Grantee Research Project Results
Final Report: Hierarchical Statistical Analysis of Global and Regional Environmental Data
EPA Grant Number: R827257Title: Hierarchical Statistical Analysis of Global and Regional Environmental Data
Investigators: Cressie, Noel A.C. , Berliner, Mark , Wilke, Christopher K.
Institution: The Ohio State University , University of Missouri - Kansas City
EPA Project Officer: Hahn, Intaek
Project Period: September 1, 1998 through August 31, 2001 (Extended to March 31, 2003)
Project Amount: $325,000
RFA: Environmental Statistics (1998) RFA Text | Recipients Lists
Research Category: Environmental Statistics , Human Health , Aquatic Ecosystems
Objective:
The objectives of this research project were to: (1)implement hierarchical spatiotemporal statistical modeling of environmental phenomena (e.g., sea-surface temperatures, disease mortality/morbidity rates, remote sensing data); (2) find computationally efficient ways to filter, statistically, massive spatiotemporal datasets, such as one obtains from polar-orbiting satellites; and (3) investigate ways to link two or more spatiotemporal environmental processes, one being explanatory for the other.
Summary/Accomplishments (Outputs/Outcomes):
We accomplished the following during the grant period:
- Defined a strategy for modeling spatial environmental data.
- Considered the least-squares approach for estimating parameters of a spatial variogram and established consistency and asymptotic normality of these estimators under general conditions. Identified two necessary and sufficient conditions for these estimators to be asymptotically efficient.
- Developed a Bayesian fingerprinting methodology for assessing anthropogenic impacts on climate. The investigators developed a spatial CO2 fingerprint based on control and forced model output from the National Center for Atmospheric Research Climate Systems Model. The prior model for the amplitude of the fingerprint of this Bayesian approach was a mixture of two distributions: one reflects prior uncertainty in the anticipated value of the amplitude under the hypothesis of no climate change, and the second reflects behavior assuming climate change forced by CO2. A robust Bayesian analysis was used, which investigated the ranges of posterior inference as prior inputs were varied.
- Reported a collection of examples demonstrating the power of hierarchical modeling of environmental processes. These included combining datasets and a variety of space-time modeling approaches. Also reviewed notions and examples of how hierarchical Bayesian modeling provides a mechanism for developing large-scale analyses bridging different sciences.
- Developed a new procedure for long-lead forecasting tropical Pacific sea surface temperatures using the methodology of hierarchical Bayesian dynamical modeling. Through its combining of substantial physical understanding and statistical modeling and learning, the procedure acquired considerable predictive skill. The approach accounted explicitly for uncertainty in the formulation of the model, which led to realistic error bounds on forecasts.
- Developed a spatially descriptive, temporally dynamic hierarchical model to be fitted to data that are aggregations in space and time. An infectious disease typically spreads via contact between infected and susceptible individuals. Because the small-scale movements and contacts between people generally were not recorded, available data regarding infectious disease often are aggregations in space and time. A Bayesian approach was taken and, using Markov chain Monte Carlo (MCMC), the posterior estimates of all parameters of interest were computed.
- Proposed a method for a Bayesian hierarchical analysis of count data that are observed at irregular locations in a bounded spatial domain. The data were modeled on a fine regular lattice, although many sites do not have observations at them. The main goal was to predict the hidden Poisson-mean process at all sites on the lattice given the spatially irregular count data; to do this, an efficient MCMC was used.
- Considered a spatiotemporal process and established the statistical methodology to analyze changes in the spatial cumulative distribution function over time. Hypothesis testing to detect a difference in the spatial random process at two time points was developed, as well as a prediction interval to quantify such discrepancy in the corresponding spatial cumulative distribution functions. The methodology was applied to an ecological index for foliage condition of red maple trees in the state of Maine in the early 1990s.
- Attempted to predict values that were spatially regular at different resolutions and also to process the data very rapidly. Polar-orbiting satellites remotely sense the earth and its atmosphere, producing datasets that give daily global coverage. For any given day, the data are many and spatially irregular. We developed a new statistical prediction methodology that preserves mass balance across resolutions and computes spatial predictions and prediction (co)variances extremely fast.
- Proposed a spatial empirical Bayes model for environmental data collected over a region and also proposed a predictor based on the kriging methodology with extra constraints that has useful unbiasedness properties in predicting nonlinear spatial functionals. This predictor, called the covariance-matching constrained kriging predictor, was an optimal linear predictor that matches not only first moments but second moments as well. A practical algorithm was determined for computing the predictor.
- Investigated how regression coefficients measuring covariate effects at the point level are modified under aggregation. Changing the level of aggregation leads to completely different conclusions about exposure-effect relationships, a phenomenon often referred to as ecological bias. The notion of maximum entropy was used to approximate that part of the within-area distribution of the exposure variable that was unknown. The approximation then was used to obtain an expression for the ecological bias. The methodology was applied to a radon-exposure study conducted in France.
- Developed hierarchical models for environmental phenomena and specifically considered computational speed-ups. The linking methodology also was explored. The general idea was to link the El Niño/La Niña forecasting skill we obtained with the ecological research we reviewed.
