Likelihood-free stochastic approximation EM for inference in complex models

TL;DR

This paper introduces a likelihood-free stochastic approximation EM algorithm that enables parameter inference in complex models with intractable likelihoods, using synthetic likelihoods and demonstrating its effectiveness through various simulation studies.

Contribution

It develops a novel likelihood-free SAEM algorithm based on synthetic likelihoods, applicable to static and dynamic models with minimal tuning.

Findings

Successfully applied to stochastic differential equation models

Effective in stochastic Lotka-Volterra models

Works with data from g-and-k distributions

Abstract

A maximum likelihood methodology for the parameters of models with an intractable likelihood is introduced. We produce a likelihood-free version of the stochastic approximation expectation-maximization (SAEM) algorithm to maximize the likelihood function of model parameters. While SAEM is best suited for models having a tractable "complete likelihood" function, its application to moderately complex models is a difficult or even impossible task. We show how to construct a likelihood-free version of SAEM by using the "synthetic likelihood" paradigm. Our method is completely plug-and-play, requires almost no tuning and can be applied to both static and dynamic models. Four simulation studies illustrate the method, including a stochastic differential equation model, a stochastic Lotka-Volterra model and data from $g$-and-$k$ distributions. MATLAB code is available as supplementary material.