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Last active July 25, 2021 14:31
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STA 2536 Data Science for Risk Modelling
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Simulations and Kernel Density Esitmation\n",
"\n",
"This notebook looks at the simulation and kernel density estimation. It foucses on data generated from the Gamma distribution, simulating random variables from it using the accept/reject method, and kernel density estimator of the probability density function from simulated data."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import numpy as np # for numerical pyhton libraries\n",
"\n",
"import scipy.stats as st # for statistical libraries\n",
"\n",
"import matplotlib.pyplot as plt # for plotting\n",
"\n",
"import matplotlib.pylab as pylab\n",
"params = {'legend.fontsize': 'x-large',\n",
" 'figure.figsize': (15, 5),\n",
" 'axes.labelsize': 'x-large',\n",
" 'axes.titlesize':'x-large',\n",
" 'xtick.labelsize':'x-large',\n",
" 'ytick.labelsize':'x-large'}\n",
"pylab.rcParams.update(params)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Plot the Gamma distribution for a few different parameters"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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JWtWspyLSfB06dIi9e/dSWlrqdyjis9jYWNLT02nXrp3foYiIhJVynTRUUlISXbp0ISqq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I1LZudxwaxJFGVE7xvYw+o+aAbCqV4NNf8wI7qBmWS49JMmeJUugawpErjEmCRRPD6hiI9Pranl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\nQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x97396d8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.linspace(0,6,1000)\n",
"\n",
"plt.subplot(1,2,1)\n",
"plt.plot(x, st.gamma.pdf(x, 1, 0, 1), label=r'$\\alpha=1$, $\\theta=1$')\n",
"plt.plot(x, st.gamma.pdf(x, 2, 0, 1), label=r'$\\alpha=2$, $\\theta=1$')\n",
"plt.plot(x, st.gamma.pdf(x, 4, 0, 1), label=r'$\\alpha=4$, $\\theta=1$')\n",
"plt.legend()\n",
"plt.xlabel(r'$x$')\n",
"plt.ylabel(r'$f_\\Gamma(x)$')\n",
"plt.title(r'Gamma PDF changing shape')\n",
"\n",
"\n",
"plt.subplot(1,2,2)\n",
"plt.plot(x, st.gamma.pdf(x, 2, 0, 0.5), label=r'$\\alpha=2$, $\\theta=0.5$')\n",
"plt.plot(x, st.gamma.pdf(x, 2, 0, 1), label=r'$\\alpha=2$, $\\theta=1$')\n",
"plt.plot(x, st.gamma.pdf(x, 2, 0, 2), label=r'$\\alpha=2$, $\\theta=2$')\n",
"plt.legend()\n",
"plt.xlabel(r'$x$')\n",
"plt.ylabel(r'$f_\\Gamma(x)$')\n",
"plt.title(r'Gamma PDF changing scale')\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Use built in random generator to simulate gamma"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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PglfgJ9GlQCIuKXMq1/mf4a3g1TjWREzV8qxgVNJTtPdOQhsAiYiISDxTgynu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\nSUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x98bdda0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"nsims=100000\n",
"\n",
"x = np.linspace(0,6,100)\n",
"Y = np.random.gamma(2, 1, nsims)\n",
"\n",
"plt.hist(Y, bins=x, label='simulation')\n",
"plt.plot(x, nsims*st.gamma.pdf(x, 2, 0, 1)*(x[1]-x[0]), linewidth=4,label='pdf')\n",
"plt.xlabel(r'$x$')\n",
"plt.ylabel(r'$f_\\Gamma(x)$')\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Use accept/reject method to generate Gamma"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def SimGamma(shape, scale, nsims):\n",
" \n",
" Y = np.zeros((nsims,1))\n",
" \n",
" a = scale*shape\n",
" c = a * np.exp( (shape-1)*np.log( (shape-1)/(1/scale-1/a) ) -1 )\n",
" \n",
" print('c=',c)\n",
" \n",
" for i in range(0,nsims):\n",
" \n",
" while True:\n",
" y = -a*np.log(np.random.uniform())\n",
" ratio = (1/c)*st.gamma.pdf(y,shape,0,scale)/(np.exp(-y/a)/a) \n",
" if np.random.uniform() < ratio:\n",
" break\n",
" \n",
" Y[i]=y\n",
"\n",
"\n",
" x = np.linspace(0,6,100)\n",
" plt.hist(Y, bins=x, label='hist')\n",
" plt.plot(x, nsims*st.gamma.pdf(x, shape, 0, scale)*(x[1]-x[0]), linewidth=4, label='gamma')\n",
" plt.plot(x, nsims*np.exp(-x/a)/a*(x[1]-x[0])*c, linewidth=4, label='scaled exp')\n",
" plt.xlabel(r'$x$')\n",
" plt.ylabel(r'Hist / pdf')\n",
" plt.legend()\n",
" plt.show()\n",
" \n",
" return Y\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"c= 1.47151776469\n"
]
},
{
"data": {
