Florian Hartig

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

Matthias Speich, Carsten F. Dormann & Florian Hartig

Ecological Modelling, 455, 109608 (2021)
Cite this
@article{speich2021sequential,
  author = {Matthias Speich and Carsten F. Dormann and Florian Hartig},
  title = {Sequential Monte-Carlo algorithms for Bayesian model calibration – A review and method comparison},
  journal = {Ecological Modelling},
  volume = {455},
  pages = {109608},
  year = {2021},
  doi = {10.1016/j.ecolmodel.2021.109608},
}

DOI: 10.1016/j.ecolmodel.2021.109608
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Funding

This study was supported through funding by Deutsche Forschungsgemeinschaft (DOR 786/8–1).

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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.

What the paper shows and why it matters

(AI-generated)

Bayesian calibration of complex ecological and environmental models mostly relies on Markov chain Monte Carlo (MCMC) samplers. These explore the parameter space step by step, each step depending on the last, so they need very many model runs and can use parallel computers only to a very limited degree. Sequential Monte Carlo (SMC) samplers instead keep a large population of candidate parameter sets (“particles”) that are reweighted and moved according to their fit to the data, which parallelises easily. SMC is thought to be less efficient and to need careful tuning for calibration, because a badly tuned SMC can lose the diversity of its particles. The main earlier comparison (Jeremiah et al. 2011) used an older, less advanced MCMC as benchmark. The paper asks whether the parallelisability of SMC can offset its lower efficiency in practice.

The study argues that sequential Monte Carlo (SMC) samplers can calibrate slow models faster than a state-of-the-art Markov chain Monte Carlo (MCMC) sampler once enough processor cores are available, even though SMC is less efficient for a single calibration. It tests up to 240 SMC settings against a differential-evolution MCMC on test cases up to a forest growth model (synthetic data for the dynamic models). At the forest model’s normal 1 ms run time, the best SMC settings came close to, but did not beat, MCMC. With a 50 ms pause added to emulate a slow model, every converged SMC run matched or beat MCMC, and five or more cores sufficed to be faster. Run time then fell almost in proportion to core number (log–log slopes −0.88 and −0.94 for 20 and 50 ms pauses, where −1 is exact proportionality; −0.5 without a pause). Convergence depended strongly on tuning: the number of MCMC moves per particle and iteration mattered more than the number of particles.

SMC is thus an alternative to MCMC worth considering for modellers with slow models and parallel hardware; on the authors’ cluster, a model run had to take about 20–50 ms for SMC to pay off. Because the best settings used many MCMC steps, the paper suggests that hybrids of SMC and MCMC may suit complex models best, and names automatic tuning and convergence monitoring for SMC as open needs. The sampler is in the BayesianTools R package.

References

  • Jeremiah et al. (2011). Bayesian calibration and uncertainty analysis of hydrological models: A comparison of adaptive Metropolis and sequential Monte Carlo samplers. Water Resources Research 47, 2010WR010217. doi:10.1029/2010wr010217