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In this paper we consider fully Bayesian inference in general state spacemodels. Existing particle Markov chain Monte Carlo (MCMC) algorithms use anaugmented model that takes into account all the variable sampled in asequential Monte Carlo algorithm. This paper describes an approach that alsouses sequential Monte Carlo to construct an approximation to the state space,but generates extra states using MCMC runs at each time point. We construct anaugmented model for our extended space with the marginal distribution of thesampled states matching the posterior distribution of the state vector. We showhow our method may be combined with particle independent Metropolis-Hastings orparticle Gibbs steps to obtain a smoothing algorithm. All the Metropolisacceptance probabilities are identical to those obtained in existingapproaches, so there is no extra cost in term of Metropolis-Hastings rejectionswhen using our approach. The number of MCMC iterates at each time point ischosen by the used and our augmented model collapses back to the model inOlsson and Ryden (2011) when the number of MCMC iterations reduces. We showempirically that our approach works well on applied examples and can outperformexisting methods.

An extended space approach for particle Markov chain Monte Carlo methods