Approaches in Bayesian Graphical Modeling

• Activity Number: 235
• Type: Topic Contributed
• Date/Time: Monday, August 10, 2015 : 2:00 PM to 3:50 PM
• Sponsor: International Society for Bayesian Analysis (ISBA)
• Author(s): Christine Peterson*
• Companies: Stanford University
• Keywords: Bayesian inference ; graphical model ; Bayesian variable selection ; informative prior

Abstract

In this talk, I will discuss approaches proposed in my dissertation for the inference of graphical models in the Bayesian framework. Since networks are complex systems, they are difficult to infer given a limited number of observations. My thesis is focused on the development of methods which allow incorporation of prior information on particular edges or on the model structure to improve inference given small to moderate sample sizes. First, I propose an extension to the Bayesian graphical lasso which utilizes informative priors specific to each edge, allowing improved learning of the network structure when relevant information is available. Next, I develop a method for estimation of networks for a collection of related sample groups, where the sample size for each subgroup may be limited. Here I use a Markov random field prior to link the graphs within each group, encouraging common edges across sample groups when supported by the data. Finally, I highlight recent work which expands on my thesis research to enable the selection of predictors linked within a network. This approach allows the identification of related predictors which jointly affect an outcome.