Adaptively switching between a particle marginal Metropolis-Hastings and a particle Gibbs kernel in SMC$^2$

TL;DR

This paper proposes an adaptive method for switching between particle MCMC kernels within SMC$^2$, enhancing efficiency by dynamically choosing between particle marginal Metropolis-Hastings and particle Gibbs kernels during sampling.

Contribution

It introduces a novel adaptive kernel switching strategy for SMC$^2$, improving sampling efficiency over fixed kernel approaches.

Findings

Adaptive switching improves sampling efficiency.

Method outperforms fixed kernel approaches.

Code is publicly available for implementation.

Abstract

Sequential Monte Carlo squared (SMC$^2$; Chopin et al., 2012) methods can be used to sample from the exact posterior distribution of intractable likelihood state space models. These methods are the SMC analogue to particle Markov chain Monte Carlo (MCMC; Andrieu et al., 2010) and rely on particle MCMC kernels to mutate the particles at each iteration. Two options for the particle MCMC kernels are particle marginal Metropolis-Hastings (PMMH) and particle Gibbs (PG). We introduce a method to adaptively select the particle MCMC kernel at each iteration of SMC$^2$, with a particular focus on switching between a PMMH and PG kernel. The resulting method can significantly improve the efficiency of SMC$^2$ compared to using a fixed particle MCMC kernel throughout the algorithm. Code for our methods is available at https://github.com/imkebotha/kernel_switching_smc2.