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

Abstract

Markov Chain Monte Carlo (MCMC) algorithms are widely used for stochastic optimization, sampling, and integration of mathematical objective functions, in particular, in the context of Bayesian inverse problems and parameter estimation. For decades, the algorithm of choice in MCMC simulations has been the Metropolis-Hastings (MH) algorithm. An advancement over the traditional MH-MCMC sampler is the Delayed-Rejection Adaptive Metropolis (DRAM).In this paper, we present MatDRAM, a stochastic optimization, sampling, and Monte Carlo integration toolbox in MATLAB which implements a variant of the DRAM algorithm for exploring the mathematical objective functions of arbitrary-dimensions, in particular, the posterior distributions of Bayesian models in data science, Machine Learning, and scientific inference. The design goals of MatDRAM include nearly-full automation of MCMC simulations, userfriendliness, fully-deterministic reproducibility, and the restart functionality of simulations. We also discuss the implementation details of a technique to automatically monitor and ensure the diminishing adaptation of the proposal distribution of the DRAM algorithm and a method of efficiently storing the resulting simulated Markov chains. The MatDRAM library is open-source, MIT-licensed, and permanently located and maintained as part of the ParaMonte library at: https://github.com/cdslaborg/paramonte.

Comparative Study of Parameter Identification with Frequency and Time Domain Fitting Using a Physics-Based Battery Model

“…where i represents the index of the measurement data points and N m is the total number of the measured voltage data points. To sample the parameter space, the adaptive Metropolis-Hastings MCMC algorithm is used to generate the parameter samples [53], the sample size for each test is set to 50,000 and the desired acceptance rate is set to 0.23 [54].…”