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

DOI10.48550/ARXIV.1907.06477arXiv1907.06477MaRDI QIDQ137298

Publication date: 15 July 2019

Abstract: Nonparametric varying coefficient (NVC) models are useful for modeling time-varying effects on responses that are measured repeatedly. In this paper, 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 significant varying coefficients, while also accounting for temporal correlations. Our model can be implemented using a computationally efficient expectation-maximization (EM) algorithm. We also employ a simple method to make our model robust to misspecification of the temporal correlation structure. In contrast to frequentist approaches, little is known about the large-sample properties for Bayesian NVC models when the dimension of the covariates

p

grows much faster than sample size

n

. In this paper, we derive posterior contraction rates for the NVC-SSL model when

p g g n

under both correct specification and misspecification of the temporal correlation structure. Thus, our results are derived under weaker assumptions than those seen in other high-dimensional NVC models which assume independent and identically distributed (iid) random errors. Finally, we illustrate our methodology through simulation studies and data analysis. Our method is implemented in the publicly available R package NVCSSL.