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Activity Number: 444 - Modern and Practical Solutions to Difficult High-Dimensional Regression Problems
Type: Invited
Date/Time: Wednesday, July 31, 2019 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistical Computing
Abstract #300335
Title: Bayesian Function-On-Scalars Regression for High-Dimensional Data
Author(s): Daniel R Kowal* and Daniel Bourgeois
Companies: Rice University and Rice University
Keywords: shrinkage; factor model; variable selection; actigraphy data; MCMC

We develop a fully Bayesian framework for function-on-scalars regression with many predictors. The functional data response is modeled nonparametrically using unknown basis functions, which produces a flexible and data-adaptive functional basis. We incorporate shrinkage priors that effectively remove unimportant scalar covariates from the model and reduce sensitivity to the number of (unknown) basis functions. For variable selection in functional regression, we propose a decision theoretic posterior summarization technique, which identifies a subset of covariates that retains nearly the predictive accuracy of the full model. Our approach is broadly applicable for Bayesian functional regression models, and unlike existing methods provides joint rather than marginal selection of important predictor variables. Computationally scalable posterior inference is achieved using a Gibbs sampler with linear time complexity in the number of predictors. The methodology is applied to actigraphy data to investigate the association between intraday physical activity and responses to a sleep questionnaire.

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

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