2024/01/31 by Austin L. Brown, Brown, Austin · 1 citation
Mathematics · #60J20 #60J27 #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2401.17963
openalex publication_date 2024/01/31 · openalex created_date 2024/02/02 · openalex updated_date 2026/07/28
Single-chain Markov chain Monte Carlo simulates realizations from a Markov chain to estimate expectations with the empirical average. The single-chain simulation is generally of considerable length and restricts many advantages of modern parallel computation. This paper constructs a novel many-short-chains Monte Carlo (MSC) estimator by averaging over multiple independent sums from Markov chains of a guaranteed short length. The computational advantage is the independent Markov chain simulations can be fast and may be run in parallel. The MSC estimator requires an importance sampling proposal and a drift condition on the Markov chain without requiring convergence analysis on the Markov chain. A non-asymptotic error analysis is developed for the MSC estimator under both geometric and multiplicative drift conditions. Empirical performance is illustrated on an autoregressive process and the Pólya-Gamma Gibbs sampler for Bayesian logistic regression to predict cardiovascular disease.