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With the widespread availability of satellite-based instruments, many geophysical processes are measured on a global scale and they often show strong nonstationarity in the covariance structure. In this paper we present a flexible class of parametric covariance models that can capture the nonstationarity in global data, especially strong dependency of covariance structure on latitudes. We apply the Discrete Fourier Transform to data on regular grids, which enables us to calculate the exact likelihood for large data sets. Our covariance model is applied to global total column ozone level data on a given day. We discuss how our covariance model compares with some existing models.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS183 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

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The objective of this study was to determine the effects of farm management and environmental factors on preharvest spinach contamination with generic Escherichia coli as an indicator of fecal contamination. A repeated cross-sectional study was conducted by visiting spinach farms up to four times per growing season over a period of 2 years (2010 to 2011). Spinach samples (n ‫؍‬ 955) were collected from 12 spinach farms in Colorado and Texas as representative states of the Western and Southwestern United States, respectively. During each farm visit, farmers were surveyed about farm-related management and environmental factors using a questionnaire. Associations between the prevalence of generic E. coli in spinach and farm-related factors were assessed by using a multivariable logistic regression model including random effects for farm and farm visit. Overall, 6.6% of spinach samples were positive for generic E. coli. Significant risk factors for spinach contamination with generic E. coli were the proximity (within 10 miles) of a poultry farm, the use of pond water for irrigation, a >66-day period since the planting of spinach, farming on fields previously used for grazing, the production of hay before spinach planting, and the farm location in the Southwestern United States. Contamination with generic E. coli was significantly reduced with an irrigation lapse time of >5 days as well as by several factors related to field workers, including the use of portable toilets, training to use portable toilets, and the use of hand-washing stations. To our knowledge, this is the first report of an association between field workers' personal hygiene and produce contamination with generic E. coli at the preharvest level. Collectively, our findings support that practice of good personal hygiene and other good farm management practices may reduce produce contamination with generic E. coli at the preharvest level.

This paper investigates the cross-correlations across multiple climate model errors. We build a Bayesian hierarchical model that accounts for the spatial dependence of individual models as well as cross-covariances across different climate models. Our method allows for a nonseparable and nonstationary cross-covariance structure. We also present a covariance approximation approach to facilitate the computation in the modeling and analysis of very large multivariate spatial data sets. The covariance approximation consists of two parts: a reduced-rank part to capture the large-scale spatial dependence, and a sparse covariance matrix to correct the small-scale dependence error induced by the reduced rank approximation. We pay special attention to the case that the second part of the approximation has a block-diagonal structure. Simulation results of model fitting and prediction show substantial improvement of the proposed approximation over the predictive process approximation and the independent blocks analysis. We then apply our computational approach to the joint statistical modeling of multiple climate model errors.1. Introduction. This paper addresses the problem of combining multiple climate model outputs while accounting for dependence across different models as well as spatial dependence within each individual model. To study the impact of human activity on climate change, the Intergovernmental Panel on Climate Change (IPCC) is coordinating efforts worldwide to develop coupled atmosphere-ocean general circulation models (AOGCMs).