book

Plenary Talks
CF5
Thursday, September 5th
15:30
ABC-CDE: Toward Approximate Bayesian
Computation with Complex High-Dimensional
Data and Limited Simulations
Rafael Izbicki
UFSCar
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.
Keywords: Nonparametric methods; Conditional density estimation; Approximate Bayesian computation;
Likelihood-free inference
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