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Friday, May 18
Computational Statistics
Advances in Bayesian Analytics
Fri, May 18, 1:30 PM - 3:00 PM
Grand Ballroom E

Likelihood, Confirmational Tenacity, and Mood Transitions in Bayesian Inference (304359)

*Nozer D. Singpurwalla, City University of Hong Kong 

Keywords: Principle of Conditionalization, Subjective Likelihood, Confirmational Tenacity

Coherence is a declared hallmark of Bayesian statistical inference. It is achieved by a faithful adherence to the calculus of probability. But in attempt- ing to do so, a Bayesian engages in the three maneouvers that need to be made transparent: i) undergoes a transition in mood from the indicative (or factual) to the irrealis (or subjunctive), and then back again to the indicative; ii) intro- duces a notion external to probability, namely, the likelihood; and iii) invokes a controversial philosophical principle called Bayesian Conditionalization. Mood transition is necessitated by the feature that assigned probabilities are in the indicative mood, whereas conditional probabilities are in the irrealis mood. The purpose of this paper is to raise awareness to these matters, which are implicit to what is referred to as a “turning of the Bayesian crank”, and to make explicit the interplay between the Bayesian inferential mechanism and the foundation- al underpinnings of probability. Our position is that the commonly practiced Bayesian prior to posterior iteration merely mimics the probability calculus, and in so doing casts pallor on the claim of coherence.