The likelihood principle does not entail a `sure thing', `evil demon' or `determinist' hypothesis

TL;DR

The paper argues that the likelihood principle does not necessarily support deterministic hypotheses dominating all evidence, challenging common interpretations through re-analysis of known counterexamples.

Contribution

It clarifies misconceptions about the scope of the likelihood principle by re-analyzing Birnbaum's counterexample, showing no conflict with intuitive evidential reasoning.

Findings

Re-analysis of Birnbaum's example removes the supposed conflict.

Proper treatment of nuisance parameters resolves apparent contradictions.

The likelihood principle does not imply deterministic hypotheses must dominate evidence.

Abstract

The likelihood principle makes strong claims about the nature of statistical evidence but is controversial. Its claims are undermined by the existence of several examples that are assumed to show that it allows, with unity probability, domination of all other hypotheses by the uninteresting, determinist hypothesis that whatever happened had to happen. Such examples are generally assumed to be important obstacles to the application of the likelihood principle: they are counter-examples to the principle. A re-analysis of Birnbaum's 1969 `counter-example', demonstrates that the standardly reported analyses of such examples involves an inappropriate treatment of a nuisance parameter and that, when the nuisance parameter is adequately considered, there is no conflict between the evidential consequences of the likelihood principle and the intuitive evidential account of the problem. It also shows that the conclusion that the likelihood principle allows the determinist hypothesis to dominate with unity probability requires a misconception about the scope of the likelihood principle or an inappropriately specified statistical model. Whatever happened did \textit{not} have to happen.