Relevant statistics for Bayesian model choice
Abstract
The choice of the summary statistics used in Bayesian inference and in particular in ABC algorithms has bearings on the validation of the resulting inference. Those statistics are nonetheless customarily used in ABC algorithms without consistency checks. We derive necessary and sufficient conditions on summary statistics for the corresponding Bayes factor to be convergent, namely to asymptotically select the true model. Those conditions, which amount to the expectations of the summary statistics to asymptotically differ under both models, are quite natural and can be exploited in ABC settings to infer whether or not a choice of summary statistics is appropriate, via a Monte Carlo validation.
 Publication:

arXiv eprints
 Pub Date:
 October 2011
 arXiv:
 arXiv:1110.4700
 Bibcode:
 2011arXiv1110.4700M
 Keywords:

 Mathematics  Statistics Theory;
 Quantitative Biology  Populations and Evolution;
 Statistics  Computation;
 Statistics  Methodology
 EPrint:
 30 pages, 8 figures, 1 table