Department of Statistics Seminar
North Carolina State University

presents

Dr. James Berger

Duke University

"P-Values for Composite Null Models"

ABSTRACT

In deciding whether an entertained model is adequate in light of the data, it is common practice to compute the P-value based on a statistic measuring departure from the model (e.g., in chi-square testing of fit). Indeed, if an alternative model is not available for comparison, even Bayesians often use P-values, at least after appropriate calibration. (We will briefly review the issues of Bayesian and frequentist calibration of P-values, based on Sellke, Bayarri, and Berger, 1999).

When the entertained model contains unknown parameters, determination of the P-value can be problematic. The most commonly used P-value is the plug-in P-value, found by simply replacing the unknown parameters of the model by estimates (usually the m.l.e.). Another common P-value is the posterior predictive P-value, found by integrating out the unknown parameters using their posterior distribution. In certain situations, parameters have also been eliminated by conditioning on an ancillary statistic, as with the Fisher exact test.

A new method for eliminating the unknown parameter will be discussed and shown to be superior to the above choices, in a variety of small sample examples and in an asymptotic sense.

Friday, October 22, 1999

3:35 - 4:35 pm

206 Cox Hall

Refreshments will be served on the second floor of Dabney Hall (left of Room 222) at 3:00 pm.