title: A new calibrated bayesian internal goodness-of-fit method: sampled posterior p-values as simple and general p-values that allow double use of the data.
abstract: BACKGROUND
  Recent approaches mixing frequentist principles with bayesian inference propose internal goodness-of-fit (GOF) p-values that might be valuable for critical analysis of bayesian statistical models. However, GOF p-values developed to date only have known probability distributions under restrictive conditions. As a result, no known GOF p-value has a known probability distribution for any discrepancy function.
  
  
  RESULTS
  We show mathematically that a new GOF p-value, called the sampled posterior p-value (SPP), asymptotically has a uniform probability distribution whatever the discrepancy function. In a moderate finite sample context, simulations also showed that the SPP appears stable to relatively uninformative misspecifications of the prior distribution.
  
  
  CONCLUSIONS
  These reasons, together with its numerical simplicity, make the SPP a better canonical GOF p-value than existing GOF p-values.
authors: Cemagref, UR EFNO, Nogent-sur-Vernisson, France. lfiorenza@senckenberg.de
authors: Frédéric
authors: F
authors: Gosselin
mesh_terms: D001499:Bayes Theorem; D002138:Calibration; D008962:Models, Theoretical; D011336:Probability