Generalised Bayesian Inference for Discrete Intractable Likelihood

Understand

Discrete state spaces represent a major computational challenge to statistical inference, since the computation of normalisation constants requires summation over large or possibly infinite sets, which can be impractical.

• This paper addresses this computational challenge through the development of a novel generalised Bayesian inference procedure suitable for discrete intractable likelihood.
• Inspired by recent methodological advances for continuous data, the main idea is to update beliefs about model parameters using a discrete Fisher divergence, in lieu of the problematic intractable likelihood.
• The result is a generalised posterior that can be sampled from using standard computational tools, such as Markov chain Monte Carlo, circumventing the intractable normalising constant.