"image/png": 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ufbEJsbyy6hWeXf4s0XHRbqpQRERERKRwUaCUYqdxcGO+uPML2lZrm6bv+33f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\nZEYUKEVERERERGRGFChFRERERERkRv4PotDskzX/t4wAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0xb519a58>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"nsims=100000\n",
"\n",
"Y = SimGamma(2, 1, nsims);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Kernel Density Estimator using Gaussian Kernel\n",
"The kernel density estimator of a sample of data (of size $N$) corresponds to placing a distribution at each location of the data with weight equal to 1/N.\n",
"$$f(x) = \\frac{1}{N}\\sum_{i=1}^N \\phi_{\\epsilon}(x;y_i)$$\n",
"where $\\phi_\\epsilon(x;y)$ is the pdf of a random variable with mean $y$ and variance $\\epsilon$. Here we will look at two examples, the normal KDE and the log-normal KDE"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Normal kernel density estimator of data Y with bandwidth ep\n",
"def KD_norm(Y, ep):\n",
" \n",
" ny = Y.size;\n",
" nx = 100\n",
" x = np.linspace(0,6,nx)\n",
" f = np.zeros(nx)\n",
" \n",
" for y in Y:\n",
" f += (1/ny)*st.norm.pdf(x, y, ep) \n",
" \n",
" return f"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"#log Normal kernel density estimator of data Y with bandwidth ep\n",
"def KD_lognorm(Y, ep):\n",
" \n",
" ny = Y.size;\n",
" nx = 100\n",
" x = np.linspace(0,6,nx)\n",
" f = np.zeros(nx)\n",
" \n",
" for y in Y:\n",
" # note lognorm pdf is such that E[Y] = y, while sqrt(V[Y]) = y*sqrt(e^(ep**2)-1)\n",
" f += (1/ny)*st.lognorm.pdf(x, ep, 0, y*np.exp(-0.5*ep*ep)) \n",
" \n",
" return f"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# a useful plotting function to show the kernel density esitmate and true distribution simultaneously\n",
"def MakePlot(x,f,shape,scale, title):\n",
" plt.plot(x,f, label='KDE')\n",
" plt.plot(x, st.gamma.pdf(x,shape, 0, scale), linewidth=1, label='gamma')\n",
" plt.xlabel(r'$x$')\n",
" plt.ylabel(r'pdf')\n",
" plt.title( title + ' ep = '+ str(ep))\n",
" plt.legend()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## simulate some data"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"c= 1.47151776469\n"
]
},
{
"data": {
"image/png": 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bY+YbY/YbY6wxZuRF/b1S2y/e7srNnJI/dajSgW87fUuTsk3S9S3Yu4DO33dm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\nIiILjIKgiIiIiIjIAvP/AGJMyVH+Er9+AAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0xb51e0b8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"Y = SimGamma(2, 1, 500);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Normal KDE use a few different bandwidths"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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xjWFwEOq1wLC+Vg40sSTNfPG+6qqr2LFjB/fffz9DhgwhNTWVyy67jJqamnrn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\nK2kfhaEW9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11nS50TgLHFcYbbjz8VTv0jPLEAatf36nVnVueyaleLnBkm6Rl+NwgDmDO6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\nFELMidpWKoSYDkzUNo0RQkwXQ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NfJ8MR58PXiGNuWLxDihhfWMOqmNzjoxjeY/vu3WbVL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\nrkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0xb5eb5f8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ep_list = np.array([0.01, 0.1, 0.2])\n",
"\n",
"for idx,ep in enumerate(ep_list):\n",
" f = KD_norm(Y, ep)\n",
" plt.subplot(1,ep_list.size,idx+1)\n",
" MakePlot(x,f,2,1, 'Nrm KDE')\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Lognormal KDE using a few different bandwidths"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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iMhF4DbgfuACYAjwqIgdU9dFmTl0NvANsxRl6Mwt4TUSmqOpSv+PmAT/0PzHa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\nhBBCCCF6OUkMhRBCCCGEEKKX+38A6kq0UWaODQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0xb35ae80>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ep_list = np.array([0.01, 0.1, 0.2])\n",
"\n",
"for idx,ep in enumerate(ep_list):\n",
" f = KD_lognorm(Y, ep)\n",
" plt.subplot(1,ep_list.size,idx+1)\n",
" MakePlot(x,f,2,1, 'LogNrm KDE')\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"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": "3.6.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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