Approximate maximum likelihood estimation using data-cloning ABC

TL;DR

This paper introduces a novel approach combining data cloning with ABC-MCMC to efficiently approximate maximum likelihood estimates for models with intractable likelihoods, reducing computational effort while maintaining accuracy.

Contribution

It presents a new methodology that allows using larger ABC thresholds with data cloning to approximate maximum likelihood estimates more efficiently.

Findings

Effective on models with intractable likelihoods like g-and-k distributions

Reduces number of ABC-MCMC iterations needed

Achieves reasonable point estimates with less computational effort

Abstract

A maximum likelihood methodology for a general class of models is presented, using an approximate Bayesian computation (ABC) approach. The typical target of ABC methods are models with intractable likelihoods, and we combine an ABC-MCMC sampler with so-called "data cloning" for maximum likelihood estimation. Accuracy of ABC methods relies on the use of a small threshold value for comparing simulations from the model and observed data. The proposed methodology shows how to use large threshold values, while the number of data-clones is increased to ease convergence towards an approximate maximum likelihood estimate. We show how to exploit the methodology to reduce the number of iterations of a standard ABC-MCMC algorithm and therefore reduce the computational effort, while obtaining reasonable point estimates. Simulation studies show the good performance of our approach on models with intractable likelihoods such as g-and-k distributions, stochastic differential equations and state-space models.