Xu Chen’s research while affiliated with Duke University and other places

Linear quantile regression is a powerful tool to investigate how predictors may affect a response heterogeneously across different quantile levels. Unfortunately, existing approaches find it extremely difficult to adjust for any dependency between observation units, largely because such methods are not based upon a fully generative model of the data. For analysing spatially indexed data, we address this difficulty by generalizing the joint quantile regression model of Yang and Tokdar (Journal of the American Statistical Association, 2017, 112(519), 1107–1120) and characterizing spatial dependence via a Gaussian or t‐copula process on the underlying quantile levels of the observation units. A Bayesian semiparametric approach is introduced to perform inference of model parameters and carry out spatial quantile smoothing. An effective model comparison criteria is provided, particularly for selecting between different model specifications of tail heaviness and tail dependence. Extensive simulation studies and two real applications to particulate matter concentration and wildfire risk are presented to illustrate substantial gains in inference quality, prediction accuracy and uncertainty quantification over existing alternatives.

Linear quantile regression is a powerful tool to investigate how predictors may affect a response heterogeneously across different quantile levels. Unfortunately, existing approaches find it extremely difficult to adjust for any dependency between observation units, largely because such methods are not based upon a fully generative model of the data. For analyzing spatially indexed data, we address this difficulty by generalizing the joint quantile regression model of Yang and Tokdar (2017) and characterizing spatial dependence via a Gaussian or t copula process on the underlying quantile levels of the observation units. A Bayesian semiparametric approach is introduced to perform inference of model parameters and carry out spatial quantile smoothing. An effective model comparison criteria is provided, particularly for selecting between different model specifications of tail heaviness and tail dependence. Extensive simulation studies and an application to particulate matter concentration in northeast US are presented to illustrate substantial gains in inference quality, accuracy and uncertainty quantification over existing alternatives.

Variable selection is a key issue when analyzing high-dimensional data. The explosion of data with large sample sizes and dimensionality brings new challenges to this problem in both inference accuracy and computational complexity. To alleviate these problems, we propose a new scalable Markov chain Monte Carlo (MCMC) sampling algorithm for "large p small n" scenarios by generalizing multiple-try Metropolis to discrete model spaces and further incorporating neighborhood-based stochastic search. The proof of reversibility of the proposed MCMC algorithm is provided. Extensive simulation studies are performed to examine the efficiency of the new algorithm compared with existing methods. A real data example is provided to illustrate the prediction performances of the new algorithm.