A comparative review of dimension reduction methods in approximate Bayesian computation

Details A comparative review of dimension reduction methods in approximate Bayesian computation A comparative review of dimension reduction methods in approximate Bayesian computation

2012-02-16

arxiv.org/abs/1202.3819v1

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Scientific paper

Approximate Bayesian computation (ABC) methods make use of comparisons between simulated and observed summary statistics to overcome the problem of a computationally intractable likelihood functions. The choice of summary statistics involves a tradeoff between informativeness and goodness of fit because a larger set of summary statistics is more informative but also more difficult to match with the observed set of summary statistics. 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 non-mutually exclusive classes consisting of best subset selection methods, projection techniques and regularisation. 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 regularisation procedure. We illustrate the performance of these dimension reduction techniques through the analysis of three challenging models and datasets.

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