SMS scnews item created by John Ormerod at Fri 31 Mar 2017 1558
Type: Seminar
Distribution: World
Expiry: 7 Apr 2017
Calendar1: 7 Apr 2017 1400-1500
CalLoc1: Carslaw 173
CalTitle1: Bayesian hypothesis tests with diffuse priors: Can we have our cake and eat it too?
Auth: jormerod@pjormerod5.pc (assumed)

# Statistics Seminar: John Ormerod (Sydney) -- Bayesian hypothesis tests with diffuse priors: Can we have our cake and eat it too?

Abstract:

We introduce a new class of priors for  Bayesian hypothesis testing, which we name
cake priors’’. These priors circumvent Bartlett’s paradox (also called the
Jeffreys-Lindley paradox); the problem associated with the use of diffuse priors
leading to nonsensical statistical inferences. Cake priors allow the use of
diffuse priors (having ones cake) while achieving theoretically justified
inferences (eating it too). Lindley’s paradox will also be discussed. We will show
the resulting Bayesian hypotheses tests, including scenarios under which the one
and two sample t-tests, linear models, and generalized linear models are typically
derived. A novel construct involving a hypothetical data-model pair will be used
to extend cake priors to handle the case where there are zero free parameters under
the null hypothesis. The resulting test statistics take the form of a penalized
likelihood ratio test statistic. By considering the sampling distribution under the
null and alternative hypotheses we show (under certain assumptions) that these
Bayesian hypothesis tests are strongly Chernoff-consistent, i.e., achieve zero type
I and II errors asymptotically. This sharply contrasts with classical tests, where
the level of the test is held constant and so are not Chernoff-consistent.

Joint work with: Michael Stewart, Weichang Yu, and Sarah Romanes.


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