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Markov Chain Monte Carlo (MCMC) algorithms are widely used for stochasticoptimization, sampling, and integration of mathematical objective functions, inparticular, in the context of Bayesian inverse problems and parameterestimation. For decades, the algorithm of choice in MCMC simulations has beenthe Metropolis-Hastings (MH) algorithm. An advancement over the traditionalMH-MCMC sampler is the Delayed-Rejection Adaptive Metropolis (DRAM). In thispaper, we present MatDRAM, a stochastic optimization, sampling, and Monte Carlointegration toolbox in MATLAB which implements a variant of the DRAM algorithmfor exploring the mathematical objective functions of arbitrary-dimensions, inparticular, the posterior distributions of Bayesian models in data science,Machine Learning, and scientific inference. The design goals of MatDRAM includenearly-full automation of MCMC simulations, user-friendliness,fully-deterministic reproducibility, and the restart functionality ofsimulations. We also discuss the implementation details of a technique toautomatically monitor and ensure the diminishing adaptation of the proposaldistribution of the DRAM algorithm and a method of efficiently storing theresulting simulated Markov chains. The MatDRAM library is open-source,MIT-licensed, and permanently located and maintained as part of the ParaMontelibrary at https://github.com/cdslaborg/paramonte.

MatDRAM: A pure-MATLAB Delayed-Rejection Adaptive Metropolis-Hastings Markov Chain Monte Carlo Sampler