High-dimensional and spatial data analysis by Bayesian inference

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Project summary: Whereas (1) standard regression models such as mean regression (ordinary least-squares regression) have been widely applied in many fields such as economics, genetics, ecology and environment and attracted huge amount of attention in literature, and (2) Bayesian inference is one of popular methods recent decades, there is relatively little work on Bayesian inference of regression models beyond mean for problems in those fields.This project aims to: develop novel methods of Bayesian autoregressive beyond mean, propose new single-index models for high-dimensional data analysis, explore effective spatial regression beyond mean, compare different algorithms for Bayesian inference of regression models above.