Bayes Reading Group: Leonardo Egidi

Friday Mar 25, 2022, 11:00 AM → 12:00 PM America/New_York

Virtual/--Flatiron Institute (162 5th Avenue)

Discussion Lead: Leonardo Egidi

Topic: A Bayesian fairy tale: the mysteries of the mixtures. Priors, likelihoods and other  'multi-headed' monsters

The Bayesian model consists of the prior–likelihood pair. A prior–data conflict arises whenever

the prior allocates most of its mass to regions of the parameter space where the likelihood is relatively

low. Once a prior–data conflict is diagnosed, what to do next is a hard question to answer. We propose

an automatic prior elicitation that involves a two-component mixture of a diffuse and an informative prior

distribution that favours the first component if a conflict emerges. Using various examples, we show that

these mixture priors can be useful in regression models as a device for regularizing the estimates and

retrieving useful inferential conclusions. According to the 'in medio stat virtus philosophy',

a mixture prior combining the two extremes—the wildly informative prior and the weakly informative prior—

can realistically average over them and represent a sound compromise to get robust inferences.

Mixture prior distributions are much used in many statistical applications, such as clinical

trials, especially to avoid prior-data conflicts for future sets of observations/experiments.

We explicitly prove that the effective sample size (ESS) of a mixture prior rarely exceeds the ESS of 

any individual mixture component density of the prior. 

Link: https://onlinelibrary.wiley.com/doi/full/10.1002/cjs.11637

https://www.sciencedirect.com/science/article/abs/pii/S0167715221002856

https://statmodeling.stat.columbia.edu/2022/01/13/the-fairy-tale-of-the-mysteries-of-mixtures/

Please email Shakemia Browne at sbrowne@flatironinstitute.org for the Zoom link or to be added to the meeting list.