Montserrat Fuentes

Handbook of Spatial Statistics

Introduction Historical Introduction, Peter J. Diggle Continuous Spatial Variation Continuous Parameter Stochastic Process Theory, Tilmann Gneiting and Peter Guttorp Classical Geostatistical Methods, Dale L. Zimmerman and Michael Stein Likelihood-Based Methods, Dale L. Zimmerman Spectral Domain, Montserrat Fuentes and Brian Reich Asymptotics for Spatial Processes, Michael Stein Hierarchical Modeling with Spatial Data, Christopher K. Wikle Low Rank Representations for Spatial Processes, Christopher K. Wikle Constructions for Nonstationary Spatial Processes, Paul D. Sampson Monitoring Network Design, James V. Zidek and Dale L. Zimmerman Non-Gaussian and Nonparametric Models for Continuous Spatial Data, Mark F.J. Steel and Montserrat Fuentes Discrete Spatial Variation Discrete Spatial Variation, Havard Rue and Leonard Held Conditional and Intrinsic Autoregressions, Leonhard Held and Havard Rue Disease Mapping, Lance Waller and Brad Carlin Spatial Econometrics, R. Kelley Pace and James LeSage Spatial Point Patterns Spatial Point Process Theory, Marie-Colette van Lieshout Spatial Point Process Models, Valerie Isham Nonparametric Methods, Peter J. Diggle Parametric Methods, Jesper Moller Modeling Strategies, Adrian Baddeley Multivariate and Marked Point Processes, Adrian Baddeley Point Process Models and Methods in Spatial Epidemiology, Lance Waller Spatio-Temporal Processes Continuous Parameter Spatio-Temporal Processes, Tilmann Gneiting and Peter Guttorp Dynamic Spatial Models Including Spatial Time Series, Dani Gamerman Spatio-Temporal Point Processes, Peter J. Diggle and Edith Gabriel Modeling Spatial Trajectories, David R. Brillinger Data Assimilation, Douglas W. Nychka and Jeffrey L. Anderson Additional Topics Multivariate Spatial Process Models, Alan E. Gelfand and Sudipto Banerjee Misaligned Spatial Data: The Change of Support Problem, Alan E. Gelfand Spatial Aggregation and the Ecological Fallacy, Jonathan Wakefield and Hilary Lyons Spatial Gradients and Wombling, Sudipto Banerjee Index

Approximate Likelihood for Large Irregularly Spaced Spatial Data

Likelihood approaches for large, irregularly spaced spatial datasets are often very difficult, if not infeasible, to implement due to computational limitations. Even when we can assume normality, exact calculations of the likelihood for a Gaussian spatial process observed at n locations requires O(n3) operations. We present a version of Whittles approximation to the Gaussian log-likelihood for spatial regular lattices with missing values and for irregularly spaced datasets. This method requires O(nlog2n) operations and does not involve calculating determinants. We present simulations and theoretical results to show the benefits and the performance of the spatial likelihood approximation method presented here for spatial irregularly spaced datasets and lattices with missing values. We apply these methods to estimate the spatial structure of sea surface temperatures using satellite data with missing values.

Bayesian Spatial Quantile Regression

Tropospheric ozone is one of the six criteria pollutants regulated by the United States Environmental Protection Agency under the Clean Air Act and has been linked with several adverse health effects, including mortality. Due to the strong dependence on weather conditions, ozone may be sensitive to climate change and there is great interest in studying the potential effect of climate change on ozone, and how this change may affect public health. In this paper we develop a Bayesian spatial model to predict ozone under different meteorological conditions, and use this model to study spatial and temporal trends and to forecast ozone concentrations under different climate scenarios. We develop a spatial quantile regression model that does not assume normality and allows the covariates to affect the entire conditional distribution, rather than just the mean. The conditional distribution is allowed to vary from site-to-site and is smoothed with a spatial prior. For extremely large datasets our model is computationally infeasible, and we develop an approximate method. We apply the approximate version of our model to summer ozone from 1997–2005 in the Eastern U.S., and use deterministic climate models to project ozone under future climate conditions. Our analysis suggests that holding all other factors fixed, an increase in daily average temperature will lead to the largest increase in ozone in the Industrial Midwest and Northeast.