- Developed hierarchical models for environmental phenomena and specifically considered computational speed-ups for massive data. The linking of spatio-temporal processes also was considered.
As a result of this Science To Achieve Results grant, a great deal has been learned about how random variability can be incorporated into physical or biological models in the presence of noisy and missing data. When those data are massive, multiresolutional algorithms give optimal spatial statistical predictors.
Journal Articles on this Report : 15 Displayed | Download in RIS Format
| Other project views: | All 103 publications | 29 publications in selected types | All 19 journal articles |
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Aldworth J, Cressie N. Prediction of nonlinear spatial functionals. Journal of Statistical Planning and Inference 2003;112(1-2):3-41. |
R827257 (2001) R827257 (Final) |
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Berliner LM, Levine RA, Shea DJ. Bayesian climate change assessment. Journal of Climate 2000;13(21):3805-3820. |
R827257 (2000) R827257 (Final) |
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Berliner LM, Wikle CK, Cressie N. Long-lead prediction of Pacific SSTs via Bayesian dynamic modeling. Journal of Climate 2000;13(22):3953-3968. |
R827257 (2000) R827257 (Final) |
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Berliner M. Hierarchical Bayesian modeling in the environmental sciences. Allgemeines Statistisches Archiv (AStA Advances in Statistical Analysis) 2000;84(2):141-153. |
R827257 (2000) R827257 (Final) |
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Cressie N, Stern HS, Wright DR. Mapping rates associated with polygons. Journal of Geographical Systems 2000;2(1):61-69. |
R827257 (1999) R827257 (Final) |
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Cressie N, Pardo L, del Carmen Pardo M. Size and power considerations for testing loglinear models using ϕ-divergence test statistics. Statistica Sinica 2003;13(2):555-570. |
R827257 (2001) R827257 (Final) |
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Gabrosek J, Cressie N. The effect on attribute prediction of location uncertainty in spatial data. Geographical Analysis 2002;34(3):262-285. |
R827257 (2001) R827257 (Final) |
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Huang H-C, Cressie N, Gabrosek J. Fast, resolution-consistent spatial prediction of global processes from satellite data. Journal of Computational and Graphical Statistics 2002;11(1):63-88. |
R827257 (2001) R827257 (Final) |
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Lahiri SN, Lee Y, Cressie N. On asymptotic distribution and asymptotic efficiency of least squares estimators of spatial variogram parameters. Journal of Statistical Planning and Inference 2002;103(1-2):65-85. |
R827257 (1999) R827257 (2001) R827257 (Final) |
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Mugglin AS, Cressie N, Gemmell I. Hierarchical statistical modelling of influenza epidemic dynamics in space and time. Statistics in Medicine 2002;21(18):2703-2721. |
R827257 (2001) R827257 (Final) |
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Stern HS, Cressie N. Posterior predictive model checks for disease mapping models. Statistics in Medicine 2000;19(17-18):2377-2397. |
R827257 (1999) R827257 (Final) |
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Wikle CK. A kernel-based spectral model for non-Gaussian spatio-temporal processes. Statistical Modelling 2002;2(4):299-314. |
R827257 (2001) R827257 (Final) |
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Wikle CK, Berliner LM, Milliff RF. Hierarchical Bayesian approach to boundary value problems with stochastic boundary conditions. Monthly Weather Review 2003;131(6):1051-1062. |
R827257 (Final) |
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Wikle CK. Hierarchical Bayesian models for predicting the spread of ecological processes. Ecology 2003;84(6):1382-1394. |
R827257 (2001) R827257 (Final) |
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Zhu J, Lahiri SN, Cressie N. Asymptotic inference for spatial CDFs over time. Statistica Sinica 2002;12(3):843-861. |
R827257 (Final) |
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Supplemental Keywords:
ambient air, atmosphere, global climate, stratospheric ozone, precipitation, health effects, ecological effects, human health, CFCs, Bayesian, biology, physics, ecology, epidemiology, mathematics, modeling, climate models, satellite, remote sensing, agriculture,, RFA, Economic, Social, & Behavioral Science Research Program, Scientific Discipline, Air, Ecosystem Protection/Environmental Exposure & Risk, Ecology, air toxics, Ecosystem/Assessment/Indicators, Mathematics, climate change, Ecological Effects - Environmental Exposure & Risk, Environmental Statistics, atmospheric, risk assessment, regional environmental data, remote sensing, EMAP, environmental monitoring, stratospheric ozone, Bayesian space-time model, global environmental data, mortality rates, satellite data, statistical models, climate models, global warming, hierarchical statistical analysis, statistical methods, EOSRelevant Websites:
Ohio State University - Department of Statistics Exit
Progress and Final Reports:
Original AbstractThe perspectives, information and conclusions conveyed in research project abstracts, progress reports, final reports, journal abstracts and journal publications convey the viewpoints of the principal investigator and may not represent the views and policies of ORD and EPA. Conclusions drawn by the principal investigators have not been reviewed by the Agency.