx57DWbp4p04mdsko9F6/OSj9PTotNCAuAfoc22QBgOkcE6SrarHzwE4AwOPvP45VN61C1YoqoEEPWFajSdaD+4SUJqV/xoiUpKoA2N3djb6+vtSafnv37s1YA9DtdqO/vz8jACZD4a5duzA8PAyn04lNmzaho6Oj6O2nxUsPgGazedHn59oDM2m+mZZLZWowAicSlYfjx48XNAC+9NJLqbX+jEYj7rzzzsRySdKZdFPiY/yU+h590/hvMzuN3D97myw8egUAoLKlGlNTUwiOJLrWPb/xoOGmBhhqDQAMQJxTcUudUj9jREpSVQAEkBHuzg5xDocjoyIIJLqOu7u7F7RlHJWeWGhmEsVSloDJtQdmoVVYZt56x44dw7XXXluQ53n77bfx29/+FkBiLbuOjg6sXp2lolfCY/yU+h7Np0kCIMcAQY/mzTacjJ1E6GQIkIH4/jgMmwXAVHpjUGm2Uv0ZIyok1QVA0pblVgCVYrIYEjNGZRnHjh0ryHMcOnQIP/vZz1LXb7nlFlx88cWz7ygoM8av3O2ajM+MM73vJYT/IoxHHnkEY2OJSTW7//AwdDdalG0kEVEODIBU1uKheGKtOpTHItBJOoMOerMemIzh1KlTiEazrCO3DF6vF7t27UI8ngjI1113Hf7sz/4sb4+vJrm2UlvsBIDKykrcdddd2LFjBwKBAELeaUhv+9F81dw/l9lmGQPLXyg6qdBbxc33+Pl4DiLKPwZAKmvxcByoSlwupwogABgbjMBkYhbwiRMn8rYNWzAYxFNPPYVQKAQAuPDCC3HLLbfk5bHVKJ9bqVksFnzjG9/AY489BgAIfRrCZPXc3cC5Zhkvd6HopEJvFcet6IjKEwMglbVYOFa+AbDRiPihREgbGRnJSwBMLvfS/0Y/gtEgKiwVWH3Rajz6k0dn3beUd0sphoUO7F/sBIA1a9bga1/7Gh7Z+/8BACb+NIX3338fl16aWeWbb5bxcheKLvRWcQv5f+F2dMs0z3aCKbXNQNcrhW8PqQoDIJW15BhAQRBQXV2tcGsWp6KpAqEzlz0eD2666aZlPZ4sy/jpT3+Kw4cPIxgNIqwPo6q1Ct6oF4hmOaGEd0sphkJ2SV5xxRVouKQGgQ8DkAE8++yzuO+++3DOOeek7jPfLOPlLhRd6K3iFvL/x+3olmme7QSJloMBkMrTmX1q46IIjPwnak066P7fZ2aOl/g+tQCgr9HDWJPoHjx69Cimp6dRUVGxsJOzVAZePRjEHz8JAAB0tXrUf6YBxiodmnItQyInwnMp7paiBpaLquENxBE8GsbDbz+Mx5yPYXXbahiqE792g6siqGmWEZLrAXAGKs0hx3aCqbU6iZaAAZDKkyRBFs5UAKf9MJt0wBwr+peqqhWJwBePx/HJJ5/gsssuW9iJZ1UG/ngqjpffT5T5BAhYce1qBBqMaIrFsOfIPBUEhRZ6VjtBEFDXWoeJYByB8QAQBYIvB2H5rAU6gw7QAzo9IMe1XYmlBcixnWBqxyOiJWAApLIlhSTIsgxUmFFvMQHmutl3KvF9aqtXVQBncuv777+/8ACYJOjwSdiK//L4gIrEODL7RTV49dxqBIDEEi/zBbwS/z8qeVMns87ibTJLgF6Hpk31OP6HGKKBKBAAhPcErLh+BcaCXkBQfoBcvmZBE1F5YQCkshUPxxNdIzf8Peo3bwbKcKZr1YoKVHorEQ6H8dFHHy16OZhj8UbsNt8H6fppAMDGjRtxw1e/CrjsQHAUMK8E7pt7iQ5aJjn7LN5d/jMXzKsx2vcaHnnkEUQiibR/o/VG/NPUv0LWTxaxodlxFm8BcRIHlTAGQCpbUnBm7EtdXZbqXxkQdAIuueQSvP3224hEIvjTn/6Eq6++ekHnng5KePJPPkxvTIS/Sy+9FF/5ylcSC0xT4S20clrbjObmZnR2duLJJ5+ELMt47bXXEJKnUGkrbBPnUqhZ0JSmWJM4clSh87WWJKkTAyCVrXhoZheQ+vp6BVuyPBs2bMDbb78NILF/9VVXXTVviPuaTsaBQ1WI6QEc2Imq5iqsvGQlBn4yAADwhrwFbjUttmKzfv16fPnLX8Yvf/lLAIDvjxPQmSthshaicfPjwsxFVOhJHDmq0PlaS5LUiQGQypYUlJKbgJR1AFyzZg1WrlyJU6dO4ejRo/B4PGhpacl5f6/XiwOvi5icBiAAxuppVF9TDW+Eoa/UXXfddfB6vXjzzTcBScbkm5Owcrs49ZtvEkeOCt68qxnMU4Ve7lqSpG4MgFS24uF46ge4XLuAgcRs0c9+9rNwuVwAgBdffBEOhwN6/ezlWUZGRrB7927EIhIgABX1BqxvvxB6U/alXJqqmgradlq8W265BePj48BbgDQtQXzzCD7/5Oehr8j8Hkprq6FDJSxxAT9RqK1UJDkqePOapwq93LUkSd0YAKlsJccA6nS6stoHOJ1XB7QNtkGWZRw/dhwRMQIcAB46/BAar23EiuoV2HXrLkiShNdffx179uyBJCVet9FixPrN9fjN3b9R9kXQouh0OnR0dMD5wr8gOhVGbCqGT37zCSw3WCDo0rr+DToAOkis4KjXIsaRLkdcBmd60ywMgFS2kmMA6+rqoNOV575mkiBgNHhmluAVQPCVIGRJRuD9AMbFcQQuDOD111/H8PAwxsbGUudVN1eg+rp66PWc8FGOKisrYdlog/d3HwPTEoyiHvoP9Gjc0Jga/+kNnILECT3qVsSZv5zpTWdjAKSyJMUkSNOJykg5jv9rkgDIscQV4UzXn9mAuqtqMfaWH0EBiJyIYPTEIfza9+vUeYIg4IYbbsCrnw5izKhL/GlPZckc/A4mVxyB8PEr+KtrzwcAfGntl3D99dcDAG5+5HJ4DcsIgFyCRPN0OgE4s9/0qrrZ+00ncaa3NjEAUlmKhcp7CZhdk/GcY37eXxPHbaPV8EWBIGTsPLATAFDZVAnr1Va8Kr6K08sJBlQyDHUrUHfpDQCOAUiM/7Rarbj44ouX/+DcR1bzmmpMgB9oNmffb5q0jQGQylJ6ACzHCuBcY3ouNQNrr5Jx9HQc8UAcgkFARWMFDPUG+OCDL+gD2DWoGtWrbLjp+vV45ZVXIMsyfvKTn+C+++6b/8T5KnzJGaTcR5aIsmAApLIUC8ysAdjQ0KBgS5Zoni635oevgG6lAAimxG4eZ/OfAuQ4muTss3+pvHz+85/H6dOn8d5772F6ehpPPfUUYqY4UDvH2NaFVvi4jywRZcEASGUpOk8AvO2Hr2HMH8l5fqnPfkt1EZtXZ9/KLfnhPd8+vyWs3L9H+TLqD+P6npcgxc3wvuPHtC8x2af6nEkYb7Ji3CigbTBL912DHrCsRlNcwi7/HEGRez0TURYMgFSW0iuAVuvsrRTG/BF1zHpb6gKxZUA136NlSt+LV1p3PYLvvAgpMgWDL4bgHyZhucEyM1M8nV4AYAAEGbj/veI2mvJi68+3LmjXnqaqJuy6dVcRWkRawgBIZSkaTARAQTf3JBCdkBgAnUvJz35b6gKxZaTsv0dLlP11VSJ6/S0Y2/cCqmQgPBqGvHcSzTdfOGt7QC4TU/68IW/2cH+W0eBo9irwGQyItBQMgFR2ZFlG7EwANFTr51wDsNlciTe+W4az34q0QGwpKNvv0TLNtRfv0aPXYee25xAN+YEw8Gd//s+45ZZbMkJg26NXYJRDQFVBJ+iy7