  This paper is concerned with Bayesian inference when the likelihood is
analytically intractable but can be unbiasedly estimated. We propose an
annealed importance sampling procedure for estimating expectations with respect
to the posterior. The proposed algorithm is useful in cases where finding a
good proposal density is challenging, and when estimates of the marginal
likelihood are required. The effect of likelihood estimation is investigated,
and the results provide guidelines on how to set up the precision of the
likelihood estimation in order to optimally implement the procedure. The
methodological results are empirically demonstrated in several simulated and
real data examples.
