{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"ein.tags": "worksheet-0",
"slideshow": {
"slide_type": "-"
}
},
"source": [
"# Monte Carlo sampling methods"
]
},
{
"cell_type": "markdown",
"metadata": {
"ein.tags": "worksheet-0",
"slideshow": {
"slide_type": "-"
}
},
"source": [
"\n",
"\n",
"This notebook is an element of the [risk-engineering.org courseware](https://risk-engineering.org/). It can be distributed under the terms of the [Creative Commons Attribution-ShareAlike licence](https://creativecommons.org/licenses/by-sa/4.0/).\n",
"\n",
"Author: Eric Marsden \n",
"\n",
"---\n",
"\n",
"This notebook contains an introduction to different sampling methods in Monte Carlo analysis (standard random sampling, latin hypercube sampling, and low discrepancy sequences such as that of Sobol’ and that of Halton). The notebook shows how to use Python, with the [SciPy](https://scipy.org/) and [SymPy](https://sympy.org/) libraries. See the [associated course materials](https://risk-engineering.org/monte-carlo-methods/) for more background information on stochastic simulation and to download this content as a Jupyter/Python notebook. "
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"autoscroll": false,
"ein.hycell": false,
"ein.tags": "worksheet-0",
"slideshow": {
"slide_type": "-"
}
},
"outputs": [],
"source": [
"import math\n",
"import numpy\n",
"import scipy.stats\n",
"import matplotlib.pyplot as plt\n",
"plt.style.use(\"bmh\")"
]
},
{
"cell_type": "markdown",
"metadata": {
"ein.tags": "worksheet-0",
"slideshow": {
"slide_type": "-"
}
},
"source": [
"Let’s start with a simple integration problem in 1D, \n",
"\n",
"$\\int_1^5 x^2$\n",
"\n",
"This is easy to solve analytically, and we can use the SymPy library in case we’ve forgotten how to resolve simple integrals."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"autoscroll": false,
"ein.hycell": false,
"ein.tags": "worksheet-0",
"slideshow": {
"slide_type": "-"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Analytical result: 41.333333333333336\n"
]
}
],
"source": [
"import sympy\n",
"# we’ll save results using different methods in this data structure, called a dictionary\n",
"result = {} \n",
"x = sympy.Symbol(\"x\")\n",
"i = sympy.integrate(x**2)\n",
"result[\"analytical\"] = float(i.subs(x, 5) - i.subs(x, 1))\n",
"print(\"Analytical result: {}\".format(result[\"analytical\"]))"
]
},
{
"cell_type": "markdown",
"metadata": {
"ein.tags": "worksheet-0",
"slideshow": {
"slide_type": "-"
}
},
"source": [
"We can estimate this integral using a standard Monte Carlo method, where we use the fact that the expectation of a random variable is related to its integral\n",
"\n",
"$\\mathbb{E}(f(x)) = \\int_I f(x) dx$\n",
"\n",
"We will sample a large number $N$ of points in $I$ and calculate their average, and multiply by the range over which we are integrating."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"autoscroll": false,
"ein.hycell": false,
"ein.tags": "worksheet-0",
"slideshow": {
"slide_type": "-"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Standard Monte Carlo result: 41.36907928748775\n"
]
}
],
"source": [
"N = 10_000\n",
"accum = 0\n",
"for i in range(N):\n",
" x = numpy.random.uniform(1, 5)\n",
" accum += x**2\n",
"volume = 5 - 1\n",
"result[\"MC\"] = volume * accum / float(N)\n",
"print(\"Standard Monte Carlo result: {}\".format(result[\"MC\"]))"
]
},
{
"cell_type": "markdown",
"metadata": {
"ein.tags": "worksheet-0",
"slideshow": {
"slide_type": "-"
}
},
"source": [
"If we increase $N$, the estimation will converge to the analytical value. (It will converge relatively slowly, following $1/\\sqrt(N)$). "
]
},
{
"cell_type": "markdown",
"metadata": {
"ein.tags": "worksheet-0",
"slideshow": {
"slide_type": "-"
}
},
"source": [
"## Latin hypercube sampling"
]
},
