A Bootstrap Likelihood approach to Bayesian Computation

TL;DR

This paper introduces a bootstrap likelihood method for Bayesian computation that simplifies implementation and can outperform existing approaches, especially when dealing with intractable likelihoods.

Contribution

It proposes a new bootstrap likelihood-based approach to Bayesian computation that overcomes challenges of parameter tuning in ABC methods.

Findings

The method is easy to implement and faster in some cases.

It performs well in Population Genetics, Time Series, and SDE examples.

Effective on real datasets.

Abstract

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 alternative 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.