{ "cells": [ { "cell_type": "markdown", "id": "3f5fb34e", "metadata": {}, "source": [ "# Simulación de Monte Carlo — Estimación de integrales definidas\n", "\n", "**Objetivo.** Derivar el estimador de Monte Carlo de una integral definida $I=\\int_a^b g(x)\\,dx$ a partir de la variable $Y=(b-a)g(X)$, demostrar que $E[Y]=I$, aplicarlo al ejemplo clásico $\\int_0^\\pi \\sin(x)\\,dx = 2$ (Law & Kelton, *Simulation Modeling and Analysis*, Tabla 13.2) y visualizar la convergencia del estimador de forma **animada e interactiva** para mostrar en clase.\n", "\n", "Curso: Modelado de Sistemas bajo Incertidumbre · Universidad de los Andes · 2026-20\n" ] }, { "cell_type": "markdown", "id": "1331461b", "metadata": {}, "source": [ "## 0. Enunciado del ejercicio\n", "\n", "Supongamos que queremos evaluar la integral\n", "\n", "$$I = \\int_a^b g(x)\\,dx$$\n", "\n", "donde $g(x)$ es una función de valor real que no es analíticamente integrable. Para abordar este problema mediante simulación de Monte Carlo, sea $Y$ la variable aleatoria\n", "\n", "$$Y = (b-a)\\,g(X)$$\n", "\n", "donde $X$ es una variable aleatoria continua distribuida uniformemente en $[a,b]$ ($U(a,b)$).\n", "\n", "**Pregunta:** ¿cuál es el valor esperado de $Y$?" ] }, { "cell_type": "markdown", "id": "7d629f29", "metadata": {}, "source": [ "## 1. Solución — Valor esperado de $Y$\n", "\n", "Como $X \\sim U(a,b)$, su densidad es $f_X(x) = \\dfrac{1}{b-a}$ para $a \\le x \\le b$. Entonces:\n", "\n", "$$\n", "E[Y] = E\\big[(b-a)\\,g(X)\\big] = (b-a)\\,E[g(X)] = (b-a)\\int_a^b g(x)\\,f_X(x)\\,dx = (b-a)\\int_a^b g(x)\\,\\frac{1}{b-a}\\,dx = \\int_a^b g(x)\\,dx\n", "$$\n", "\n", "$$\\boxed{E[Y] = I}$$\n", "\n", "Es decir, el valor esperado de $Y$ es **exactamente** el valor de la integral que queremos estimar. Esto reduce el problema de \"evaluar una integral\" al problema de \"estimar un valor esperado\", que sabemos resolver por simulación: generamos $X_1,\\dots,X_n \\stackrel{iid}{\\sim} U(a,b)$, calculamos $Y_i=(b-a)g(X_i)$, y estimamos $I$ con la media muestral\n", "\n", "$$\n", "\\bar Y(n) = \\frac{1}{n}\\sum_{i=1}^n Y_i = (b-a)\\,\\frac{1}{n}\\sum_{i=1}^n g(X_i)\n", "$$\n", "\n", "Este estimador es **insesgado** ($E[\\bar Y(n)] = I$) y su varianza $\\mathrm{Var}[\\bar Y(n)] = \\mathrm{Var}(Y)/n \\to 0$ cuando $n \\to \\infty$, así que por la Ley (Fuerte) de los Grandes Números, $\\bar Y(n) \\to I$ con probabilidad 1." ] }, { "cell_type": "markdown", "id": "38be3197", "metadata": {}, "source": [ "## 2. Ejemplo aplicado: $I = \\displaystyle\\int_0^\\pi \\sin(x)\\,dx = 2$\n", "\n", "Este es el ejemplo clásico de Law & Kelton (Tabla 13.2): $a=0$, $b=\\pi$, $g(x)=\\sin(x)$. Por cálculo elemental, $I=2$ exactamente — lo usamos como referencia para verificar qué tan bien converge el estimador." ] }, { "cell_type": "code", "execution_count": 1, "id": "f2a2af8c", "metadata": { "execution": { "iopub.execute_input": "2026-08-14T06:55:21.459615Z", "iopub.status.busy": "2026-08-14T06:55:21.459226Z", "iopub.status.idle": "2026-08-14T06:55:22.393821Z", "shell.execute_reply": "2026-08-14T06:55:22.393402Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Con n=100 muestras: Ȳ(100) = 1.9258 (valor exacto I = 2.0)\n" ] } ], "source": [ "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "from matplotlib import animation\n", "from IPython.display import HTML\n", "\n", "np.random.seed(2026)\n", "\n", "a, b = 0.0, np.pi\n", "g = np.sin\n", "I_exacto = 2.0\n", "\n", "def estimar_montecarlo(n, semilla=None):\n", " \"\"\"Estima I = (b-a) * E[g(X)] con n muestras X ~ U(a,b).