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Last active November 9, 2020 14:29
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RandomWalkLongRun
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{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "RandomWalkLongRun",
"provenance": [],
"collapsed_sections": [],
"authorship_tag": "ABX9TyOwd0EwUt3OjiPUOsF0MUej",
"include_colab_link": true
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"<a href=\"https://colab.research.google.com/gist/neoyipeng2018/f962a7bc42304879175fb0efe55c05e8/randomwalklongrun.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "qL8lcSBheDXD"
},
"source": [
"# Unexpected Effects of Random Walks - Relative vs Absolute Difference\n",
"If we toss a fair coin many times, by law of large numbers, we expect the number of heads to approach half the number of tosses, i.e. $\\frac{n}{2}$.\n",
"\n",
"But what about the absolute differences between heads and tails? Does the law of large numbers apply to that as well?\n",
"\n",
"Let's look at it via 2 methods, simulation and the square root law."
]
},
{
"cell_type": "code",
"metadata": {
"id": "4ljlabsGWj9c"
},
"source": [
"import random\n",
"import matplotlib.pyplot as plt\n",
"plt.style.use('seaborn-dark-palette')\n",
"plt.rcParams[\"figure.figsize\"] = (11,7)"
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "XiNz8wJrXGJd"
},
"source": [
"def toss(): return 1 if random.random() < 0.5 else -1\n",
"\n",
"def randomwalkCum(tosses=10_000):\n",
" nHeads=0\n",
" diffs=[]\n",
" for i in range(tosses):\n",
" if toss() >= 0: \n",
" nHeads+=1\n",
" diffs.append(nHeads-i/2)\n",
" return diffs,nHeads/tosses"
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "SUDniJOSjG5n"
},
"source": [
"## Simulations\n",
"Unintuitively, we see that as we increase the number of tosses, the difference between the expected number of heads($\\frac{n}{2}$) and the actual heads deviate **more and more**!\n",
"\n",
"The trick is to differentiate between relative frequency and deviation. The law of large numbers implies that as we flip more coins, we will get closer and closer to 0.5 heads per toss on average. However, that does not translate to absolute difference. We can, and typically find the absolute difference increase even as relative frequency goes down. We see this in math using the square root law."
]
},
{
"cell_type": "code",
"metadata": {
"id": "hpoHtwbOiCUy",
"outputId": "13766475-8f8d-40b2-f007-e4a14127fec3",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 482
}
},
"source": [
"sim1k,prop=randomwalkCum(1_000)\n",
"print('Deviations:',sim1k[-1])\n",
"print('Relative Frequency:',prop)\n",
"plt.plot(sim1k)"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"text": [
"Deviations: -23.5\n",
"Relative Frequency: 0.476\n"
],
"name": "stdout"
},
{
"output_type": "execute_result",
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7fddcfdd0be0>]"
]
},
"metadata": {
"tags": []
},
"execution_count": 23
},
{
"output_type": "display_data",
"data": {
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\n",
"text/plain": [
"<Figure size 792x504 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "Xe7z02wSiN4h",
"outputId": "c24abfff-094c-4033-93ad-b6da7f4fc2af",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 479
}
},
"source": [
"sim100k,prop=randomwalkCum(100_000)\n",
"print('Deviations:',sim100k[-1])\n",
"print('Relative Frequency:',prop)\n",
"plt.plot(sim100k)"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"text": [
"Deviations: 249.5\n",
"Relative Frequency: 0.50249\n"
],
"name": "stdout"
},
{
"output_type": "execute_result",
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7fddcfbf22e8>]"
]
},
"metadata": {
"tags": []
},
"execution_count": 24
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 792x504 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "OxsLmbz1YtXM"
},
"source": [
"## Square Root Law\n",
"Square root law states that for a sequence of n independent events with standard deviation of $\\sigma$, the standard deviation of the sequence is $\\sqrt{n}$ * $\\sigma$. Hence it is actually expected that the deviation from the mean ($\\frac{n}{2}$) gets wider and wider from the mean, proportionately increasing by $\\sqrt{n}$!"
]
},
{
"cell_type": "code",
"metadata": {
"id": "f_RNJbJ1lIEK",
"outputId": "240db6b9-138d-4e13-96fb-322e732716d3",
"colab": {
"base_uri": "https://localhost:8080/"
}
},
"source": [
"100**0.5"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"10.0"
]
},
"metadata": {
"tags": []
},
"execution_count": 25
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "8i9IvL6vk787",
"outputId": "d24ce3cc-f412-48b7-f1f5-51653c9addb7",
"colab": {
"base_uri": "https://localhost:8080/"
}
},
"source": [
"abs(sim100k[-1]/sim1k[-1])"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"10.617021276595745"
]
},
"metadata": {
"tags": []
},
"execution_count": 26
}
]
}
]
}
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