Adaptive Bayesian inference of Markov transition rates. (22nd February 2023)

• Record Type: Journal Article
• Authors: Barendregt, Nicholas W.; Webb, Emily G.; Kilpatrick, Zachary P.
• Is Part Of: Proceedings. Volume 479:Number 2270(2023)
• Publication Date: 2023-02-22
• Subjects: adaptive optimal design -- transition rates -- Markov process -- sequential Bayesian inference; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rspa.2022.0453
• Languages: English
• ISSNs: 1364-5021

Abstract

Abstract : Optimal designs minimize the number of experimental runs (samples) needed to accurately estimate model parameters, resulting in algorithms that, for instance, efficiently minimize parameter estimate variance. Governed by knowledge of past observations, adaptive approaches adjust sampling constraints online as model parameter estimates are refined, continually maximizing expected information gained or variance reduced. We apply adaptive Bayesian inference to estimate transition rates of Markov chains, a common class of models for stochastic processes in nature. Unlike most previous studies, our sequential Bayesian optimal design is updated with each observation and can be simply extended beyond two-state models to birth–death processes and multistate models. By iteratively finding the best time to obtain each sample, our adaptive algorithm maximally reduces variance, resulting in lower overall error in ground truth parameter estimates across a wide range of Markov chain parameterizations and conformations.