Bayes Reading Group: Leonardo Egidi

Date & Time

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. 


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


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