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Abstract:
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We analyze the behavior of ABC when the model generating the simulated data differs from that generating the observed data, i.e., when the data simulator in ABC is misspecified. We demonstrate both theoretically, and in simple but practically relevant examples, that certain versions of ABC can suffer severely when the model is misspecified. Graphical and posterior predictive checks are proposed as means of detecting model misspecification in ABC. Lastly, theoretical results demonstrate that under regularity a version of the ABC accept/reject approach concentrates on sets containing an appropriately defined pseudo-true parameter value.
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