Bayesian system identification is a theoretically well-founded and currently emerging area. We describe and evaluate two recent state-of-the-art sample-based methods for Bayesian parameter inference from the statistics literature, particle Metropolis-Hastings (PMH) and SMC2, and apply them to a non-trivial real world system identification problem with large uncertainty present. We discuss their different properties from a user perspective, and conclude that they show similar performance in practice, while PMH is significantly easier to implement than SMC2.
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