Miscellaneous
Colloquium Mathematical Philosophy, Greg Gandenberger (Pittsburgh) gives a talk at the MCMP Colloquium (22 April, 2015) titled "New Responses to Some Purported Counterexamples to Likelihoodist Principles". Abstract: The Likelihood Principle is important because the frequentist statistical methods that are most commonly used in science violate it, while rival likelihoodist and Bayesian methods do not. It is supported by a variety of arguments, including several proofs from intuitively plausible axioms. It also faces many objections, including several purported counterexamples. In this talk, I provide new responses to four purported counterexamples to the Likelihood Principle and its near-corollary the Law of Likelihood that are not adequately addressed in the existing literature. I first respond to examples due to Fitelson and Titelbaum that I argue are adequately addressed by restricting the Law of Likelihood to mutually exclusive hypotheses. I then respond to two counterexamples from the statistical literature. My responses to these latter examples are novel in that they do not appeal to prior probabilities, which is important for attempts to use the Likelihood Principle to provide an argument for Bayesian approaches that does presuppose the permissibility of using prior probabilities in science.