tqTHg4XEhSJFoMBkMpOIBCAFJPP7IOr0k9ArsumaWvWrMGWq+vw9B/8kAD84Q9/QF1dHT7zmc8o3TQqgKaqJuzpnD3Wd74uYm/IC4kzuWmJGACp7IyPz+xtaahRaQAkzbtwRQVuu8iA50cS14eGhlBbW4urr75a2YZR0czXrds22MbKIC0ZAyCVnYmJidRlIwNgyeIs3+W79hw9pqIR7Pn9fwIAnn/9f6HyGjMubjYBFoC/woloqfjbg8oOK4DlgbN88+PGtQL8kSDePBaHBGD3m37cdZURsKxRumlEVMYYAKnspAdAVgBLn1Zn+S7bmQk+AoBbrpERMvjx7okI4gCe/khAeE0caDYAc0yCIiLKhQGQys7YWGKhXEEnMACWAa3O8l22tIlAOgBfi8cRHRzEBx98gCiAk289AeN1UXitJi4RQkSLxgBIZUWSJHi9iVlx+ho9BB3XQSNt0Ov16OjowNNPP42DBw9CikoQfy+i4cYGjMqcCEBEi8MASGVlYmICsVgMAGCo448vaYvBYMDXv/51/PjHP0b1R9VAFIjtjaHp802oqKvIuC+XCFHe1no9vJbVgKAHslRpF7ILCFGh8BOUykqy+xcA9Oby7f6db4Zs0gqzac4Fg0l7jEYj7rzzTsRiMRw7dgwAUDNeg3tvvRcrV65M3Y9LhCjPqwNG9Wc+Zgv4vfCGvPPvF51tS8mk2mauPapBDIBUVkZHZ36JGszl++PLGbK0HCaTCXfffTeeeOIJHD9+HIFAADt37sS9996LVatWKd08OotOltFUszLn8fRdQERRxAcffICjR4/C5/MBAMxmM8477zxccsklqK+vn3W+JEtz7xeNmOq3lKTFK99PUNKk9AqgGrqAc82QHfWHIckKNIjKRlVVFe699178+Mc/xtGjRxEMBrFz507cc889WL16tdLNozRNErLu9JFubGwMe/bswYcffghZnv3mP3DgAF544QVccsklaGtrQ1NTU9bt49J5A6OQBCS6oM1ZfiamTib2GydNKv9PUNKU1AxgAdDX6oEyD0m5ZshufmAPK4Q0r8rKStxzzz148skncfjwYYRCIezcuRN333230k2jBZIkCa+++ipeffVVSNLcYUyWZbz//vv48MMP8fnPfx5Pf+XpOfdCTw0DMK8E7ssSQB+8lJVBDWMApLIRj8dTM4CNyRnA8TJPgETLlOwOfuqpp3Do0CFEIhE8/vjjCJqDwOzeQiohgUAALpcLIyMjqdvMZjM2bdqEiy++GI2NjQAAr9eLDz/8EPv27YPf74ckSXjppZdw6NAhdHR0oLq6WqmXQGWMK4hS2RgbG0vNAK6oNyrcGqLSUVFRgbvuugs2mw0AEI1Gcep3pxA6HFK4ZZSLKIp45JFHUuFPp9Phpptuwj/+4z/ic5/7HFauXAmDwQCDwYBVq1bhpptuwre//W189rOfhSAklr/yeDz4P//n/2ByclLJl0JlihVAKhvJGY8AYLIYMP8cWiLtSM4Ofu6553DgwAHIkgzffh9EiJBlORUaSslCZ8PPp9xmy3u9XuzcuRN+vx9AourX0dGB888/f87zKioq0NbWhpaWFrhcLkxNTWFsbAyPPvoo/vqv/xoNDQ3FaD6pBAMglY3jx2fGqlQwABLNYjAY0NHRgZqaGuw8sBMAcHT4KK79v66F9WprZghMLhEi66HUPiFanA0/OTmJJ554IhX+mpqacM8992Sd3ZvLBRdcgL/5m7/BE088gfHx8dRjfvOb34TZbC5U00llGACpbCQDoCAIMFkM8CvcHqJSJAgCvvzlL8O6z4rAcACyLOP4geM4PX4adRvroDOcGfmTXCKkBMbRzrdfdC7lNls+EAjg8ccfT3XZrly5Evfeey9qamoW/VgNDQ247777sHPnToyNjWF8fDwVAquqqvLddFIhBkAqC7FYDKdOnQKQ+Is59SFGRLMIgoD1reuhN+nhHfZClmTAC8TeiGHlZ1bCWGOEN3AKUol0Cy91v+hymi0fjUbx1FNP4fTp0wCAxsZG3HPPPUsKf0m1tbW455578Oijj0IURYyOjmLXrl245557oNeX70L5VBwMgFQWTp48mVoi4dxzzwXGFW4QUYnbdesu4Fbg4MGDGBwcRDicCEo1YzX4etvX8ddDX8boXBmh/yZgagG7V2h5F4n5/o8sAGCALMt4/vnnU+OY6+rqcO+996K2tnbZTUg+1iOPPIJAIIBDhw7hV7/6Fb761a8u+7FJ3RgAqSwcPnw4dXn16tUMgEQL1NLSgm9961t46qmnMD4+jkAggMceewy+6RDkljm6CqdGuUbcPLbqT8NryX3ce6YKJ34UxHtV7wFITOS48847FzXmbz5WqxVf//rX8dhjjyEej2Pfvn1YsWJF3h6f1IkBkMrCoUOHUpcvuOAC4D3FmrIoo/4wNj8wewHWUX95dFvNZb4ZnGp4jWrR1NSEbdu2Yffu3RgZGUmsqflHP+ITUQjX1M6/j6w/y5CLEtpFItf7bCHnLUfGXr85hI+FMfVhELgm0TV/++23F2S7vrVr1+Iv/uIv8OyzzwIAXnjhBQStQaAu709FKsEASCVPkiR8+umnAICampqy+stWklE2Y5QWS4szOMtZVVUV7r77bgwNDeGNN94AAISPhhGbjCF2nTx7a8XkJBFBBu7P8hdXCe0iofT7LNdevxExguC7QVRXJ7Zsa2trwyWXXFKwdlx11VUYHR3Fa6+9BlmWMfrGKCpuqIBX8M4d8hWcCU7KYQCkknf8+HFEIolK07p160pyPbOzrTCb8nq/UjbfDE41vEa10Ov1uOWWW3Deeefh2T/+CIjFgclpTL/kRe0VNTCfX5l6f3n1+pKZJJJLvn62lvs42fb6DQQCGBgYwOTFiRm/V199NT7zmc8s63kWoq2tDWNjY/jwww8hTUuYfGMSDTc1YFTOMlaxhGaCU/ExAFJJ2vrzrfCGEtu+iR+IGD+QGPTXVNWEHw3+CN4SnwRcTovSLtdSZ3CSci677DK8/JkW7P69B6f8MQAy8IcpXOiZxp9fVgtzpR5tDUhMEpljr1mller7LB6PY/fu3anlXtasWYPbbrutKH+8JruZH374YVQbq4EwgHeBFZ9ZMev5S2kmOBUfAyCVJG/Im9jEHMDEpxOYjk4DACprKxEOhgH+0iJalsb7f49v/WMUv/71r7Fv3z4AwMcAfmSsxq1fvhU48G0gOArUzDPkYupkojs4i59OhxE3AWK0AcBwfl9ACXvhhRdSw1bMZjO2bt0Kg6F4H7cmkwnf+MY34Pf7U7O/b1pxE26++eaM+7U9esXcM8FJ1Ur3TzsiAJgGKnwVqDHWwGK14JwV56C5uhnNcRnNsRiaSmMMOlFZMhqNuPXWW3HnnXemliQJBoPYvXs3Tv3+FOKh+PwPIkuJsYBZvpoxjnOEcTTKEwV+JaVj//792Lt3L4BEl/vWrVsV2Z3DarWis7MzVfV75ZVX8Kc//ano7aDSxQoglbTK8UrccdkdAIAbb7wRdrs9cSA5AN28WsHWKSdfe6gC5bePKuXfRRddhL//+7/Hz372M7z//vsAgMDRAEJHQ6i+thqSJEF3dldwbfO8jxv3n4Qe2vkr7fDhw/jlL3+Zun7bbbdhzZo1irWnpaUFX/ziF/HrX/8aAPDcc8+hsbERK1fOnrBC2sMASKUpMAYIQODjE8Dh/wQAXCb9GHjHmDg+dVLBximPM3Ap36qrq7Flyxa89957eOGFFwAAUlTCkb1HcNnfXYbGaxpR2ZQ22cdqAKyr0VTVlFh0OovT/7oOzRpZtHN8fBzPPPMM4vFE1XTz5s245pprlG3UmXacPHkS77zzDqLRKJ5++mk4HA5UV1cr3TRSGAMglSZJghSTEfZGgGk/LJUCzhGmAT/H/qVb6h6qQPnto0qFJwgCrrzySqxfvx4//tcfI/BhYi/h8VPjGP/1OCrPrUTt5bXQ13DgWLp4RMKTTz6JYDAIALDZbPjiF7+ocKsSBEHArbfeCq/Xi2PHjkEURQwODuLuu+9WummkMAZAKlmhw6HEHqYVZlxxfjWEuix7Zi6gG0rNljMDt5z2UaXiqqqqwiWfvQS1F9TCu9+L6cnEJCyMAmFvGHUX1iF+fhyoWNjjNULMOlFEDZNE5JiMU29O4vT5iT1+m5ubsWXLltld5goyGo3YunUrBgYGMDU1hZGREbzwwguQZRkA/6jWKgZAKkmyJCM0EkKloANu+Hu0/uM/Alar0s0i0oxkt64kSRgeHsbLL7+MQCCQOv7ES09AWiuh8crGeR9LDynrotHNACAA58jjOWcSAyjZ/YaluIzJfT4YxqPA+YkZv3fddRcqK5dWlS+kuro6bN26NbVd3N69eyGGgsBly9+PmMoTAyCVpMDxCOKBxFialpYWWBn+CkapbbSoPOh0OmzcuBFXXnklXnvtNbz++uuIxWKQYhICHwVw5MgRvLjyRWzevBl1dZn7jp0WGhCXEusNZx2qkB4KS2RXkXTp65GeTZZkeIZ9iJyKwIDEHr933XVXXvf4zbe1a9fiz//8z/Hcc88BACY+CEBn0gEXzLEnNKkWAyCVHEmSIH4UTF0vxur5Wqb0NlpUHkwmE9ra2rBp0ya89tprePz9xwEAU+EpdO3ogvCIgJo1Nai7sA6VjYmwN7a2GnGpCga5Hu9s++Wsx3z/e62wSBO5A6LC+w2nr0eaTo7JmNw3iciJxEx8nV7AXXfdVZA9fvPt6quvRjAYTM0M9v/RD78gqbaLnnJjAKSSs3fvXkz7Y4AAVDYYsW7dOqWbpEqlso0WlZe6ujp85Stfwdqxtfj0j58idCiEQDTRNTx1cAqnDp6CscGIqnVVMK02QWfUQY5nH2f2TeO/4aQvjFV1lXjj/ixjWefbb7j/JmAqyxZnZ1tmF7JO0KGpKrGfb3w6jlN/OAWD1wCDHIGgk3HJJgvOP//8JT9+sV1//fUIhULY+db/BgB8+k4Amy6XUWc7qxJoSYRySzyMnxS7kVRwDICkjBy/uCdDcbz8ugjoJUDQwXpFbVns/VuOuPYfLceqxlUwbDYgdnUM/oN++A76EI+cWTh6Coi/G4f3j6dRudqEqjUmyLKc//fy1Ojyuo7nC5ANekAvoCkWx57Dx+ENxLDrbT/GpmIAgIp4AF+/wgBbRfnNir755ptR/4saBA4GIAP49EAQtZIO1RdXz/o+SRpay1FLGABJGVl+ccclGYNvRxEOSECdGVXnVaHSalSogUQ0l7PX/ovFYnj33Xfxxhtv4NSpUwCAH731KEKHQwgdPoKL/uoiVJ9bjZo1NahsqoSgExBcFUFNs4yQXA9gjtnsubabS64HKuiA2izdr/N1Ic8XIC2rARgAOY4/eY7g+Q9iiMQTayfVGAXcdY0Rq82lM9t3MQRBwEWf3wSh9mOIfxIBAPInMoRpAU0bm6Az6LhXsMoxAJKyzvzijksyfvJHP46GI0AFYKwxwnhlbUlvRE9EMwwGA6699lpcc801OHbsGN5++20I7z4GOQ4AMiZ9k5j0TQLvAzqTDqZzTKhorkDFigrI+nlChpx9FnFK7Srg/vdn3z5fF3JSrgAp6CFFJIy+HcDuTyoBPQA90FxrwNZr6tCYXA+xTJej2n3bbuA24Pe//z1efPHF1O2rJlfhjjvuwJaffh5eAwOgWjEAkrJqVyHwt/vw3HPP4ZPAJ0BL4oOkecULmKyYBKqzb0Q/31ZoapmhmmuGrlpeH6mPIAhYs2YN1qxZg+Yj/4nAqZOIHAsi6o0gufK4HAbCIzJCh3wQBMBYH8HL617G+eefj3PPPRcm05lxpQsNVssNYFkCZDQaxWTf9Tj9zlFUyVXADf8AALjqqqtw6623oqJigYsgloEbbrgBVqsVzz77LKanp3Hy5En09/djMhiEfGGW9VdJFRgASTFxScYfj4Wx50c/wtTUFIBE+Pv617+Ol996GQjmPlcrW6Fxhi6Vs+qJf4YvHIahEdDXRxGdOIao9zBiEycgSzEYrb8FdBFMi37c97/vA5AIkBX1FTA1mWCymmBqaILRbISgy12JaqpqQvbN6M7I0YW81SzBa1kNCHpgMNEFHQvFMHVoCr5PfPD5fYnFko2JxbG/9KUv4eqrr1bluORLLrkE3/rWtzA4OIixsTHEYjGMvzeF6WMR1F7KEKhGqguAfX19sFgsAABRFNHd3V2Qc2hpZFnG8ePHcdfxEI4dqUQsEgCO/C8AgL5Sj+bNzXj5rZdzrr11tvm2QivXGaoLbXe5vj7Shsyfz0rAegnQcgmkeAzT4ilMyu8g4p1AzBdLzSQGAIyd+TpD0AkwmA0w1BtgqDNAX6OHvkYPXY0OOsMChonk6EL2WlbjlF6P+FQc058ewvTJaUyPTSd2IEo+tyCg9vxa/MM//ANqatQdhJqbm+FwOLBnzx688cYbAIDYZAwjb0zi0r+/FPUX16P6nNmTRObaD5pKl6oCYF9fHwDA4XAAANxuN7q6utDf35/Xc2h+8kOfw9TpkxDDEiaCcYxOxXHSH8NxXwzBaQmfVgIBnS6xC1E0ANM5JlRdXQV/lR/+oH/Bz7OcrdBKGWfokhrM93O89ee/gDfkRSwYQ3gsjPDpMCLeCKYnp89sU5YmmPiSTkiQICGKKIKxIHQmHSaqJ3DF766A3qSHrlKX+NeggxCJQzCsAHQC5LgMWQLkuIx4WEIsFMfEYR+i/jjkqIRqYw0MMMCgNyTG+gGoWVODhssasPqc1aoPf0lGoxG33HILLrvsMjztGUDQF4MM4PTx0zh9/DT01XpUnlsJ07kmGOoNc1ZmqbQJ8qx3WflqaGjAyMhIqpoHJP56m+slLuWcJJ/Ph/r6ekxOTs5aAb/spS2PEJdkRGKJr+n4zL/BaQkBgwXBL/4AwWAQgUAAwWAQU1NTGHjpvyMg5Z59F9TpAEFA5aoKnHvlWlStyL4Sfa6/LJP72K6qU2cAJNKySCSCY8eO4dixYzh16hROnTqF06dPQzrrd8rOAzszK4dLVGOswV9d/lcAEuscXnPNNbj22mvR0NCw7McuZ7f3X4pjJ8IQPw5hemr27/NwhQDjChNWWIzYdd+vsXLlStTWlsfSXar+/F4g1VQAPR4PRFHMCHJJbrcbdrs9L+cUw5EjRzA9nfgLWJIkyLKccXmu23Idi8fjiMViiMViiMfj+P7r38dkeBKyJJ/5yzjtX0mGPOWDFI1DiskZ3SGzCAHA861ZNweArDN4dSYdjFYjzKtMqFhZgXMqDdjz17/P338eEZU9k8kEm80Gm82Wui0Wi2FsbAxjY2OYmJjAxMQEfjHxCxgmDIiFYkt+LmONEY3NjbDb7Vi/fj1WrlxZFgGmGB46EUYzxiGvl/HxuIS9xyQcnJAgnSmQ7KwzI3A8jKPHw2i//wYAiV1R9FU6GCr10