Archive for the ‘Probabilities’ Category


Why the Law of Likelihood Applies Only to Mutually Exclusive Hypotheses

March 20, 2014

Greg Gandenberger

Abstract: The Law of Likelihood is the central thesis of likelihoodism, one of three major schools of thought about the notion of evidence in science (Sober, 2008, Ch. 1). It says that datum E favors hypothesis H1 over H2 if and only if the likelihood function k = Pr(E|H1)/Pr(E|H2) > 1, in which case k measures the degree of that favoring. I propose to restrict the Law of Likelihood to mutually exclusive hypotheses. This proposal seems natural and suffices to block a counterexample due to Fitelson (2007, 476- 7), but it faces at least three significant objections: (1) it conflicts with plausible constraints on the notion of evidential favoring, (2) it fails to address the tacking paradox, and (3) it seems to exclude cases involving competing causal claims and cases involving nested models. I respond to each of those objections.


The Likelihood Principle (Prospectus Preview)

January 19, 2012

Greg Gandenberger

This talk will provide an overview of the ideas I plan to develop in my prospectus. The presentation will be informal and will feature at least one leaping cat. Feel free to share both feedback on the content and general advice on writing a prospectus, forming a committee, and so on.


Debates between frequentists and Bayesians often revolve around prior probabilities, but the frequentist and Bayesian positions also differ in that Bayesian methods conform to the Likelihood Principle while frequentist methods do not. There are strong arguments for the Likelihood Principle that do not depend on the familiar coherence arguments for Bayesianism. These arguments are controversial and raise many deep issues that are ripe for philosophical scrutiny. They constitute a strong case for the Likelihood Principle, but they do not directly address key questions about the performance characteristics of likelihood-based methods. If it turns out that likelihood-based methods perform well even without appealing to priors, then frequentist methods are in serious trouble. If it turns out that likelihood-based methods perform poorly despite the strong first-principles arguments for the Likelihood Principle, then the choice between frequentist and Bayesian/likelihoodist methods involves a genuine tradeoff between evidentialist and reliabilist considerations. Widespread acceptance of the Likelihood Principle would have many important effects on science, including that it would allow ethically superior sequential clinical trials to be performed without elaborate and restrictive pre-trial planning.