ABC–CDE: Toward Approximate Bayesian Computation With Complex High-Dimensional Data and Limited Simulations

By Rafael Izbicki, Ann B. Lee, Taylor Pospisil. 2018

37 citations recorded by the source corpus.

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 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. Supplemental materials for this article are available online.

Subfields: Artificial Intelligence, Statistics and Probability, Probabilistic & Bayesian Methods

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Statistics and Probability

In Probabilistic & Bayesian Methods

Citations in the corpus

Likelihood-free inference with emulator networks (2018, background): “A complementary use of density-estimation in ABC is to directly target the posterior distribution [6, 37, 38, 39].”
(f)RFCDE: Random Forests for Conditional Density Estimation and Functional Data (2019, methodology): “This feature is particularly useful for estimating Bayesian posterior distributions in e.g. likelihood free inference Izbicki et al. [2018].”