Open Access
May 2013 A Comparative Review of Dimension Reduction Methods in Approximate Bayesian Computation
M. G. B. Blum, M. A. Nunes, D. Prangle, S. A. Sisson
Statist. Sci. 28(2): 189-208 (May 2013). DOI: 10.1214/12-STS406


Approximate Bayesian computation (ABC) methods make use of comparisons between simulated and observed summary statistics to overcome the problem of computationally intractable likelihood functions. As the practical implementation of ABC requires computations based on vectors of summary statistics, rather than full data sets, a central question is how to derive low-dimensional summary statistics from the observed data with minimal loss of information. In this article we provide a comprehensive review and comparison of the performance of the principal methods of dimension reduction proposed in the ABC literature. The methods are split into three nonmutually exclusive classes consisting of best subset selection methods, projection techniques and regularization. In addition, we introduce two new methods of dimension reduction. The first is a best subset selection method based on Akaike and Bayesian information criteria, and the second uses ridge regression as a regularization procedure. We illustrate the performance of these dimension reduction techniques through the analysis of three challenging models and data sets.


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M. G. B. Blum. M. A. Nunes. D. Prangle. S. A. Sisson. "A Comparative Review of Dimension Reduction Methods in Approximate Bayesian Computation." Statist. Sci. 28 (2) 189 - 208, May 2013.


Published: May 2013
First available in Project Euclid: 21 May 2013

zbMATH: 1331.62123
MathSciNet: MR3112405
Digital Object Identifier: 10.1214/12-STS406

Keywords: Approximate Bayesian Computation , Dimension reduction , likelihood-free inference , regularization , Variable selection

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.28 • No. 2 • May 2013
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