  We consider the combined use of resampling and partial rejection control in
sequential Monte Carlo methods, also known as particle filters. While the
variance reducing properties of rejection control are known, there has not been
(to the best of our knowledge) any work on unbiased estimation of the marginal
likelihood (also known as the model evidence or the normalizing constant) in
this type of particle filter. Being able to estimate the marginal likelihood
without bias is highly relevant for model comparison, computation of
interpretable and reliable confidence intervals, and in exact approximation
methods, such as particle Markov chain Monte Carlo. In the paper we present a
particle filter with rejection control that enables unbiased estimation of the
marginal likelihood.
