Fast $\epsilon$-free Inference of Simulation Models with Bayesian Conditional Density Estimation

TL;DR

This paper introduces a Bayesian conditional density estimation method for likelihood-free inference, significantly reducing the number of simulations needed compared to traditional ABC methods, especially as the tolerance approaches zero.

Contribution

The authors propose a novel Bayesian conditional density estimation approach that improves efficiency and accuracy in likelihood-free inference over existing ABC techniques.

Findings

Requires fewer simulations than Monte Carlo ABC

Provides more accurate posterior estimates with limited data

Reduces computational cost in likelihood-free inference

Abstract

Many statistical models can be simulated forwards but have intractable likelihoods. Approximate Bayesian Computation (ABC) methods are used to infer properties of these models from data. Traditionally these methods approximate the posterior over parameters by conditioning on data being inside an $\epsilon$-ball around the observed data, which is only correct in the limit $\epsilon\!\rightarrow\!0$. Monte Carlo methods can then draw samples from the approximate posterior to approximate predictions or error bars on parameters. These algorithms critically slow down as $\epsilon\!\rightarrow\!0$, and in practice draw samples from a broader distribution than the posterior. We propose a new approach to likelihood-free inference based on Bayesian conditional density estimation. Preliminary inferences based on limited simulation data are used to guide later simulations. In some cases, learning an accurate parametric representation of the entire true posterior distribution requires fewer model simulations than Monte Carlo ABC methods need to produce a single sample from an approximate posterior.