Multi-Chain and Sequential MCMC for Engineering Inference: A Theoretical Review

Tajinder Singh

Assistant Professor

Department of Mathematics

Government college, Hoshiarpur

Email: tajindersi786@gmail.com

Abstract

Bayesian model updating has become a standard tool for parameter identification in modern engineering systems, yet the classical single-chain Metropolis-Hastings sampler frequently breaks down when confronted with the posterior geometries produced by physical processes. Strong nonlinearity, weak identifiability, multimodality, and heavy measurement noise routinely generate target densities  whose regions of high probability mass are fragmented across parameter space that a single chain cannot traverse within any practical computational budget[3]. The consequence is silent failure: chains report apparent convergence while sampling only a narrow basin of attraction, producing posterior credible intervals that are both biased and over-confident[2]. This review argues that two algorithmic families directly address these pathologies. Multi-chain methods, exemplified by the DREAM family and its derivatives, exploit parallel population dynamics, snooker proposals, and adaptive randomized subspace updates to bridge isolated modes while preserving detailed balance. Sequential and particle-based MCMC, by contrast, factor the posterior across time or across an annealing schedule, propagating weighted ensembles through state-space models that are themselves dyna[5]. We synthesize the theoretical foundations of both families, examine their convergence diagnostics under engineering noise structures, and trace their deployment across oscillatory systems, degradation processes, and high-dimensional inverse problems. The objective is a coherent map of where each methodology earns its computational cost, and where hybridization remains an open problem.

Keywords: Markov chain Monte Carlo, Bayesian model updating, DREAM algorithm, multi-chain sampling, Sequential Monte Carlo.