MCMC Toolbox

Markov Chain Monte Carlo (MCMC) methods provide a powerful approach for estimating parameters of Gaussian distributions, with the distinct advantage of handling nonlinear models effectively. To facilitate user adoption of this methodology, we have developed a comprehensive MATLAB toolbox that simplifies the implementation process. Users only need to provide source data, define appropriate data structures, and configure relevant parameters to run MCMC algorithms directly and obtain results. The toolbox features an intuitive interface that makes it accessible even for users without programming experience. The implementation includes core MCMC algorithms such as Metropolis-Hastings and Gibbs sampling, with built-in functions for proposal distribution generation, acceptance probability calculation, and chain convergence monitoring. Additionally, the toolbox offers multiple parameter configuration options and flexible result output formats, accommodating diverse user requirements. Various diagnostic functions are included to assess chain convergence through metrics like Gelman-Rubin statistics and autocorrelation plots. By automating the complex computational processes involved in MCMC estimation, this toolbox significantly enhances both the efficiency and accuracy of Gaussian distribution parameter estimation. The package includes visualization capabilities for tracking chain evolution and distribution fitting, making it a highly recommended tool for statistical analysis and probabilistic modeling applications.