Bayesian Variable Selection for the Seemingly Unrelated Regression Models with a Large Number of Predictors

Ando, Tomohiro

doi:10.14490/jjss.41.187

Cited by 10 publications

(8 citation statements)

References 26 publications

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“…The DMC method seemed to be more efficient in the computation process according to the real size of the generated posterior samples (DMC method was 10,000 and Gibbs was 33,000), similar to the inferences in other studies [58]. However, the computational efficiency may not become the future's primary indicator in evaluating the quality of the estimation method, since computing capacity has been exponentially increased over the years.…”

Section: Non-informative Vs Informative Priors In Bayesian Methodssupporting

confidence: 64%

A Bayesian Approach to Estimating Seemingly Unrelated Regression for Tree Biomass Model Systems

Xie

Zhang

et al. 2020

Forests

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Accurate estimation of tree biomass is required for accounting for and monitoring forest carbon stocking. Allometric biomass equations constructed by classical statistical methods are widely used to predict tree biomass in forest ecosystems. In this study, a Bayesian approach was proposed and applied to develop two additive biomass model systems: one with tree diameter at breast height as the only predictor and the other with both tree diameter and total height as the predictors for planted Korean larch (Larix olgensis Henry) in the Northeast, P.R. China. The seemingly unrelated regression (SUR) was used to fit the simultaneous equations of four tree components (i.e., stem, branch, foliage, and root). The model parameters were estimated by feasible generalized least squares (FGLS) and Bayesian methods using either non-informative priors or informative priors. The results showed that adding tree height to the model systems improved the model fitting and performance for the stem, branch, and foliage biomass models, but much less for the root biomass models. The Bayesian methods on the SUR models produced narrower 95% prediction intervals than did the classical FGLS method, indicating higher computing efficiency and more stable model predictions, especially for small sample sizes. Furthermore, the Bayesian methods with informative priors performed better (smaller values of deviance information criterion (DIC)) than those with the non-informative priors. Therefore, our results demonstrated the advantages of applying the Bayesian methods on the SUR biomass models, not only obtaining better model fitting and predictions, but also offering the assessment and evaluation of the uncertainties for constructing and updating tree biomass models.

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Section: Non-informative Vs Informative Priors In Bayesian Methodssupporting

confidence: 64%

A Bayesian Approach to Estimating Seemingly Unrelated Regression for Tree Biomass Model Systems

Xie

Zhang

et al. 2020

Forests

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“…The performance of this model is obtained using their available R package MBSP (Bai & Ghosh, 2018). Ando selection model: The Ando prior (Ando, 2012) considers a spike‐and‐slab prior that allows any β jk to be zero or nonzero without restricting a common set of predictors across all models (as in Brown et al, 1998). Sparse Partial Least Square (SPLS) model: This paper considers a partial least squares regression framework with a penalty function to select the most important covariates in frequentist approach.…”

Section: Simulation Studymentioning

confidence: 99%

“…In each case, we generate 100 datasets, and for each dataset and model choice we run the MCMC chain for 90,000 iterations with a burn‐in of 10,000 iterations. As the Ando (2012) model is computationally time‐consuming, we run only 1,000 iterations (and exclude the first 100 as burn‐in) for this approach. The computational time required for these 1,000 iterations of the Ando model is roughly the same amount of time required for the 100,000 iteration of the MONG and MOHS models.…”

Section: Simulation Studymentioning

confidence: 99%

“…We will discuss differences that distinguish our work in later sections. Other Bayesian approaches include a selection prior approach by Ando (2012) that allows different predictors to be active for different responses, but this model does not encourage similarity in predictor sets across responses. Additionally, Cheng, Kizilkaya, Zeng, Garrick, and Fernando (2018) developed a related proposal that is specific to genomic predictions.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian variable selection for multioutcome models through shared shrinkage

Kundu

Mitra

Gaskins

2020

Scandinavian J Statistics

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Variable selection over a potentially large set of covariates in a linear model is quite popular. In the Bayesian context, common prior choices can lead to a posterior expectation of the regression coefficients that is a sparse (or nearly sparse) vector with a few non-zero components, those covariates that are most important. This article extends the "global-local" shrinkage idea to a scenario where one wishes to model multiple response variables simultaneously. Here, we have developed a variable selection method for a K-outcome model (multivariate regression) that identifies the most important covariates across all outcomes. The prior for all regression coefficients is a mean zero normal with coefficient-specific variance term that consists of a predictor-specific factor (shared local shrinkage parameter) and a modelspecific factor (global shrinkage term) that differs in each model. The performance of our modeling approach is evaluated through simulation studies and a data example.

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“…However, since its introduction by Zellner (1996), Bayesian inference for the SUR model has become very popular. Several more recent references include but are not limited to Verzilli et al (2005); Ando and Zellner (2010); Ando (2011) and Billio et al (2016).…”

Section: Introductionmentioning

confidence: 99%

Robust Bayesian seemingly unrelated regression model

et al. 2018

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A robust Bayesian model for seemingly unrelated regression is proposed. By using heavy-tailed distributions for the likelihood, robustness in the response variable is attained. In addition, this robust procedure is combined with a diagnostic approach to identify observations that are far from the bulk of the data in the multivariate space spanned by all variables. The most distant observations are downweighted to reduce the effect of leverage points. The resulting robust Bayesian model can be interpreted as a heteroscedastic seemingly unrelated regression model. Robust Bayesian estimates are obtained by a Markov Chain Monte Carlo approach. Complications by using a heavy-tailed error distribution are resolved efficiently by representing these distributions as a scale mixture of normal distributions. Monte Carlo simulation experiments confirm that the proposed model outperforms its traditional Bayesian counterpart when the data are contaminated in the response and/or the input variables. The method is demonstrated on a real dataset.

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Bayesian Variable Selection for the Seemingly Unrelated Regression Models with a Large Number of Predictors

Cited by 10 publications

References 26 publications

A Bayesian Approach to Estimating Seemingly Unrelated Regression for Tree Biomass Model Systems

A Bayesian Approach to Estimating Seemingly Unrelated Regression for Tree Biomass Model Systems

Bayesian variable selection for multioutcome models through shared shrinkage

Robust Bayesian seemingly unrelated regression model

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