Greg Gandenberger, PhD

L.J. Savage once hoped to show that "the superficially incompatible systems of ideas associated on the one hand with [subjective Bayesianism] and on the other hand with [classical statistics]...lend each other mutual support and clarification." By 1972, however, he had largely "lost faith in the devices" of classical statistics. One aspect of those "devices" that he found objectionable is that differences among the "stopping rules" that are used to decide when to end an experiment which are… Show more

L.J. Savage once hoped to show that "the superficially incompatible systems of ideas associated on the one hand with [subjective Bayesianism] and on the other hand with [classical statistics]...lend each other mutual support and clarification." By 1972, however, he had largely "lost faith in the devices" of classical statistics. One aspect of those "devices" that he found objectionable is that differences among the "stopping rules" that are used to decide when to end an experiment which are "noninformative" from a Bayesian perspective can affect decisions made using a classical approach. Two experiments that produce the same data using different stopping rules seem to differ only in the intentions of the experimenters regarding whether or not they would have carried on if the data had been different, which seem irrelevant to the evidential import of the data and thus to facts about what actions the data warrant.

I argue that classical and Bayesian ideas about stopping rules do in fact "lend each other" the kind of "mutual support and clarification" that Savage had originally hoped to find. They do so in a kind of case that is common in scientific practice, in which those who design an experiment have different interests from those who will make decisions in light of its results. I show that, in cases of this kind, Bayesian principles provide qualified support for the classical statistical practice of "penalizing" "biased" stopping rules. However, they require this practice in a narrower range of circumstances than classical principles do, and for different reasons. I argue that classical arguments for this practice are compelling in precisely the class of cases in which Bayesian principles also require it, and thus that we should regard Bayesian principles as clarifying classical statistical ideas about stopping rules rather than the reverse. Show less

Frequentist statistical methods continue to predominate in many areas of science despite prominent calls for "statistical reform." They do so in part because their main rivals, Bayesian methods, appeal to prior probability distributions that arguably lack an objective justification in typical cases. Some methodologists find a third approach called likelihoodism attractive because it avoids important objections to frequentism without appealing to prior probabilities. However, likelihoodist… Show more

Frequentist statistical methods continue to predominate in many areas of science despite prominent calls for "statistical reform." They do so in part because their main rivals, Bayesian methods, appeal to prior probability distributions that arguably lack an objective justification in typical cases. Some methodologists find a third approach called likelihoodism attractive because it avoids important objections to frequentism without appealing to prior probabilities. However, likelihoodist methods do not provide guidance for belief or action, but only assessments of data as evidence. I argue that there is no good way to use those assessments to guide beliefs or actions without appealing to prior probabilities, and that as a result likelihoodism is not a viable alternative to frequentism and Bayesianism for statistical reform efforts in science. Show less

I present a new proof of the likelihood principle that avoids two responses to a well-known proof due to Birnbaum ([1962]). I also respond to arguments that Birnbaum’s proof is fallacious, which if correct could be adapted to this new proof. On the other hand, I urge caution in interpreting proofs of the likelihood principle as arguments against the use of frequentist statistical methods.

When a technique purports to provide information that is not available to the unaided senses, it is natural to think that the only way to validate that technique is by appealing to a theory of the processes that lead from the object of study to the raw data. In fact, scientists have a variety of strategies for validating their techniques. Those strategies can yield multiple independent arguments that support the validity of the technique. Thus, it is possible to produce a robust body of data… Show more

When a technique purports to provide information that is not available to the unaided senses, it is natural to think that the only way to validate that technique is by appealing to a theory of the processes that lead from the object of study to the raw data. In fact, scientists have a variety of strategies for validating their techniques. Those strategies can yield multiple independent arguments that support the validity of the technique. Thus, it is possible to produce a robust body of data with a single technique. I illustrate and support these claims with a historical case study. Show less