Stopping rules and the likelihood function

Abstract

Conditions are investigated whereby the likelihood function contains all of the relevant information from the data necessary for inference, with no knowledge of the sample design. Certain designs which result in the same reported likelihood for the final stopped experiment in fact have different underlying likelihood functions. For a likelihood function to be valid, it must, at least, contain the minimum information necessary for the experiment to be performable; this is shown to be the minimal filtration of the experiment.