Comments on: ABC with indirect summary statistics
https://xianblog.wordpress.com/2014/02/03/abc-with-indirect-summary-statistics/
an attempt at bloggin, nothing more...Mon, 03 Feb 2014 06:30:29 +0000
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By: Chris Drovandi
https://xianblog.wordpress.com/2014/02/03/abc-with-indirect-summary-statistics/comment-page-1/#comment-43067
Sun, 02 Feb 2014 23:55:42 +0000http://xianblog.wordpress.com/?p=23055#comment-43067Actually even if the true model was incorporated in the auxiliary then ABC II methods still do not produce sufficient statistics (in general, via a simple dimensionality of summary statistic argument). Thus the assumption is not particularly useful in the context of ABC II methods, since even if it were true ABC II will not converge to the true posterior (as the ABC tolerance goes to zero). This gives me a slightly uneasy feeling about ABC II. In contrast, the Bayesian indirect likelihood (BIL) method I review and investigate further in my paper does appear to converge to the true posterior (as the sample size of the simulated data goes to infinity) if this assumption is met. But of course this assumption will not in general be satisfied in practice, which then gives an uneasy feeling about BIL. I have a simple example on a slide of the talk I have given at Warwick, Linz and Reading now (and plan to incorporate all this in a revision to my paper).
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