Markov Chain Monte Carlo Simulation with MATLAB Implementation

This document presents MATLAB source code for implementing Markov Chain Monte Carlo (MCMC) simulations. MCMC is a powerful computational methodology used to approximate probability distributions of complex systems through stochastic sampling techniques. The MATLAB implementation includes key algorithmic components such as: - Metropolis-Hastings algorithm for Markov chain transitions - Proposal distribution mechanisms for state space exploration - Convergence monitoring functions to ensure sampling accuracy - Posterior distribution estimation routines This codebase enables simulation of diverse systems ranging from particle physics models to financial market analyses. The implementation features modular architecture with clearly defined functions for: - Chain initialization and burn-in period handling - Sample generation with proper mixing properties - Statistical analysis of sampled distributions - Visualization tools for convergence diagnostics The code is structured with comprehensive comments and follows MATLAB best practices, making it accessible for beginners while providing customization flexibility for advanced users. Key functions include mcmc_sampler() for core simulation logic, proposal_generator() for state transitions, and convergence_check() for monitoring sampling quality. This resource serves as both an educational tool for understanding MCMC fundamentals and a practical framework for solving real-world probabilistic modeling challenges across various scientific and engineering domains.