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@mbeltagy
Created December 9, 2015 15:55
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The error propagation enigma. Some problems are harder than they first appear
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"using Distributions\n",
"using PyPlot"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this execrise we have a random variable x that is described by a unifrom distribution. There is relationship between x and y and we desire to obtain the distribution in y. "
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"x=rand(Uniform(1,10),1000000);\n",
"y_sample=(5-x).^2;"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Applying what learned we could derive the y distribution as $$p(y)=\\frac{1}{18\\sqrt{x}}.$$\n",
"\n",
"How did we do that? Is there anything wrong with this expresion?"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7ff9442a1d50>)"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"figure(\"hist\",figsize=(7,3))\n",
"a=axes();\n",
"a[:hist](y_sample,40, normed=1, facecolor=\"green\", alpha=0.5);\n",
"y=0:0.1:25;\n",
"plot(y,1./(18*sqrt(y)),\"b\");\n",
"axis([0,25,0,0.2]);\n",
"xlabel(L\"y\");\n",
"ylabel(L\"p(y)\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The Mont Carlo simulation shown a significant discrepancy between our prediction\n",
"and the histogram. Can you explain why?\n",
"\n",
"Hint:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7ff93247d390>)"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"figure(\"hist\",figsize=(7,3))\n",
"a=axes();\n",
"a[:hist](y_sample,40, normed=1, facecolor=\"green\", alpha=0.5);\n",
"p(y)=(y<16)? 1/(9*sqrt(y)):1/(18*sqrt(y));\n",
"py=Float64[];\n",
"y=0:0.01:25\n",
"for ye in y\n",
" push!(py,p(ye))\n",
"end\n",
"plot(y,py,\"b\");\n",
"axis([0,25,0,0.2]);\n",
"xlabel(L\"y\");\n",
"ylabel(L\"p(y)\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A much better fit above. Explain why?"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 0.4.0",
"language": "julia",
"name": "julia-0.4"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "0.4.1"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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