分野別セミナー

Having the ability to work with complex models can be highly beneficial. However, complex models often have intractable likelihoods, so methods that involve evaluation of the likelihood function are infeasible. In these situations, the benefits of working with likelihood-free methods become apparent. Likelihood-free methods, such as parametric Bayesian indirect likelihood that uses the likelihood of an alternative parametric auxiliary model, have been explored throughout the literature as a viable alternative when the model of interest is complex. One of these methods is called the synthetic likelihood (SL), which uses a multivariate normal approximation of the distribution of a set of summary statistics. In this talk, I will explore the accuracy and computational efficiency of the Bayesian version of the synthetic likelihood (BSL) approach in comparison to a competitor known as approximate Bayesian computation (ABC) and its sensitivity to its tuning parameters and assumptions. BSL is accelerated by using a sparse estimation of the precision matrix. A novel, unbiased estimator of the SL for the case where the summary statistics have a multivariate normal distribution will also be explored. The findings will be illustrated through several applications, including a non-linear state space model and a cell biology model.
Joint work with: Christopher C. Drovandi, Anthony Lee, David J. Nott and Ziwen An.