Markov Chain Monte Carlo Simulation

This document provides MATLAB source code for Markov Chain Monte Carlo (MCMC) simulation. The implementation includes key functions for probability distribution sampling, state transition mechanisms, and convergence monitoring algorithms. These codes are designed to help you better understand and apply this widely-used mathematical methodology. MCMC simulation is a probability-based computational approach that employs Markov chain principles to generate random samples from complex probability distributions, making it particularly useful for solving real-world problems in Bayesian inference, optimization, and statistical modeling.

The MATLAB implementation covers essential MCMC components including: proposal distribution functions that determine candidate state generation, acceptance probability calculations using Metropolis-Hastings criteria, and burn-in period management for chain convergence. Through these practical code examples, you can learn how to implement MCMC methods in actual applications, including parameter tuning techniques and convergence diagnostics. Additionally, this document provides fundamental background knowledge and conceptual explanations covering Markov chain theory, stationary distributions, and detailed balance conditions to help you better understand the methodological principles and practical applications. We believe this resource will be valuable for both learning and practical implementation of MCMC techniques.