Weixuan Zhu (Universidad Carlos III de Madrid): Bootstrap Likelihood and Bayesian Computations

During the past ten years, for addressing problems with an intractable likelihood, a new class of algorithms has been proposed in the literature. They are customary called Approximate Bayesian Computational (ABC) Methods or also, likelihood-free techniques. Unfortunately, ABC methods suffers some calibration problems. Recently, Mergensen, Pudlo and Robert (2013) proposed an interesting alternative approach, based on empirical likelihood, which bypasses some of the typical problems of such algorithms. In a similar flavor, in this work we propose an approach based on Bootstrap Likelihood or alternatively, the Bootstrap Likelihood representation of the empirical Likelihood. There are some benefits in using this approach. Precisely, it is faster by a computational point of view and there are less parameters to set. The effectiveness of the method is tested on Time Series and Bioinformatics models.

Mengersen, K., Pudlo, P., and Robert, C.P. (2013). Bayesian computation via empirical likelihood. Proceedings of the National Academy of Sciences 110 (4), 1321–1326.
Davison, A.C., Hinkley D.V. (1992). Bootstrap likelihoods. Biometrika 79(1), 113-130

Joint work with Juan Miguel Marin (Universidad Carlos III de Madrid) and Fabrizio Leisen (University of Kent)