We consider Bayesian inference by importance sampling when the likelihood is analytically intractable but can be unbiasedly estimated. We refer to this procedure as importance sampling squared (IS2), as we can often estimate the likelihood itself by importance sampling. We provide a formal...

Andrieu et al. (2010) prove that Markov chain Monte Carlo samplers still converge to the correct posterior distribution of the model parameters when the likelihood is estimated by the particle filter (with a finite number of particles) is used instead of the likelihood. A critical issue for...