## Brazilian Journal of Probability and Statistics

- Braz. J. Probab. Stat.
- Volume 31, Number 4 (2017), 732-745.

### Barker’s algorithm for Bayesian inference with intractable likelihoods

Flávio B. Gonçalves, Krzysztof Łatuszyński, and Gareth O. Roberts

#### Abstract

In this expository paper, we abstract and describe a simple MCMC scheme for sampling from intractable target densities. The approach has been introduced in Gonçalves, Łatuszyński and Roberts (2017a) in the specific context of jump-diffusions, and is based on the Barker’s algorithm paired with a simple Bernoulli factory type scheme, the so called *2-coin algorithm*. In many settings, it is an alternative to standard Metropolis–Hastings pseudo-marginal method for simulating from intractable target densities. Although Barker’s is well known to be slightly less efficient than Metropolis–Hastings, the key advantage of our approach is that it allows to implement the “marginal Barker’s” instead of the extended state space pseudo-marginal Metropolis–Hastings, owing to the special form of the accept/reject probability. We shall illustrate our methodology in the context of Bayesian inference for discretely observed Wright–Fisher family of diffusions.

#### Article information

**Source**

Braz. J. Probab. Stat., Volume 31, Number 4 (2017), 732-745.

**Dates**

Received: December 2016

Accepted: August 2017

First available in Project Euclid: 15 December 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.bjps/1513328765

**Digital Object Identifier**

doi:10.1214/17-BJPS374

**Mathematical Reviews number (MathSciNet)**

MR3738176

**Zentralblatt MATH identifier**

1385.65013

**Keywords**

Intractable likelihood Bayesian inference Barker’s algorithm Bernoulli factory 2-coin algorithm stochastic differential equations Wright–Fisher diffusion

#### Citation

Gonçalves, Flávio B.; Łatuszyński, Krzysztof; Roberts, Gareth O. Barker’s algorithm for Bayesian inference with intractable likelihoods. Braz. J. Probab. Stat. 31 (2017), no. 4, 732--745. doi:10.1214/17-BJPS374. https://projecteuclid.org/euclid.bjps/1513328765