A Bootstrap Likelihood Approach to Bayesian Computation

There is an increasing amount of literature focused on Bayesian computational methods to address problems with intractable likelihood. One approach is a set of algorithms known as Approximate Bayesian Computational (ABC) methods. One of the problems with these algorithms is that their performance depends on the appropriate choice of summary statistics, distance measure and tolerance level. To circumvent this problem, an alternative method based on the empirical likelihood has been introduced. This method can be easily implemented when a set of constraints, related to the moments of the distribution, is specified. However, the choice of the constraints is sometimes challenging. To overcome this difficulty, we propose an alternative method based on a bootstrap likelihood approach. The method is easy to implement and in some cases is actually faster than the other approaches considered. We illustrate the performance of our algorithm with examples from population genetics, time series and stochastic differential equations. We also test the method on a real dataset.