Sequential Monte-Carlo algorithms for Bayesian model calibration – A review and method comparison✰

Abstract

Bayesian inference has become an important framework for calibrating complex ecological and environmental models. Markov-Chain Monte Carlo (MCMC) algorithms are the methodological backbone of this framework, but they are not easily parallelizable and can thus not make optimal use of modern computer architectures. A possible solution is the use of Sequential Monte Carlo (SMC) algorithms. Currently, SMCs are used mainly for Bayesian state updating, for example in weather forecasting, and are thought to be less efficient for parameter calibration than MCMCs. Unlike MCMCs, however, SMCs are easily parallelizable. Thus, SMCs may become an interesting alternative when modelers have access to parallel computing environments. The purpose of this paper is to provide an introduction to SMC algorithms for Bayesian model calibration, and to explore the trade-off between efficiency and parallelizability for MCMC and SMC algorithms. To that end, we discuss different SMC variants, and benchmark them against a state-of-the-art MCMC algorithm by calibrating three ecological models of increasing complexity. Our results show that, with appropriately chosen settings, SMCs can be faster than state-of-the-art MCMC algorithms when a sufficiently large number of parallel cores are available and when the model runtime is large compared to communication overhead for parallelization (on our hardware, a model runtime of 20 ms was enough to favor SMC algorithms). Efficient SMC settings were characterized by a balanced mix of SMC filtering and MCMC mutation steps, suggesting that mixing MCMC and SMC principles may be ideal for creating efficient and parallelizable calibration algorithms. The algorithms used in this study are provided within the BayesianTools R package for Bayesian inference with complex ecological models.