Intractable likelihoods and semi-complete data likelihoods Seminar

Event details

Intrac​table likelihoods arise in many situations where we cannot write down an explicit closed form for the likelihood function; alternatively the likelihood may be very computationally expensive to calculate. A common technique that can be applied in many situations is to use a Bayesian data augmentation approach where the parameter space is expanded via the specification of auxiliary variables. This is done in such a way so that the “complete data likelihood” of the observed data and auxiliary variables given the parameters is straightforward and efficient to calculate. This is a very powerful technique, however, the associated (standard) MCMC algorithms can perform very poorly in these situations due to highly correlated parameters (and auxiliary variables). We propose a “semi-complete data likelihood” approach, which can significantly improve the performance of standard “vanilla” MCMC algorithms. We demonstrate the approach by applying the idea to applications in statistical ecology.