FfqoDMKaDAa8D++9jhMJhOMRiN0Oh30en3qK3ldEITUF4DUZYPBgObm8pxpXcpUFQCzsVgsEEUxL+dEIhFEIjMzTycnJwEk/pLIp6effhoTExN47d3n8Wn8VF4fOymYt7K9BMQyu2x1Rl2iG6ZaD32VHvpKM/Q1BhjqjNBV6md+ucaBUz4zNv7fP130s3qnIpBkIBaO5/3/n4hKU01NDWpqanDBBRcAAL7whS8AAOLxOILBYEZPxPT0NCRJSv3RazAYoNfrYTQaUVtbC7PZDLPZjKqqzN4Hv3/hQ1DU7tNIHcQz6yjqa4HNFwNXTks4eDqKI2IMggxI0cTx1P9aDEAkDiCaepxjAL7x3p8vqQ3n61fits/9Nf72b/92ya8jm+Tnhoo6QRdNNQEwF6vVivHx8byc09PTg+9973uzbl+7du2S20cA4F7ymUcA1P8/+WsJERHl3+klnncE43jtF044nc68tifJ7/ejvr6+II9d6lQfABcb/uY6Z/v27finf/qn1HVJkjA+Po7GxkbVdRn4fD6sXbsWR44c0eT4CK2/foD/B3z92n79AP8P1Pz6ZVmG3+/H6tWrlW6KYlQTANPHiqQTRTHnscWeYzKZZhYoPSPb+EE1qaurU90bfzG0/voB/h/w9Wv79QP8P1Dr69dq5S9JNfts2Ww2WCyWrOP6ck3mWMo5REREROVONQEQSHTRut0z48lcLldqfT8gMekjue7fQs8hIiIiUhtVBcDu7m6IogiXywWXy4W9e/dmLOjsdrtnLfA83zlaZTKZ8C//8i+zury1QuuvH+D/AV+/tl8/wP8Drb9+tVPVQtBEREREND9VVQCJiIiIaH4MgEREREQawwBIREREpDGqWQeQCs/pdKKlpQVAYreUjo4OhVuknPb2dgwNDSndjKJKzqA/ePAgAKh6slRfX19qjU9RFNHd3a1sg4pMS9/rhdDi+x3g73zVk4nmMTExIbe2tsoTExOyLMvy/v37ZS3/6AwODmru9Xd3d2dcdzgcst1uV6g1hdXb2yv39vamrg8NDckOh0PBFhWXlr7XC6HF9zt/52sDu4BpXk6nE1u3bk1VRFpbWzX51zCQqAYtZXvBciaKIoaHhyGKYuq2rq4uuN3urIuol7uenp6MtUDtdjsGBgYUbFHxaO17PR8tvt8B/s7XCgZAmtfAwAA6Ojrg8XhSi2ZrdaeU3bt3Y8uWLUo3o+j27duXEQCSWyWmBwU18Hg8EEUx6xaP6QvGq5lWvtcLodX3O3/nawMDIM0p+UGQrArYbLZURUBr3G63Jn8JWiwWTExMoLW1NXVb8vufaz/tcpWrymWxWDQRgLT0vZ6PVt/v/J2vHZwEQnNK/jKwWCypD4Xe3l6sW7cOExMTSjat6JK/DLUQBObT09OD/v7+rJUyNbJarZrsCgS0971O0ur7nb/ztYMBUGNcLhd27do17/22b9+eUQXYuHFj6nKyGlKufyEv5f9gYGBANXtEL/VnICk5Pkgt/x8LodXwp8XvNaCu9/tSqel3PmXHAKgxHR0di5rKn6vbx2KxlO2g8MX+HwwPD2f8Mix3i3396VwuF1paWlT74Zjr5z1ZDdIStX+vc1Hb+32x1Pg7n7JjAKQ52Ww22Gw2eDyejGqQKIqa+SU5Pj6O4eHh1BiY5NpofX19sNlsmlkbK/n6k4EgOUNSTcHIZrOlPujOfl1aqnxo4Xudi9bf7/ydrx2CLMuy0o2g0uZyubB371709vamrvf392t2WYDh4WFs2LABWnrrJD8Q0z/8XC4XHA6H6saGJReBToYfl8uFoaEhzSyGrKXv9UJo8f3O3/nawABICzIwMJAaDH369OnULwatSY6fc7lc6O7uRnt7u+orQ6IoYt26dVkHw6v110ey2gMg44NQ7bT4vZ6LFt/vSfydr34MgEREREQaw3UAiYiIiDSGAZCIiIhIYxgAiYiIiDSGAZCIiIhIYxgAiYiIiDSGAZCIiIhIYxgAiYiIiDSGAZCIiIhIYxgAiYiIiDSGAZCIiIhIYxgAiYiIiDSGAZCIiIhIYxgAiYiIiDSGAZCIiIhIYwxKN4CIqJT09fXBYrFgaGgI27dvR2trK/r6+gAABw8eRH9/v8ItJCJaPkGWZVnpRhARlQKn04nt27fDYrFgeHgYnZ2d6OjoQG9vL4aHh7FhwwYMDQ3Bbrcr3VQiomVhFzAREQC3241NmzbBYrEAACwWCzweDxobGwEA4+Pj6OjoYPgjIlVgBZCICIDL5UJHR0fG9c7OTkxMTKRCIRGRWjAAEhFl0dXVhX379mH//v1KN4WIKO/YBUxElIXb7WZ3LxGpFgMgEdFZPB4PPB4P2tvbM253u90KtYiIKL8YAImIkOjyHR4eBpAY/wcAGzduTB13uVywWq2KtI2IKN8YAIlI81wuFwYGBjJus1gsGB8fBwCIogiPx4PW1lYlmkdElHecBEJEmieKIpxOJzZs2ABRFNHd3Q23243BwUFs2LABAOBwOBRuJRFR/jAAEhEREWkMu4CJiIiINIYBkIiIiEhjGACJiIiINIYBkIiIiEhjGACJiIiINIYBkIiIiEhj/n9++ZcCTJokWgAAAABJRU5ErkJggg==", - "text/plain": [ - "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "\n", - "fig, ax = pp.subplots()\n", - "\n", - "xx = np.linspace(-7,7,1000)\n", - "ax.plot(xx, met.f(xx)/np.trapz(met.f(xx),x=xx), \n", - " color='k', linewidth=2, alpha=0.5,\n", - " label=\"$P(x)$\"\n", - "\n", - " )\n", - "\n", - "\n", - "for n,x_dat in enumerate((x_dat1, x_dat2, x_dat3)):\n", - " x_dat = np.array(x_dat)\n", - " #ax2 = ax.twinx(sharey=True)\n", - " bins = np.arange(-7,7.1, 0.25)\n", - " ax.hist(x_dat, bins=bins, \n", - " density=True,\n", - " histtype='step',\n", - " alpha=1,\n", - " linewidth = 2,\n", - " label=f\"N = {Ns[n]}\"\n", - " )\n", - " \n", - "ax.legend(fontsize=12)\n", - "ax.set_xlabel(\"$x$\", fontsize=16)\n", - "ax.set_ylabel(\"Density\", fontsize=16)\n", - "pp.xticks(fontsize=12)\n", - "pp.yticks(fontsize=12)" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": {}, - "outputs": [], - "source": [ - "fig.savefig(\"../../res/multiple_histograms.png\", dpi=600)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Test output of `metropolis.py`" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(array([3.99992000e-04, 9.59980800e-04, 3.19993600e-04, 1.75996480e-03,\n", - " 1.11997760e-03, 2.23995520e-03, 2.39995200e-03, 6.55986880e-03,\n", - " 3.07993840e-02, 1.10157797e-01, 2.59594808e-01, 4.28231435e-01,\n", - " 4.51030979e-01, 2.77514450e-01, 1.37597248e-01, 7.15985680e-02,\n", - " 6.95186096e-02, 7.94384112e-02, 9.27181456e-02, 1.03517930e-01,\n", - " 1.10717786e-01, 1.23037539e-01, 1.29517410e-01, 1.35197296e-01,\n", - " 1.39917202e-01, 1.29917402e-01, 1.23437531e-01, 1.14557709e-01,\n", - " 1.06797864e-01, 9.70380592e-02, 8.11983760e-02, 6.93586128e-02,\n", - " 5.41589168e-02, 4.34391312e-02, 3.65592688e-02, 2.57594848e-02,\n", - " 2.20795584e-02, 9.59980800e-03, 1.19197616e-02, 7.43985120e-03,\n", - " 3.51992960e-03, 4.39991200e-03, 3.19993600e-03, 5.59988800e-03,\n", - " 1.14397712e-02, 2.64794704e-02, 4.27191456e-02, 5.37589248e-02,\n", - " 5.33589328e-02, 5.09589808e-02, 2.52794944e-02, 1.44797104e-02,\n", - " 4.39991200e-03, 1.27997440e-03, 0.00000000e+00, 0.00000000e+00]),\n", - " array([-7. , -6.75, -6.5 , -6.25, -6. , -5.75, -5.5 , -5.25, -5. ,\n", - " -4.75, -4.5 , -4.25, -4. , -3.75, -3.5 , -3.25, -3. , -2.75,\n", - " -2.5 , -2.25, -2. , -1.75, -1.5 , -1.25, -1. , -0.75, -0.5 ,\n", - " -0.25, 0. , 0.25, 0.5 , 0.75, 1. , 1.25, 1.5 , 1.75,\n", - " 2. , 2.25, 2.5 , 2.75, 3. , 3.25, 3.5 , 3.75, 4. ,\n", - " 4.25, 4.5 , 4.75, 5. , 5.25, 5.5 , 5.75, 6. , 6.25,\n", - " 6.5 , 6.75, 7. ]),\n", - " [])" - ] - }, - "execution_count": 15, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "application/vnd.jupyter.widget-view+json": { - "model_id": "560d140d17b6451e9790069a145f86b0", - "version_major": 2, - "version_minor": 0 - }, - "image/png": 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- "text/plain": [ - "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "x_dat = np.loadtxt('output.dat')\n", - "fig, ax = pp.subplots()\n", - "\n", - "xx = np.linspace(-7,7,1000)\n", - "ax.plot(xx, met.f(xx)/np.trapz(met.f(xx),x=xx), \n", - " color='k', linewidth=2, alpha=0.5,\n", - " label=\"$P(x)$\"\n", - "\n", - " )\n", - "\n", - "x_dat = np.array(x_dat)\n", - "#ax2 = ax.twinx(sharey=True)\n", - "bins = np.arange(-7,7.1, 0.25)\n", - "ax.hist(x_dat, bins=bins, \n", - " density=True,\n", - " histtype='step',\n", - " alpha=1,\n", - " linewidth = 2,\n", - " label=f\"N = {Ns[n]}\"\n", - " )" - ] - }, - { - "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": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.7.10" - } - }, - "nbformat": 4, - "nbformat_minor": 4 -} diff --git a/contents/metropolis_hastings/code/python/.ipynb_checkpoints/metropolis-checkpoint.py b/contents/metropolis_hastings/code/python/.ipynb_checkpoints/metropolis-checkpoint.py deleted file mode 100644 index 36fc65f59..000000000 --- a/contents/metropolis_hastings/code/python/.ipynb_checkpoints/metropolis-checkpoint.py +++ /dev/null @@ -1,54 +0,0 @@ -import numpy as np -import matplotlib.pyplot as pp - -def f(x): - '''Function proportional to target distribution, a sum of Gaussians''' - # Gaussian heights, width parameters, and mean positions respectively: - a1, b1, x1 = 10, 4, -4 - a2, b2, x2 = 3, 0.2, -1 - a3, b3, x3 = 1, 2, 5 - - return a1*np.exp( -b1*(x-x1)**2 ) + \ - a2*np.exp( -b2*(x-x2)**2 ) + \ - a3*np.exp( -b3*(x-x3)**2 ) - -def g(): - '''Random step vector''' - return np.random.uniform(-1,1) - -def iterate(x, f=f, g=g): - '''Perform one full iteration and return new position''' - - x_proposed = x + g() - A = min(1, f(x_proposed)/f(x) ) - - u = np.random.uniform(0,1) - if u <= A: - x_new = x_proposed - else: - x_new = x - - return x_new - -if __name__ == "__main__": - xmin, xmax = -10, 10 - x0 = np.random.uniform(xmin, xmax) - - x_dat = [x0] # for storing values - N = 50_000 # no. of iterations - - x = x0 - for n in range(N): - x = iterate(x) - x_dat.append(x) - - # Write data to file - output_string = "\n".join(str(x) for x in x_dat) - - with open("output.dat", "w") as out: - out.write(output_string) - out.write("\n") - - - - diff --git a/contents/metropolis_hastings/code/python/.ipynb_checkpoints/monte_carlo-checkpoint.py b/contents/metropolis_hastings/code/python/.ipynb_checkpoints/monte_carlo-checkpoint.py deleted file mode 100644 index c21bb054e..000000000 --- a/contents/metropolis_hastings/code/python/.ipynb_checkpoints/monte_carlo-checkpoint.py +++ /dev/null @@ -1,35 +0,0 @@ -import math -import random - - -def in_circle(x, y, radius = 1): - """Return True if the point is in the circle and False otherwise.""" - return (x*x + y*y) < radius*radius - -def monte_carlo(n_samples, radius = 1): - """Return the estimate of pi using the monte carlo algorithm.""" - in_circle_count = 0 - for i in range(n_samples): - - # Sample x, y from the uniform distribution - x = random.uniform(0, radius) - y = random.uniform(0, radius) - - # Count the number of points inside the circle - if(in_circle(x, y, radius)): - in_circle_count += 1 - - # Since we've generated points in upper right quadrant ([0,radius], [0, radius]) - # We need to multiply the number of points by 4 - pi_estimate = 4 * in_circle_count / (n_samples) - - return pi_estimate - -if __name__ == '__main__': - - pi_estimate = monte_carlo(100000) - percent_error = 100*abs(math.pi - pi_estimate)/math.pi - - print("The estimate of pi is: {:.3f}".format(pi_estimate)) - print("The percent error is: {:.3f}".format(percent_error)) - From 37f40dbe9610d7dc174aaf1b6d2f1bd0a3111e8d Mon Sep 17 00:00:00 2001 From: Kazi Shudipto Amin Date: Sat, 6 Nov 2021 14:42:07 -0600 Subject: [PATCH 06/76] Untrack ipynb_checkpoints --- .../metropolis_hastings-checkpoint.md | 127 ------------------ 1 file changed, 127 deletions(-) delete mode 100644 contents/metropolis_hastings/.ipynb_checkpoints/metropolis_hastings-checkpoint.md diff --git a/contents/metropolis_hastings/.ipynb_checkpoints/metropolis_hastings-checkpoint.md b/contents/metropolis_hastings/.ipynb_checkpoints/metropolis_hastings-checkpoint.md deleted file mode 100644 index e9739eab7..000000000 --- a/contents/metropolis_hastings/.ipynb_checkpoints/metropolis_hastings-checkpoint.md +++ /dev/null @@ -1,127 +0,0 @@ -# Metropolis-Hastings Algorithm - -We saw how [Monte Carlo Integration](../monte_carlo_integration/monte_carlo_integration.html) uses random numbers to approximate the area of pretty much any shape we choose. -The Metropolis-Hastings algorithm is a slightly more advanced Monte Carlo method which uses random numbers to approximate a probability distribution. -What's really powerful about this approach is that you don't need to know the probability function itself - you just need a function which is _proportional_ to it. - -Why is this helpful? Well, we often have probability functions of the following form: - -$$ -P(\mathbf{x}) = \frac{f(\mathbf{x})}{\int_D f(\mathbf{x})d\mathbf{x}} -$$ -where $$D$$ is the domain, i.e., all possible values of the coordinates $$\mathbf{x}$$. -It's often easy for us to know $$f(x)$$ (eg. for a Gaussian distribution, it is $$e^{-x^2}$$). -But the integral at the bottom can be quite difficult to calculate, even numerically. -This is especially true when the coordinates ($$\mathbf{x}$$) are multidimensional, and $$f(\mathbf{x})$$ is an expensive calculation. - -## Random walk in 1D - -The Metropolis-Hastings Algorithm is very similar to a random walk, so let's first see how we can get a distribution from a random walk. - -

