To improve the efficiency of sequential Monte Carlo (SMC) algorithms, it is desirable to reduce the dimension of the target distribution by analytically integrating out as many components as possible. This leads to so-called Rao-Blackwellised particle filters (RBPFs).

Unfortunately, the necessary integrals can usually not be calculated except in special cases such as conditionally linear/Gaussian hidden Markov models. To deal with more general problems, an exactly approximated Rao-Blackwellised particle filter (EARBF) was proposed by A. M. Johansen, N. Whiteley and A. Doucet (2012).

The EARBF is a pseudo-marginal SMC algorithm in which each particle is associated with its own sub-level SMC algorithm. The latter is designed to approximate the integral that would have to be calculated for a RBPF. This leads to a hierarchical SMC algorithm not unlike the SMC^2 algorithm by N. Chopin, P. E. Jacob and O. Papaspiliopoulos (2012).

We investigate the relationship between the performance of the algorithm and a number of design parameters.

This is joint work with Adam M. Johansen and Dario Spano.

* Keywords:* sequential Monte Carlo, Rao-Blackwellised particle filters, pseudo-marginal approach