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 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, Mengersen, Pudlo and Robert (2013) introduced an alterna-

tive method based on empirical likelihood, which can be easily implemented when

a set of constraints, related to the moments of the distribution, is known. However,

the choice of the constraints is sometimes challenging. 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 Stochastic Differential Equations. Finally, we test the method

on a real dataset.