- <FIG> Random Walk in 1D -

- -The dot above is a "walker", whose initial position is randomly chosen. We also divide the domain into discrete locations or "bins" and set the visit counter to be zero for each bin. Then at each iteration, the walker randomly choses to go either to the right ($$x \rightarrow x+1$$) or left ($$x \rightarrow x-1$$). Each time it visits a bin, the visit count for that bin goes up by one. Over time, we get a distribution of visits, in this case a random one. - -## Random walk, but with an acceptance criteria - -The Metropolis-Hastings algorithm works in a similar way, but differs crucially in one way - after choosing a random step for the walker (left or right), a decision is made about whether to __reject__ or __accept__ the step. This decision is guided by $$f(x)$$, or any function that is proportional to the target probability function. - -

- <FIG> Metropolis Walk in 1D -

- -## The function for generating a random step - -So far we used a very simple function for generating the next step: it will be either +1 or -1 to the current location. For the simple version of the algorithm to work, this can actually be any symmetric function. For example, it can be any real number between $$-a$$ and $$+a$$, or it can be sampled from some symmetric distribution, $$g$$, such as a Gaussian. - -## The full algorithm for a 1D example function - -### Initialize - -Let our target distribution be: -$$ -P(x) = \frac{\exp\left[ -x^4 + x^3 - 2x^2 - x \right]}{\int_{-10}^{10} \exp\left[ -x^4 + x^3 - 2x^2 - x \right]} -$$ - -and the function which is proportional to it is -$$ -f(x) = \exp\left[ -x^4 + x^3 - 2x^2 - x \right] -$$ - -{% method %} -{% sample lang="py" %} -[import:4-8, lang:"python"](code/python/metropolis.py) -{% endmethod %} - -Next, we choose some symmetric step generating function. Here we will use a random number in the interval $$(-1,1)$$ -{% method %} -{% sample lang="py" %} -[import:10-14, lang:"python"](code/python/metropolis.py) -{% endmethod %} - -Choose the domain of $$x$$, and an initial point for $$ x_0 $$ ($$x_t$$ at $$t = 0$$) chosen randomly from the domain of $$x$$. -{% method %} -{% sample lang="py" %} -[import:30-31, lang:"python"](code/python/metropolis.py) -{% endmethod %} - -Then iterate: - -1. Generate new position $$x' = x_t + g()$$ -2. Calculate the acceptance probability, $$A = \min\left(1, \frac{f(x_{t+1})}{f(x)}\right)$$ -3. Choose a random real number, $$u$$, between $$0$$ and $$1$$ -4. Accept or reject: - * If $$ u \leq A $$, then __accept__ move, and set new position, $$x_{t+1} = x' $$ - * Otherwise, __reject__ move, and set new position to current, $$x_{t+1} = x_t $$ -5. Increment $$t \rightarrow t + 1$$ and repeat from step 1. - -The code for steps 1 to 4 is: -{% method %} -{% sample lang="py" %} -[import:19-31, lang:"python"](code/python/metropolis.py) -{% endmethod %} - -The following plot shows the result of running the algorithm for different numbers of iterations ($$N$$), with the same initial position. The histograms are normalized so that they integrate to 1. We can see the convergence toward $$P(x)$$ as we increase $$N$$. - -

- <FIG> multiple histograms -

- -## Full Example Code -The following code puts everything discussed together, and runs Metropolis-Hastings algorithm for $$N$$ steps. All the positions visited by the algorithm are then written to a file, which can be later read and fed into a histogram or other density calculating scheme. -{% method %} -{% sample lang="py" %} -[import, lang:"python"](code/python/metropolis.py) -{% endmethod %} - - -# === Monte Carlo === - - - - -## License - -##### Code Examples - -The code examples are licensed under the MIT license (found in [LICENSE.md](https://github.com/algorithm-archivists/algorithm-archive/blob/master/LICENSE.md)). - -##### Text - -The text of this chapter was written by [K. Shudipto Amin](https://github.com/shudipto-amin) and is licensed under the [Creative Commons Attribution-ShareAlike 4.0 International License](https://creativecommons.org/licenses/by-sa/4.0/legalcode). - -[

