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Activity Number: 376 - All Things Bayesian: The Next Generation
Type: Invited
Date/Time: Tuesday, July 30, 2019 : 2:00 PM to 3:50 PM
Sponsor: International Indian Statistical Association
Abstract #300466 Presentation
Title: Honey I Shrunk the Intercept
Author(s): Ananda Sen* and Phil Boonstra
Companies: University of Michigan and University of Michigan
Keywords: Bayesian Inference; Exponential-Power Distribution; Pivotal Separation; Quasi-Complete Separation; Rare Events

In logistic regression, separation occurs when a linear combination of predictors perfectly discriminates the binary outcome. Because finite-valued maximum likelihood parameter estimates do not exist under separation, Bayesian regressions with informative shrinkage of the regression coefficients offer a suitable alternative. Efficiency in estimating regression coefficients may also depend upon the choice of intercept prior, yet relatively little focus has been given on whether and how to shrink the intercept parameter. In this talk we focus on a class of alternative prior distributions for the intercept that down-weight implausibly extreme regions of the parameter space, rendering regression estimates less sensitive to separation. Relative to diffuse priors, these proposed priors generally yield more efficient estimators of the regression coefficients when the data are nearly separated. The estimators are equally efficient in non-separated datasets, making them suitable for default use. Extensive simulation studies highlight key findings of the investigation.

Authors who are presenting talks have a * after their name.

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