Hierarchical Shrinkage Priors for Dynamic Regressions With Many Predictors
نویسنده
چکیده
This paper builds on a simple unified representation of shrinkage Bayes estimators based on hierarchical Normal-Gamma priors. Various popular penalized least squares estimators for shrinkage and selection in regression models can be recovered using this single hierarchical Bayes formulation. Using 129 U.S. macroeconomic quarterly variables for the period 1959 – 2010 I exhaustively evaluate the forecasting properties of Bayesian shrinkage in regressions with many predictors. Results show that for particular data series hierarchical shrinkage dominates factor model forecasts, and hence is a valuable addition to existing methods for handling large dimensional data.
منابع مشابه
Bayesian Factor Regression Models in the “Large p, Small n” Paradigm
I discuss Bayesian factor regression models and prediction with very many explanatory variables. Such problems arise in many areas; my motivating applications are in studies of gene expression in functional genomics. I first discuss empirical factor (principal components) regression, and the use of general classes of shrinkage priors, with an example. These models raise foundational questions f...
متن کاملBayesian Rank Selection in Multivariate Regression
Estimating the rank of the coefficient matrix is a major challenge in multivariate regression, including vector autoregression (VAR). In this paper, we develop a novel fully Bayesian approach that allows for rank estimation. The key to our approach is reparameterizing the coefficient matrix using its singular value decomposition and conducting Bayesian inference on the decomposed parameters. By...
متن کاملHierarchical priors for Bayesian CART shrinkage
The Bayesian CART (classiication and regression tree) approach proposed by Chipman, George and McCulloch (1998) entails putting a prior distribution on the set of all CART models and then using stochastic search to select a model. The main thrust of this paper is to propose a new class of hierarchical priors which enhance the potential of this Bayesian approach. These priors indicate a preferen...
متن کاملChoice of Hierarchical Priors: Admissibility in Estimation of Normal Means1 Byjames
In hierarchical Bayesian modeling of normal means, it is common to complete the prior specification by choosing a constant prior density for unmodeled hyperparameters (e.g., variances and highest-level means). This common practice often results in an inadequate overall prior, inadequate in the sense that estimators resulting from its use can be inadmissible under quadratic loss. In this paper, ...
متن کاملBayesian Models for Structured Sparse Estimation via Set Cover Prior
A number of priors have been recently developed for Bayesian estimation of sparse models. In many applications the variables are simultaneously relevant or irrelevant in groups, and appropriately modeling this correlation is important for improved sample efficiency. Although group sparse priors are also available, most of them are either limited to disjoint groups, or do not infer sparsity at g...
متن کامل