The choice of the summary statistics in Bayesian inference and in particular in ABC algorithms is paramount to produce a valid outcome. We derive necessary and sufficient conditions on those statistics for the corresponding Bayes factor to be convergent, namely to asymptotically select the true...

Missing variable models are typical benchmarks for new computational techniques in that the ill-posed nature of missing variable models offer a challenging testing ground for these techniques. This was the case for the EM algorithm and the Gibbs sampler, and this is also true for importance...

Hidden Markov models lead to intricate computational problems when considered directly. In this paper, we propose an approximation method based on Gibbs sampling which allows an effective derivation of Bayes estimators for these models.