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Fast Algorithms and Theory for High-Dimensional Bayesian Varying Coefficient Models

Speaker Name: 
Ray Bai
Speaker Title: 
Postdoctoral Researcher
Speaker Organization: 
University of Pennsylvania
Start Time: 
Friday, January 17, 2020 - 10:00am
End Time: 
Friday, January 17, 2020 - 11:15am
Mariko Walton


Nonparametric varying coefficient (NVC) models are widely used for modeling time-varying effects on responses that are measured repeatedly. In this talk, we introduce the nonparametric varying coefficient spike-and-slab lasso (NVC-SSL) for Bayesian estimation and variable selection in NVC models. The NVC-SSL simultaneously selects and estimates the functionals of the significant time-varying covariates, while also accounting for temporal correlations. Our model can be implemented using a highly efficient expectation-maximization (EM) algorithm, thus avoiding the computational intensiveness of Markov chain Monte Carlo (MCMC) in high dimensions. In contrast to frequentist NVC models, hardly anything is known about the large-sample properties for Bayesian NVC models. In this talk, we take a step towards addressing this longstanding gap between methodology and theory by deriving posterior contraction rates under the NVC-SSL model when the number of covariates grows at nearly exponential rate with sample size. Finally, we introduce a simple method to make our method robust to misspecification of the temporal correlation structure. We illustrate our methodology through simulation studies and data analysis.







 Ray Bai received his PhD in Statistics from the University of Florida in 2018 under the supervision of Dr. Malay Ghosh. He is currently employed as a Postdoctoral Researcher at the University of Pennsylvania Perelman School of Medicine in the Department of Biostatistics, Epidemiology, and Informatics. His research interests include flexible Bayesian methodology, scalable algorithms for big data, and data mining electronic health records and observational health data.

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