Calibration of posterior predictive p-values for model checking

ABSTRACT

When assessing the compatibility of an assumed model and the observed data, one popular method is the posterior predictive p-value (ppp). However, the posterior predictive p-values typically do not have uniform distributions and tend to be conservative when detecting the misfit of the assumed model. In this paper, we consider a calibrated p-value which is initially proposed in Hjort et al. [Post-processing posterior predictive p-values. J Am Stat Assoc. 2006;1011157–1174]. We further explore its theoretical properties by proving the asymptotic uniformity of the calibrated p-value under some mild conditions. For testing hypotheses under local Pitman alternatives, we investigate its power performance in the asymptotic sense. Theoretical analysis and simulation results show that the calibrated p-value enjoys some desirable properties and is superior to the original posterior predictive p-values.

Keywords:

• p-value
• posterior predictive assessment
• discrepancy measure
• asymptotic property
• score vector

Acknowledgements

The authors would like to thank the anonymous referee for the insightful suggestions and comments which significantly improve the quality and the exposition of the paper. This work was supported by the National Natural Science Foundation of China under Grant No. 11471035.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11471035].