High-Dimensional ABC

Authored by: David J. Nott , Victor M.-H. Ong , Y. Fan , S. A. Sisson

Handbook of Approximate Bayesian Computation

Print publication date:  August  2018
Online publication date:  August  2018

Print ISBN: 9781439881507
eBook ISBN: 9781315117195
Adobe ISBN:

10.1201/9781315117195-8

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Abstract

Other chapters in this volume have discussed the curse of dimensionality that is inherent to most standard approximate Bayesian computation (ABC) methods. For a p-dimensional parameter of interest θ = (θ 1,…,θp ), ABC implementations make use of a summary statistic s = S(y) for data π A B C ,   h ( θ | s o b s )   ∝   ∫ K h ( ‖ s   −   s o b s ‖ ) p ( s | θ ) π ( θ )   d s , of dimension q, where typically qp. When either θ or s is high dimensional, standard ABC methods have difficulty in producing simulated summary data that are acceptably close to the observed summary sobs = S(yobs ), for observed data yobs . This means that standard ABC methods have limited applicability in high-dimensional problems.

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