P-values, p-values everywhere!

P-values for classification

Let (X,Y ) be a random variable consisting of an observed feature vector X ∈ X and an unobserved class label Y ∈ {1, 2, . . . , L} with unknown joint distribution. In addition, let D be a training data set consisting of n completely observed independent copies of (X,Y ). Usual classification procedures provide point predictors (classifiers) Ŷ (X,D) of Y or estimate the conditional distribution ...

Understanding posterior p-values

Posterior predictive p-values do not in general have uniform distributions under the null hypothesis (except in the special case of pivotal test statistics) but instead tend to have distributions more concentrated near 0.5. From different perspectives, such nonuniform distributions have been portrayed as desirable (as reflecting an ability of vague prior distributions to nonetheless yield accur...

Very small P values.

Subsampling p-values

A construction of p-values for hypothesis tests based on subsampling and the related m out of n bootstrap is introduced. The p-values are based on a modification of the usual subsampling hypothesis tests that involves an appropriate centering of the subsampled or bootstrapped test statistics as in the construction of confidence intervals. This modification makes the hypothesis tests more powerf...

The Variability of P -Values

P-values are used as evidence against a null hypothesis. But is it enough to report a p-value without some indication of its variability? Bootstrap prediction intervals and standard errors on the log scale are proposed to complement the standard p-value.