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

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