Advanced & Applied Topics · Simulation & Monte Carlo Methods

Simulation: Markov chain Monte Carlo (MCMC) methods

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction Simulation · Bayesian Inference

Overview

Topics covered

  • Introduction
  • Markov Chain Monte Carlo (MCMC) Methods
  • From Classical Integration to Monte Carlo Integration
  • Markov Chains in Continuous State Spaces
  • Regularity Properties
  • -Irreducibility

Related concepts

Main connections

  • Markov chain Monte Carlo (MCMC)
  • Bayes' theorem & priors
  • Time series & ARIMA
  • Variance & standard deviation
  • Linear algebra & matrices
  • Normal (Gaussian) distribution

Compatible notation

Mathematical sample in LaTeX

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

𝔼π[g(𝛉)]=∫Θg(𝛉)π(𝛉)d𝛉
View LaTeX source\mathbb{E}_{\pi}[g(\mathbf{\theta})] = \int_{\Theta} g(\mathbf{\theta}) \pi(\mathbf{\theta})\, d\mathbf{\theta}