Bayesian inference in state-space models is challenging due to high-dimensional state trajectories. A viable approach is particle Markov chain Monte Carlo (PMCMC), combining MCMC and sequential Monte Carlo to form ``exact approximations'' to otherwise-intractable MCMC methods. The performance of the approximation is limited to that of the exact method. We focus on particle Gibbs (PG) and particle Gibbs with ancestor sampling (PGAS), improving their performance beyond that of the ideal Gibbs sampler (which they approximate) by marginalizing out one or more parameters. This is possible when the parameter(s) has a conjugate prior relationship with the complete data likelihood. Marginalization yields a non-Markov model for inference, but we show that, in contrast to the general case, the methods still scale linearly in time. While marginalization can be cumbersome to implement, recent advances in probabilistic programming have enabled its automation. We demonstrate how the marginalized methods are viable as efficient inference backends in probabilistic programming, and demonstrate with examples in ecology and epidemiology.

The marginalisation of variables within some steps of an MCMC algorithm is delicate. The main proposal here appears well justified, but it would have been nice to see the argument made a little more explicitly. The type of marginalisation described here seems to be more or less what would be described as a (partially) collapsed Gibbs sampler in the sense of [David A Van Dyk and Taeyoung Park. "Partially collapsed Gibbs samplers: Theory and methods". It was less clear to me exactly how the "blocking" strategy detailed in Section 4.1 would be justified from a formal perspective, and I do think that this needs clarifying. I.e. the collection of variables to be sampled is divided into three parts -- x', x and theta and the decomposition of the kernel seems to involve sampling: x from a kernel invariant to its distribution conditional on both x' and theta (starting from the previous x) x' from a kernel invariant with respect to its distribution conditional only upon x (starting from the previous x') \theta from its full conditional distribution and it's not completely transparent how one knows that this is invariant with respect to the correct joint distribution.

This paper makes a solid contribution to improving inference in certain state space models that a used extensively in practice, particularly when implementing such models in a probabilistic programming language.

Bayesian inference in state-space models is challenging due to high-dimensional state trajectories. A viable approach is particle Markov chain Monte Carlo (PMCMC), combining MCMC and sequential Monte Carlo to form exact approximations'' to otherwise-intractable MCMC methods. The performance of the approximation is limited to that of the exact method. We focus on particle Gibbs (PG) and particle Gibbs with ancestor sampling (PGAS), improving their performance beyond that of the ideal Gibbs sampler (which they approximate) by marginalizing out one or more parameters. This is possible when the parameter(s) has a conjugate prior relationship with the complete data likelihood.

Bayesian inference in state-space models is challenging due to high-dimensional state trajectories. A viable approach is particle Markov chain Monte Carlo (PMCMC), combining MCMC and sequential Monte Carlo to form exact approximations'' to otherwise-intractable MCMC methods. The performance of the approximation is limited to that of the exact method. We focus on particle Gibbs (PG) and particle Gibbs with ancestor sampling (PGAS), improving their performance beyond that of the ideal Gibbs sampler (which they approximate) by marginalizing out one or more parameters. This is possible when the parameter(s) has a conjugate prior relationship with the complete data likelihood.