B0426
Title: The conditional predictive $p-$value in ABC
Authors: Stefano Cabras - University Carlos III of Madrid (Spain) [presenting]
Maria Eugenia Castellanos Nueda - Universidad Rey Juan Carlos (Spain)
Oliver Ratmann - Imperial College (United Kingdom)
Abstract: The approach to evaluate the goodness of fit of statistical models is via calibrated $p-$values that are uniformly distributed in $[0,1]$ under the true model. While such $p-$values are available for very simple models, these are prohibitively expensive to calculate for complex ones. We show that, even for models whose likelihood is not available in a closed form expression, asymptotically calibrated $p-$values can be efficiently obtained as a by-product of Approximate Bayesian Computations. Such models often arise in stochastic processes with many latent variables. Specifically, given a set of summary statistics and test statistics, we are able to derive the conditional predictive distribution of the test statistic given the summary statistic. After the exposition of the theory, we illustrate the technique in some examples.
