MATLAB Implementation of Metropolis-Hastings Sampling with Code Description

This article discusses the Metropolis-Hastings sampling method and its MATLAB implementation. To help readers better understand this method and its practical applications, we can explore several important aspects in detail. For instance, we can examine the advantages and limitations of this sampling approach and demonstrate how to apply it to solve various real-world problems through MATLAB code examples. The implementation typically involves these key components: - Target distribution specification using function handles - Proposal distribution implementation (e.g., Gaussian random walk) - Acceptance probability calculation with logarithmic scaling for numerical stability - Markov chain initialization and burn-in period handling Additionally, we can introduce related concepts and algorithms such as Gibbs sampling and the basic Metropolis algorithm, highlighting their connections and differences with Metropolis-Hastings. For Gibbs sampling, we might show how it simplifies the acceptance probability to 1 when using full conditional distributions. Through these in-depth discussions and code demonstrations, readers will gain a comprehensive understanding of the method and be able to apply it effectively in their research and practical applications. The MATLAB implementation will include diagnostic features like trace plots and autocorrelation functions to monitor chain convergence.