A Note on Using Discretized Simulated Data to Estimate Implicit Likelihoods in Bayesian Analyses

TL;DR

This paper introduces a Bayesian inference method that estimates implicit likelihoods by discretizing simulated data, enabling analysis when the likelihood function is unknown but simulation is feasible.

Contribution

It proposes a novel approach to estimate implicit likelihoods through data discretization within MCMC, expanding Bayesian analysis capabilities.

Findings

Effective in estimating likelihoods from simulated data

Demonstrated on three example problems

Analyzed method properties through a small study

Abstract

This article presents a Bayesian inferential method where the likelihood for a model is unknown but where data can easily be simulated from the model. We discretize simulated (continuous) data to estimate the implicit likelihood in a Bayesian analysis employing a Markov chain Monte Carlo algorithm. Three examples are presented as well as a small study on some of the method's properties.