\"\"\"\n", " if semilla is not None:\n", " np.random.seed(semilla)\n", " X = np.random.uniform(a, b, size=n)\n", " Y = (b - a) * g(X)\n", " return Y.mean(), X, Y\n", "\n", "Ybar_100, _, _ = estimar_montecarlo(100, semilla=2026)\n", "print(f\"Con n=100 muestras: Ȳ(100) = {Ybar_100:.4f} (valor exacto I = {I_exacto})\")\n" ] }, { "cell_type": "markdown", "id": "86ca59b6", "metadata": {}, "source": [ "## 3. Reproduciendo la Tabla 13.2 (Law & Kelton)\n", "\n", "En el libro, $\\bar Y(n)$ se calcula como el promedio acumulado de una **misma** secuencia de muestras a medida que $n$ crece (no corridas independientes por cada $n$). Replicamos ese experimento con nuestra propia semilla y comparamos contra los valores originales del libro." ] }, { "cell_type": "code", "execution_count": 2, "id": "8cfc7510", "metadata": { "execution": { "iopub.execute_input": "2026-08-14T06:55:22.396052Z", "iopub.status.busy": "2026-08-14T06:55:22.395891Z", "iopub.status.idle": "2026-08-14T06:55:22.408700Z", "shell.execute_reply": "2026-08-14T06:55:22.408343Z" } }, "outputs": [ { "data": { "application/vnd.microsoft.datawrangler.viewer.v0+json": { "columns": [ { "name": "index", "rawType": "int64", "type": "integer" }, { "name": "n", "rawType": "int64", "type": "integer" }, { "name": "Ȳ(n) — nuestra corrida", "rawType": "float64", "type": "float" }, { "name": "Ȳ(n) — Tabla 13.2 (libro)", "rawType": "float64", "type": "float" } ], "ref": "592553ea-e838-4131-895b-9a7b7f6ffefc", "rows": [ [ "0", "10", "2.418", "2.213" ], [ "1", "20", "2.094", "1.951" ], [ "2", "40", "2.094", "1.948" ], [ "3", "80", "1.963", "1.989" ], [ "4", "160", "1.947", "1.993" ] ], "shape": { "columns": 3, "rows": 5 } }, "text/html": [ "
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nȲ(n) — nuestra corridaȲ(n) — Tabla 13.2 (libro)
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" ], "text/plain": [ " n Ȳ(n) — nuestra corrida Ȳ(n) — Tabla 13.2 (libro)\n", "0 10 2.418 2.213\n", "1 20 2.094 1.951\n", "2 40 2.094 1.948\n", "3 80 1.963 1.989\n", "4 160 1.947 1.993" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N_MAX = 400\n", "X_all = np.random.uniform(a, b, size=N_MAX)\n", "Y_all = (b - a) * g(X_all)\n", "Ybar_all = np.cumsum(Y_all) / np.arange(1, N_MAX + 1) # promedio acumulado\n", "\n", "valores_libro = {10: 2.213, 20: 1.951, 40: 1.948, 80: 1.989, 160: 1.993}\n", "\n", "tabla = pd.DataFrame({\n", " \"n\": list(valores_libro.keys()),\n", " \"Ȳ(n) — nuestra corrida\": [round(Ybar_all[n - 1], 3) for n in valores_libro],\n", " \"Ȳ(n) — Tabla 13.2 (libro)\": list(valores_libro.values()),\n", "})\n", "tabla\n" ] }, { "cell_type": "markdown", "id": "4e295ae5", "metadata": {}, "source": [ "## 4. Visualización dinámica — Convergencia animada\n", "\n", "La siguiente celda genera una animación (con controles de reproducción) que muestra, cuadro a cuadro, cómo se van acumulando las muestras $X_i$ bajo la curva $g(x)=\\sin(x)$ (panel izquierdo) mientras el estimador $\\bar Y(n)$ converge al valor exacto $I=2$ (panel derecho, línea punteada). Queda embebida en el notebook — se puede reproducir, pausar y adelantar directamente al proyectarla en clase, sin necesidad de volver a ejecutar la celda." ] }, { "cell_type": "code", "execution_count": 3, "id": "7f8a87ee", "metadata": { "execution": { "iopub.execute_input": "2026-08-14T06:55:22.409679Z", "iopub.status.busy": "2026-08-14T06:55:22.409595Z", "iopub.status.idle": "2026-08-14T06:55:26.476535Z", "shell.execute_reply": "2026-08-14T06:55:26.473270Z" } }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", "\n", "\n", "
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Conclusiones\n", "\n", "- $E[Y] = I$: construir $Y=(b-a)g(X)$ con $X\\sim U(a,b)$ convierte cualquier integral definida en un valor esperado, que se puede estimar con una media muestral — esta es la idea central de la integración por Monte Carlo.\n", "- El estimador $\\bar Y(n)$ es insesgado y su varianza decrece como $1/n$: se nota en la tabla y en la animación que las fluctuaciones grandes de los primeros $n$ (p. ej. $\\bar Y(10)=2.21$ en el libro) se van apaciguando a medida que $n$ crece, sin necesidad de conocer una antiderivada de $g$.\n", "- El mismo esquema funciona para cualquier $g$ acotada e integrable en $[a,b]$, incluso cuando no existe una forma cerrada para $\\int g(x)\\,dx$ — que es justamente el caso de interés práctico que motiva usar Monte Carlo en primer lugar." ] } ], "metadata": { "kernelspec": { "display_name": "research (3.12.9)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, 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", 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