Abstract
The aim of this work is to tackle the problem of sampling from multi-modal distributions when Hybrid Monte Carlo (HMC) algorithm is employed for performing Bayesian inference in dynamical systems. Hybrid Monte Carlo is a powerful Markov Chain Monte Carlo (MCMC) algorithm but it still suffers from the “multiple peaks” problem. Due to non-trivial structure in the space of (a class of) dynamical systems, posterior distribution of its model parameters could exhibit complicated structures such as multiple ridges. We examined a MCMC algorithm combining HMC with so-called Parallel Tempering (PT) - a well-known strategy for tackling the problem highlighted above. The new algorithm is referred to as PT-HMC. Our numerical experiment demonstrated that when compared to the ground truth, the posterior distributions derived from PT-HMC samples is more accurate than those from HMC.
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Sun, S., Shen, Y. (2020). “Parallel-Tempering”-Assisted Hybrid Monte Carlo Algorithm for Bayesian Inference in Dynamical Systems. In: Ju, Z., Yang, L., Yang, C., Gegov, A., Zhou, D. (eds) Advances in Computational Intelligence Systems. UKCI 2019. Advances in Intelligent Systems and Computing, vol 1043. Springer, Cham. https://doi.org/10.1007/978-3-030-29933-0_30
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DOI: https://doi.org/10.1007/978-3-030-29933-0_30
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