Ronald R. Hocking Lectures: Merlise Clyde

MERLISE CLYDE 

 

GUEST LECTURER FOR THE RONALD R. HOCKING ENDOWED LECTURE SERIES

 

Professor & Chair Department of Statistical Science
Duke University

 

Bayesian Analysis of Linear Models

 

ABSTRACT

Linear models have a long and rich history and continue to play an important role in statistical inference and decision making, providing the foundations for more complex hierarchical models. Building on this, Bayesian treatments of linear models offer a perhaps overwhelming smorgasbord of prior choices. Prior distributions such as Zellner’s g-prior and related mixtures of g-priors greatly simplify the array of options and have been widely used for inference, model selection and model averaging, with many desirable theoretical and computational properties. These priors may be appealing to non-Bayesians as posterior distributions are functions of the usual OLS or maximum likelihood estimates and test statistics, with posterior probabilities or Bayes Factors providing evidence in favor or against a hypothesis. Recent results, however, suggest that using a common g to scale the variances of all coefficients within a model may inadvertently lead to a Lindley/Bartlett paradox with Bayes factors favoring the null hypothesis or simpler models in direct contradiction to likelihood ratio tests and desiderata proposed in Bayarri et al. Turning attention to models based on factorial designs, we present a new family of block g-priors and mixtures for multi-way arrays with desirable theoretical properties that encompass both mixed and random effect models and can be employed in over-parameterized linear models. In the special case of 2k factorials we draw connections between these priors and popular shrinkage priors such as the horseshoe prior.

 

 

Monday, 12/3/2018, BLOC 457, 11:30 AM