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Title: Bayesian high-dimensional seemingly unrelated regression model with global-local shrinkage Authors:  Dongu Han - Korea University (Korea, South) [presenting]
Taeryon Choi - Korea University (Korea, South)
Abstract: Seemingly Unrelated Regression(SUR) is a general framework that can accommodate many useful models, such as multivariate regression or vector autoregressive model. In the era of big data, the number of predictors and the equations to be estimated simultaneously can be both large compared to the sample size. We handle this problem by adopting a variant of horseshoe prior to the parameters. Implementing this prior, we provide an efficient Markov Chain Monte Carlo(MCMC) algorithm without any additional tuning procedures. We also provide some theoretical results, indicating our model works well under mild conditions and provides better estimation compared to the conventional ones. Additionally, we also propose a variational Bayesian method that brings much computational gain without sacrificing the precision of estimation. Several empirical studies show that our proposed method works better than conventional ones.