Right, absolutely right! The outcome that is the Bayes factor should be treated as a summary, maybe a sufficient summary for testing purposes, and its value or better its predictive should be compared with what happens under each model or each hypothesis.

]]>Why constrain the output to reject or accept? Surely a rational human is not constrained to respond to a Bayes factor in a dichotomous manner.

(The simplicity of arithmetic that comes from dichotomisation is possibly what led Neyman & Pearson to their framework with the 0-1 loss function that you mention.)

]]>Thanks Keith!!! My main point, really. We should back off from providing definite conclusions and decisions, and only offer a calibration of our uncertainty…

]]>Agree with your points here but especially point 2 and 5 may well look like this to others “the statistical profession does not [have] solutions but rather just (hopefully sensible) ways to struggle through [making sense of] observations we some how get”.

What they really need to hear and grasp but not what a statistical association and many statistician want to convey.

By the way, for my experiments, Bayes factor of 2, yours 10¹⁰!

Keith O’Rourke

]]>If Bayes factors are used to reject hypotheses and to select models, what is a sufficiently large value for a Bayes factor? 2? 10? 10¹⁰? This is what I mean.

]]>Thanks!

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