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Programming & Scientific Computing · Statistical & Parallel Computing

Monte Carlo Methods Based on Markov Chains (MCMC)

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction Statistical Computing and Probability

Overview

Topics covered

  • Introduction
  • Monte Carlo Integration and Numerical Infeasibility in High Dimensions
  • Acceptance-Rejection Sampling and Importance Sampling
  • 2.1 Acceptance-Rejection Sampling
  • 2.2 Infeasibility of Acceptance-Rejection Sampling in High Dimensions
  • 2.3 Importance Sampling

Related concepts

Main connections

  • Markov chain Monte Carlo (MCMC)
  • Variance & standard deviation
  • Bayes' theorem & priors
  • Calculus & differentiation
  • Monte Carlo simulation
  • Mean & expected value

Compatible notation

Mathematical sample in LaTeX

The expression is rendered accessibly, with its LaTeX source preserved below.

E[g(X)]=∫ℝdg(x)p(x)dx
View LaTeX sourceE[g(X)] = \int_{\mathbb{R}^d} g(x) p(x) \, dx