p-values for Model Evaluation

A quantitative procedure to decide whether a model provides a good descriptionof data is often based on a specific test statistic and a p-value summarizingboth the data and the statistic's sampling distribution. We provide a Bayesianmotivation for using p-values in the goodness-of-fit problem with no explicitalternative models considered. Some typical pitfalls encountered with commonstatistics are reviewed for Poisson and Gaussian uncertainties. Finally, wepresent a new test statistic for ordered Gaussian data, the runs statistic.