**Speaker**: Arnaud Doucet (Oxford)

**Title**: On the efficient implementation of pseudo-marginal methods

**Abstract**: When an unbiased estimator of the likelihood is used within a Metropolis–Hastings chain, it is necessary to trade off the number of Monte Carlo samples used to construct this estimator against the asymptotic variances of the averages computed under this chain. Using many Monte Carlo samples will typically result in Metropolisâ€“Hastings averages with lower asymptotic variances than the corresponding averages that use fewer samples; however, the computing time required to construct the likelihood estimator increases with the number of samples. Under the assumption that the distribution of the additive noise introduced by the loglikelihood estimator is Gaussian with variance inversely proportional to the number of samples and independent of the parameter value at which it is evaluated, we provide guidelines on the number of samples to select.