A multivariate semiparametric Bayesian spatial modeling framework for hurricane surface wind fields

Storm surge, the onshore rush of sea water caused by the high winds and low pressure associated with a hurricane, can compound the effects of inland flooding caused by rainfall, leading to loss of property and loss of life for residents of coastal areas. Numerical ocean models are essential for creating storm surge forecasts for coastal areas. These models are driven primarily by the surface wind forcings. Currently, the gridded wind fields used by ocean models are specified by deterministic formulas that are based on the central pressure and location of the storm center. While these equations incorporate important physical knowledge about the structure of hurricane surface wind fields, they cannot always capture the asymmetric and dynamic nature of a hurricane. A new Bayesian multivariate spatial statistical modeling framework is introduced combining data with physical knowledge about the wind fields to improve the estimation of the wind vectors. Many spatial models assume the data follow a Gaussian distribution. However, this may be overly-restrictive for wind fields data which often display erratic behavior, such as sudden changes in time or space. In this paper we develop a semiparametric multivariate spatial model for these data. Our model builds on the stick-breaking prior, which is frequently used in Bayesian modeling to capture uncertainty in the parametric form of an outcome. The stick-breaking prior is extended to the spatial setting by assigning each location a different, unknown distribution, and smoothing the distributions in space with a series of kernel functions. This semiparametric spatial model is shown to improve prediction compared to usual Bayesian Kriging methods for the wind field of Hurricane Ivan.

Bayesian entropy for spatial sampling design of environmental data

We develop a spatial statistical methodology to design national air pollution monitoring networks with good predictive capabilities while minimizing the cost of monitoring. The underlying complexity of atmospheric processes and the urgent need to give credible assessments of environmental risk create problems requiring new statistical methodologies to meet these challenges. In this work, we present a new method of ranking various subnetworks taking both the environmental cost and the statistical information into account. A Bayesian algorithm is introduced to obtain an optimal subnetwork using an entropy framework. The final network and accuracy of the spatial predictions is heavily dependent on the underlying model of spatial correlation. Usually the simplifying assumption of stationarity, in the sense that the spatial dependency structure does not change location, is made for spatial prediction. However, it is not uncommon to find spatial data that show strong signs of nonstationary behavior. We build upon an existing approach that creates a nonstationary covariance by a mixture of a family of stationary processes, and we propose a Bayesian method of estimating the associated parameters using the technique of Reversible Jump Markov Chain Monte Carlo. We apply these methods for spatial prediction and network design to ambient ozone data from a monitoring network in the eastern US.

A Real-Time Hurricane Surface Wind Forecasting Model: Formulation and Verification

A real-time hurricane wind forecast model is developed by 1) incorporating an asymmetric effect into the Holland hurricane wind model; 2) using the National Oceanic and Atmospheric Administration (NOAA)/ National Hurricane Center’s (NHC) hurricane forecast guidance for prognostic modeling; and 3) assimilating the National Data Buoy Center (NDBC) real-time buoy data into the model’s initial wind field. The method is validated using all 2003 and 2004 Atlantic and Gulf of Mexico hurricanes. The results show that 6- and 12-h forecast winds using the asymmetric hurricane wind model are statistically more accurate than using a symmetric wind model. Detailed case studies were conducted for four historical hurricanes, namely, Floyd (1999), Gordon (2000), Lily (2002), and Isabel (2003). Although the asymmetric model performed generally better than the symmetric model, the improvement in hurricane wind forecasts produced by the asymmetric model varied significantly for different storms. In some cases, optimizing the symmetric model using observations available at initial time and forecast mean radius of maximum wind can produce comparable wind accuracy measured in terms of rms error of wind speed. However, in order to describe the asymmetric structure of hurricane winds, an asymmetric model is needed.

Comparison of exposure estimation methods for air pollutants: ambient monitoring data and regional air quality simulation.

