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Discussion on ‘Hierarchical Bayesian auto‐regressive models for large space time data with applications to ozone concentration modelling’ by Sujit Kumar Sahu and Khandoker Shuvo Bakar

Discussion on ‘Hierarchical Bayesian auto‐regressive models for large space time data with... It is a pleasure to congratulate the authors on their presentation of a significant research work on modeling ‘big‐ n ’ multivariate spatio‐temporal data through the Bayesian paradigm. The work excels in novelty as well as in extent. The application to air pollution, and more specifically to ozone concentration, using data from eastern USA is also a useful exercise. The problem of modeling such a big‐ n large data set, consisting of more than a million data points, includes the inversion of very high‐dimensional matrices iteratively. The authors avoid this and also possible multi‐collinearity problems by using an auto‐regressive Gaussian predictive processes formulation and then by choosing a much smaller dimensional set of knots. The results are shown to be quite favorable using several criteria. The paper addresses and quite comprehensively covers the main relevant issues. However, a few remarks may be in order. Although three covariates have been identified, the inclusion of the wind direction, a circular variable, is desirable because of its significant impact on air pollution. This would of course increase non‐trivially both the theoretical and computational complexities of model building. It is evident from the time series plots in Figure 3 that the temporal ‘growth’ has prominent differing patterns spatially, with a number of change points. This aspect could possibly be more rigorously included in the analysis by using the Dirichlet prior process approach with proper mixture priors for the relevant mean parameters (see, e.g., ). It has been pointed out in the paper that there is non‐compliance of primary ozone standard at several sites. In this backdrop, formal detection of hot spots through trend analysis would be quite desirable from also the practical usefulness of the analysis performed. The choice of the number as well as the locations of the knots should be made with care for the efficiency of the proposed methodology. Although the grid approach is convenient to apply, it may not lead to an efficient predictive model. Spatial heterogeneity is a major concern when such a large geographical region is to be encompassed by a single model. The celluloid surface plot in terms of the ozone concentration levels may be exploited for this purpose; for example, spatial clustering maybe enhanced to shed better light on both these choices. It is expected that the work in this paper will motivate and help future research in the general area of analysis of very large spatio‐temporal multivariate data sets. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Stochastic Models in Business and Industry Wiley

Discussion on ‘Hierarchical Bayesian auto‐regressive models for large space time data with applications to ozone concentration modelling’ by Sujit Kumar Sahu and Khandoker Shuvo Bakar

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References (2)

Publisher
Wiley
Copyright
Copyright © 2012 John Wiley & Sons, Ltd.
ISSN
1524-1904
eISSN
1526-4025
DOI
10.1002/asmb.1950
Publisher site
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Abstract

It is a pleasure to congratulate the authors on their presentation of a significant research work on modeling ‘big‐ n ’ multivariate spatio‐temporal data through the Bayesian paradigm. The work excels in novelty as well as in extent. The application to air pollution, and more specifically to ozone concentration, using data from eastern USA is also a useful exercise. The problem of modeling such a big‐ n large data set, consisting of more than a million data points, includes the inversion of very high‐dimensional matrices iteratively. The authors avoid this and also possible multi‐collinearity problems by using an auto‐regressive Gaussian predictive processes formulation and then by choosing a much smaller dimensional set of knots. The results are shown to be quite favorable using several criteria. The paper addresses and quite comprehensively covers the main relevant issues. However, a few remarks may be in order. Although three covariates have been identified, the inclusion of the wind direction, a circular variable, is desirable because of its significant impact on air pollution. This would of course increase non‐trivially both the theoretical and computational complexities of model building. It is evident from the time series plots in Figure 3 that the temporal ‘growth’ has prominent differing patterns spatially, with a number of change points. This aspect could possibly be more rigorously included in the analysis by using the Dirichlet prior process approach with proper mixture priors for the relevant mean parameters (see, e.g., ). It has been pointed out in the paper that there is non‐compliance of primary ozone standard at several sites. In this backdrop, formal detection of hot spots through trend analysis would be quite desirable from also the practical usefulness of the analysis performed. The choice of the number as well as the locations of the knots should be made with care for the efficiency of the proposed methodology. Although the grid approach is convenient to apply, it may not lead to an efficient predictive model. Spatial heterogeneity is a major concern when such a large geographical region is to be encompassed by a single model. The celluloid surface plot in terms of the ozone concentration levels may be exploited for this purpose; for example, spatial clustering maybe enhanced to shed better light on both these choices. It is expected that the work in this paper will motivate and help future research in the general area of analysis of very large spatio‐temporal multivariate data sets.

Journal

Applied Stochastic Models in Business and Industry – Wiley

Published: Sep 1, 2012

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