ABC-CDE: Towards Approximate Bayesian Computation with Complex High-Dimensional Data and Limited Simulations

TL;DR

This paper introduces ABC-CDE, a nonparametric framework that improves approximate Bayesian computation for high-dimensional data with limited simulations by directly estimating and assessing the posterior distribution.

Contribution

It proposes a novel ABC-CDE method that addresses challenges in high-dimensional data, limited simulations, and performance assessment in ABC.

Findings

ABC-CDE effectively estimates posteriors with fewer simulations.

It provides a new way to compare ABC methods based on posterior estimation.

The approach outperforms standard ABC in complex, high-dimensional scenarios.

Abstract

Approximate Bayesian Computation (ABC) is typically used when the likelihood is either unavailable or intractable but where data can be simulated under different parameter settings using a forward model. Despite the recent interest in ABC, high-dimensional data and costly simulations still remain a bottleneck in some applications. There is also no consensus as to how to best assess the performance of such methods without knowing the true posterior. We show how a nonparametric conditional density estimation (CDE) framework, which we refer to as ABC-CDE, help address three nontrivial challenges in ABC: (i) how to efficiently estimate the posterior distribution with limited simulations and different types of data, (ii) how to tune and compare the performance of ABC and related methods in estimating the posterior itself, rather than just certain properties of the density, and (iii) how to efficiently choose among a large set of summary statistics based on a CDE surrogate loss. We provide theoretical and empirical evidence that justify ABC-CDE procedures that {\em directly} estimate and assess the posterior based on an initial ABC sample, and we describe settings where standard ABC and regression-based approaches are inadequate.