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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, but require a well-designed initial distribution constructed from importance sampling. Alternatively, the MSC estimator introduced here is a method to improve estimation properties in importance sampling by additionally simulating a Markov chain. A non-asymptotic error analysis is developed for the MSC estimator under both geometric and multiplicative drift conditions on the Markov chain that allows a theory for estimation of highly irregular and unbounded functions. Empirical performance is illustrated on an autoregressive process and the P\u00f3lya-Gamma Gibbs sampler for Bayesian logistic regression to predict cardiovascular disease.<\/jats:p>","DOI":"10.1007\/s11222-025-10741-4","type":"journal-article","created":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T07:15:48Z","timestamp":1761030948000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A non-asymptotic error analysis for parallel Monte Carlo estimation from many short Markov chains"],"prefix":"10.1007","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1576-8381","authenticated-orcid":false,"given":"Austin","family":"Brown","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,10,21]]},"reference":[{"issue":"3","key":"10741_CR1","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1214\/17-STS611","volume":"32","author":"S Agapiou","year":"2017","unstructured":"Agapiou, S., Papaspiliopoulos, O., Sanz-Alonso, D., Stuart, A.M.: Importance sampling: intrinsic dimension and computational cost. 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