{
"cell_type": "markdown",
"metadata": {
"ein.tags": "worksheet-0",
"slideshow": {
"slide_type": "-"
}
},
"source": [
"The LHS method consists of dividing the input space into a number of equiprobable regions, then taking random samples from each region. We can use it conveniently in Python thanks to the [pyDOE library](https://pythonhosted.org/pyDOE/), which you will probably need to install on your computer, using a command such as \n",
"\n",
"> pip install pyDOE\n",
"\n",
"or if you’re using a Google CoLaboratory notebook, execute a code cell containing\n",
"\n",
"> !pip install pyDOE\n",
"\n",
"The `lhs` function in this library returns an “experimental design” consisting of points in the $[0, 1]^d$ hypercube, where $d$ is the dimension of your problem (it’s 2 in this simple example). You need to scale these points to your input domain. "
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"autoscroll": false,
"ein.hycell": false,
"ein.tags": "worksheet-0",
"slideshow": {
"slide_type": "-"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Latin hypercube result: 41.33330900198177\n"
]
}
],
"source": [
"# obtain the pyDOE library from https://pythonhosted.org/pyDOE/\n",
"from pyDOE import lhs\n",
"\n",
"seq = lhs(2, N)\n",
"accum = 0\n",
"for i in range(N):\n",
" x = 1 + seq[i][0]*(5 - 1)\n",
" y = 1 + seq[i][1]*(5**2 - 1**2)\n",
" accum += x**2\n",
"volume = 5 - 1\n",
"result[\"LHS\"] = volume * accum / float(N)\n",
"print(\"Latin hypercube result: {}\".format(result[\"LHS\"]))"
]
},
{
"cell_type": "markdown",
"metadata": {
"ein.tags": "worksheet-0",
"slideshow": {
"slide_type": "-"
}
},
"source": [
"Note that the error in this estimation is significantly lower than that obtained using standard Monte Carlo sampling (and if you repeat this experiment many times, you should find this is true in most cases)."
]
},
{
"cell_type": "markdown",
"metadata": {
"ein.tags": "worksheet-0",
"slideshow": {
"slide_type": "-"
}
},
"source": [
"## Halton’s low discrepency sequences"
]
},
{
"cell_type": "markdown",
"metadata": {
"ein.tags": "worksheet-0",
"slideshow": {
"slide_type": "-"
}
},
"source": [
"A [low discrepancy (or quasi-random) sequence](https://en.wikipedia.org/wiki/Low-discrepancy_sequence) is a deterministic mathematical sequence of numbers that has the property of low discrepancy. This means that there are no clusters of points and that the sequence fills space roughly uniformly. The [Halton sequence](https://en.wikipedia.org/wiki/Halton_sequence) is a low discrepancy sequence that has useful properties for pseudo-stochastic sampling methods (also called “quasi-Monte Carlo” methods). "
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"autoscroll": false,
"ein.hycell": false,
"ein.tags": "worksheet-0",
"slideshow": {
"slide_type": "-"
}
},
"outputs": [],
"source": [
"# adapted from https://mail.scipy.org/pipermail/scipy-user/2013-June/034744.html\n",
"def halton(dim: int, nbpts: int):\n",
" h = numpy.full(nbpts * dim, numpy.nan)\n",
" p = numpy.full(nbpts, numpy.nan)\n",
" P = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31]\n",
" lognbpts = math.log(nbpts + 1)\n",
" for i in range(dim):\n",
" b = P[i]\n",
" n = int(math.ceil(lognbpts / math.log(b)))\n",
" for t in range(n):\n",
" p[t] = pow(b, -(t + 1))\n",
"\n",
" for j in range(nbpts):\n",
" d = j + 1\n",
" sum_ = math.fmod(d, b) * p[0]\n",
" for t in range(1, n):\n",
" d = math.floor(d / b)\n",
" sum_ += math.fmod(d, b) * p[t]\n",
"\n",
" h[j*dim + i] = sum_\n",
" return h.reshape(nbpts, dim)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"autoscroll": false,
"ein.hycell": false,
"ein.tags": "worksheet-0",
"slideshow": {
"slide_type": "-"
}
},
"outputs": [
{
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",
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