A Bootstrap Likelihood approach to Bayesian Computation

Recently, an increasingly amount of literature focused on Bayesian computational methods to address problems with intractable likelihood. These algorithms are known as Approximate Bayesian Computational (ABC) methods. One of the problems of these algorithms is that the performance depends on the tuning of some parameters, such as the summary statistics, distance and tolerance level. To bypass this problem, an alternative method based on empirical likelihood was introduced by Mengersen et al. (2013), which can be easily implemented when a set of constraints, related with the moments of the distribution, is known. However, the choice of the constraints is crucial and sometimes challenging in the sense that it determines the convergence property of the empirical likelihood. To overcome this problem, we propose an alternative method based on a bootstrap likelihood approach. The method is easy to implement and in some cases it is faster than the other approaches. The performance of the algorithm is illustrated with examples in Population Genetics, Time Series and a recent non-explicit bivariate Beta distribution. Finally, we test the method on simulated and real data random fields.