Daniel Kowal (Rice University)

“Scalable Bayesian Inference and Summarization for Functional Data”

Modern scientific monitoring systems, such as wearable and implantable devices, commonly record data over a continuous domain at high resolutions. These functional data are high-dimensional, strongly correlated, and usually measured concurrently with other variables of interest. Bayesians models for functional data are particularly appealing: they accommodate multiple dependence structures, handle missing or irregularly-spaced data, and provide regularization via shrinkage priors. However, these models are often complex, computationally intensive, and difficult to interpret. This talk will focus on two fundamental challenges for Bayesian functional data analysis: (1) constructing sufficiently flexible and scalable functional regression models and (2) extracting interpretable posterior summaries. The proposed modeling framework is nonparametric and uses an unknown functional basis to learn prominent functional features, which are associated with scalar predictors within a regression model. A customized projection-based Gibbs sampler provides posterior inference with linear time complexity in the number of predictors, which is empirically faster than existing frequentist and Bayesian alternatives. Using the posterior distribution, a decision theoretic approach for Bayesian variable selection is developed, which identifies a subset of covariates that retains nearly the predictive accuracy of the full model. The methodology is applied to actigraphy data to investigate the association between intraday physical activity and responses to a sleep questionnaire.