A comparison between p-values for goodness-of-fit checking
M.J. Bayarri and M.E. Castellanos
The problem of checking the compatibility of a proposed parametric
model with the observed data is an old one. If no alternative models
are proposed, Bayes factors are precluded and only measures of
`surprise' can be given. The p-value is, by far, the most ubiquitous
of such measures. Also, model checking is often done in a `casual'
manner, using statistics that are not distribition-free, nor even
parameter-free under the assumed model. In these situations, we
compare several p-values that can be used for model checking. We
investigate both their distribution under the `null' model, and their
power under families of alternatives.