](https://creativecommons.org/licenses/by-sa/4.0/) - -##### Images/Graphics -- The image "[squarecircle](res/square_circle.png)" was created by [James Schloss](https://github.com/leios) and is licensed under the [Creative Commons Attribution-ShareAlike 4.0 International License](https://creativecommons.org/licenses/by-sa/4.0/legalcode). -- The animation "[simplemontecarlo](res/monte_carlo.gif)" was created by [James Schloss](https://github.com/leios) and is licensed under the [Creative Commons Attribution-ShareAlike 4.0 International License](https://creativecommons.org/licenses/by-sa/4.0/legalcode). - - -##### Pull Requests - -After initial licensing ([#560](https://github.com/algorithm-archivists/algorithm-archive/pull/560)), the following pull requests have modified the text or graphics of this chapter: -- none From 9420dc0de088fc6e3aef6ccffab4ce0ab11a03b8 Mon Sep 17 00:00:00 2001 From: Kazi Shudipto Amin Date: Sat, 6 Nov 2021 14:57:42 -0600 Subject: [PATCH 07/76] Fix algorithm steps list --- contents/metropolis_hastings/metropolis_hastings.md | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/contents/metropolis_hastings/metropolis_hastings.md b/contents/metropolis_hastings/metropolis_hastings.md index acf0d099a..7e5c643f5 100644 --- a/contents/metropolis_hastings/metropolis_hastings.md +++ b/contents/metropolis_hastings/metropolis_hastings.md @@ -66,9 +66,10 @@ Next, we choose some symmetric step generating function. Here we will use a rand {% endmethod %} Choose the domain of $$x$$, and an initial point for $$ x_0 $$ ($$x_t$$ at $$t = 0$$) chosen randomly from the domain of $$x$$. + {% method %} {% sample lang="py" %} -[import:30-31, lang:"python"](code/python/metropolis.py) +[import:34-35, lang:"python"](code/python/metropolis.py) {% endmethod %} Then iterate: From 5c894c2ab77ba4d33e9cc254e8efc5dd1d773c8b Mon Sep 17 00:00:00 2001 From: Kazi Shudipto Amin Date: Sat, 6 Nov 2021 15:04:32 -0600 Subject: [PATCH 08/76] Really fix markdown list --- contents/metropolis_hastings/metropolis_hastings.md | 5 +++++ 1 file changed, 5 insertions(+) diff --git a/contents/metropolis_hastings/metropolis_hastings.md b/contents/metropolis_hastings/metropolis_hastings.md index 7e5c643f5..6ad758e1b 100644 --- a/contents/metropolis_hastings/metropolis_hastings.md +++ b/contents/metropolis_hastings/metropolis_hastings.md @@ -56,10 +56,13 @@ $$ {% endmethod %} We chose a sum of three Guassians because it is easy to verify - we know what the integral of it will be. The plot of $$P(x)$$ in the figure below shows three different peaks of varying width and height, with some overlap as well. +

<FIG> Plot of P(x)

+ Next, we choose some symmetric step generating function. Here we will use a random number in the interval $$(-1,1)$$ + {% method %} {% sample lang="py" %} [import:15-17, lang:"python"](code/python/metropolis.py) @@ -83,6 +86,7 @@ Then iterate: 5. Increment $$t \rightarrow t + 1$$ and repeat from step 1. The code for steps 1 to 4 is: + {% method %} {% sample lang="py" %} [import:19-31, lang:"python"](code/python/metropolis.py) @@ -96,6 +100,7 @@ The following plot shows the result of running the algorithm for different numbe ## Full Example Code The following code puts everything discussed together, and runs Metropolis-Hastings algorithm for $$N$$ steps. All the positions visited by the algorithm are then written to a file, which can be later read and fed into a histogram or other density calculating scheme. + {% method %} {% sample lang="py" %} [import, lang:"python"](code/python/metropolis.py) From 794c177623b5858cb7f53dd6d9ffb54c1a6efbe9 Mon Sep 17 00:00:00 2001 From: Kazi Shudipto Amin Date: Mon, 8 Nov 2021 17:44:49 -0700 Subject: [PATCH 09/76] Add plot of P to chapter --- .../metropolis_hastings/metropolis_hastings.md | 6 +++--- contents/metropolis_hastings/res/plot_of_P.png | Bin 0 -> 157529 bytes 2 files changed, 3 insertions(+), 3 deletions(-) create mode 100644 contents/metropolis_hastings/res/plot_of_P.png diff --git a/contents/metropolis_hastings/metropolis_hastings.md b/contents/metropolis_hastings/metropolis_hastings.md index 6ad758e1b..c127d7d06 100644 --- a/contents/metropolis_hastings/metropolis_hastings.md +++ b/contents/metropolis_hastings/metropolis_hastings.md @@ -19,7 +19,7 @@ This is especially true when the coordinates ($$\mathbf{x}$$) are multidimension The Metropolis-Hastings Algorithm is very similar to a random walk, so let's first see how we can get a distribution from a random walk.

- <FIG> Random Walk in 1D + <FIG> Random Walk in 1D

The dot above is a "walker", whose initial position is randomly chosen. We also divide the domain into discrete locations or "bins" and set the visit counter to be zero for each bin. Then at each iteration, the walker randomly choses to go either to the right ($$x \rightarrow x+1$$) or left ($$x \rightarrow x-1$$). Each time it visits a bin, the visit count for that bin goes up by one. Over time, we get a distribution of visits, in this case a random one. @@ -29,7 +29,7 @@ The dot above is a "walker", whose initial position is randomly chosen. We also The Metropolis-Hastings algorithm works in a similar way, but differs crucially in one way - after choosing a random step for the walker (left or right), a decision is made about whether to __reject__ or __accept__ the step. This decision is guided by $$f(x)$$, or any function that is proportional to the target probability function.

- <FIG> Metropolis Walk in 1D + <FIG> Metropolis Walk in 1D

## The function for generating a random step @@ -58,7 +58,7 @@ $$ We chose a sum of three Guassians because it is easy to verify - we know what the integral of it will be. The plot of $$P(x)$$ in the figure below shows three different peaks of varying width and height, with some overlap as well.

- <FIG> Plot of P(x) + <FIG> Plot of P(x)

Next, we choose some symmetric step generating function. 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