Hypothesis Selection and Testing by the MDL Principle

ses where the variance is known or taken as a parameter. 1. INTRODUCTION Although the term `hypothesis in statistics is synonymous with that of a probability `model as an explanation of data, hypothesis testing is not quite the same problem as model selection. This is because usually a particular hypothesis, called the `null hypothesis, has already been selected as a favorite model and it will be abandoned in favor of another model only when it clearly fails to explain the currently available data. In model selection, by contrast, all the models considered are regarded on the same footing and the objective is simply to pick the one that best explains the data. For the Bayesians certain models may be favored in terms of a prior probability, but in the minimum description length (MDL) approach to be outlined below, prior knowledge of any kind is to be used in selecting the tentative models, which in the end, unlike in the Bayesians case, can and will be fitted to data