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Summary Statistics

Authored by: Dennis Prangle

Handbook of Approximate Bayesian Computation

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

Print ISBN: 9781439881507
eBook ISBN: 9781315117195
Adobe ISBN:

10.1201/9781315117195-5

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Abstract

To deal with high dimensional data, ABC algorithms typically reduce them to lower dimensional summary statistics and accept when simulated summaries S(y) are close to the observed summaries S(yobs ). This has been an essential part of ABC methodology since the first publications in the population genetics literature. Overviewing this work Beaumont et al. (2002) wrote: ‘A crucial limitation of the…method is that only a small number of summary statistics can usually be handled. Otherwise, either acceptance rates become prohibitively low or the tolerance…must be increased, which can distort the approximation’, and related the problem to the general issue of the curse of dimensionality: many statistical tasks are substantially more difficult in high dimensional settings. In ABC, the dimension in question is the number of summary statistics used.

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