Likelihood-free inference in high-dimensional models

TL;DR

This paper introduces a novel likelihood-free MCMC method that updates one parameter at a time using subsets of sufficient statistics, significantly improving acceptance rates and scalability for high-dimensional models.

Contribution

The method combines parameter-wise updates with subset-based acceptance, enabling likelihood-free inference in very high-dimensional models, demonstrated on biological data.

Findings

Dramatic increase in acceptance rates for high-dimensional models

Effective for models with hundreds of parameters

Successfully applied to influenza drug-resistance evolution data

Abstract

Methods that bypass analytical evaluations of the likelihood function have become an indispensable tool for statistical inference in many fields of science. These so-called likelihood-free methods rely on accepting and rejecting simulations based on summary statistics, which limits them to low dimensional models for which the absolute likelihood is large enough to result in manageable acceptance rates. To get around these issues, we introduce a novel, likelihood-free Markov-Chain Monte Carlo (MCMC) method combining two key innovations: updating only one parameter per iteration and accepting or rejecting this update based on subsets of statistics sufficient for this parameter. This increases acceptance rates dramatically, rendering this approach suitable even for models of very high dimensionality. We further derive that for linear models, a one dimensional combination of statistics per parameter is sufficient and can be found empirically with simulations. Finally, we demonstrate that our method readily scales to models of very high dimensionality using both toy models as well as by jointly inferring the effective population size, the distribution of fitness effects of new mutations (DFE) and selection coefficients for each locus from data of a recent experiment on the evolution of drug-resistance in Influenza.