Air quality modeling could potentially improve exposure estimates for use in epidemiological studies. We investigated this application of air quality modeling by estimating location-specific (point) and spatially-aggregated (county level) exposure concentrations of particulate matter with an aerodynamic diameter less than or equal to 2.5 μm (PM(2.5)) and ozone (O(3)) for the eastern U.S. in 2002 using the Community Multi-scale Air Quality (CMAQ) modeling system and a traditional approach using ambient monitors. The monitoring approach produced estimates for 370 and 454 counties for PM(2.5) and O(3), respectively. Modeled estimates included 1861 counties, covering 50% more population. The population uncovered by monitors differed from those near monitors (e.g., urbanicity, race, education, age, unemployment, income, modeled pollutant levels). CMAQ overestimated O(3) (annual normalized mean bias=4.30%), while modeled PM(2.5) had an annual normalized mean bias of -2.09%, although bias varied seasonally, from 32% in November to -27% in July. Epidemiology may benefit from air quality modeling, with improved spatial and temporal resolution and the ability to study populations far from monitors that may differ from those near monitors. However, model performance varied by measure of performance, season, and location. Thus, the appropriateness of using such modeled exposures in health studies depends on the pollutant and metric of concern, acceptable level of uncertainty, population of interest, study design, and other factors.

Impact of Climate Change on Ambient Ozone Level and Mortality in Southeastern United States

There is a growing interest in quantifying the health impacts of climate change. This paper examines the risks of future ozone levels on non-accidental mortality across 19 urban communities in Southeastern United States. We present a modeling framework that integrates data from climate model outputs, historical meteorology and ozone observations, and a health surveillance database. We first modeled present-day relationships between observed maximum daily 8-hour average ozone concentrations and meteorology measured during the year 2000. Future ozone concentrations for the period 2041 to 2050 were then projected using calibrated climate model output data from the North American Regional Climate Change Assessment Program. Daily community-level mortality counts for the period 1987 to 2000 were obtained from the National Mortality, Morbidity and Air Pollution Study. Controlling for temperature, dew-point temperature, and seasonality, relative risks associated with short-term exposure to ambient ozone during the summer months were estimated using a multi-site time series design. We estimated an increase of 0.43 ppb (95% PI: 0.14–0.75) in average ozone concentration during the 2040’s compared to 2000 due to climate change alone. This corresponds to a 0.01% increase in mortality rate and 45.2 (95% PI: 3.26–87.1) premature deaths in the study communities attributable to the increase in future ozone level.

Maternal exposure to criteria air pollutants and congenital heart defects in offspring: results from the national birth defects prevention study.

Background: Epidemiologic literature suggests that exposure to air pollutants is associated with fetal development. Objectives: We investigated maternal exposures to air pollutants during weeks 2–8 of pregnancy and their associations with congenital heart defects. Methods: Mothers from the National Birth Defects Prevention Study, a nine-state case–control study, were assigned 1-week and 7-week averages of daily maximum concentrations of carbon monoxide, nitrogen dioxide, ozone, and sulfur dioxide and 24-hr measurements of fine and coarse particulate matter using the closest air monitor within 50 km to their residence during early pregnancy. Depending on the pollutant, a maximum of 4,632 live-birth controls and 3,328 live-birth, fetal-death, or electively terminated cases had exposure data. Hierarchical regression models, adjusted for maternal demographics and tobacco and alcohol use, were constructed. Principal component analysis was used to assess these relationships in a multipollutant context. Results: Positive associations were observed between exposure to nitrogen dioxide and coarctation of the aorta and pulmonary valve stenosis. Exposure to fine particulate matter was positively associated with hypoplastic left heart syndrome but inversely associated with atrial septal defects. Examining individual exposure-weeks suggested associations between pollutants and defects that were not observed using the 7-week average. Associations between left ventricular outflow tract obstructions and nitrogen dioxide and between hypoplastic left heart syndrome and particulate matter were supported by findings from the multipollutant analyses, although estimates were attenuated at the highest exposure levels. Conclusions: Using daily maximum pollutant levels and exploring individual exposure-weeks revealed some positive associations between certain pollutants and defects and suggested potential windows of susceptibility during pregnancy. Citation: Stingone JA, Luben TJ, Daniels JL, Fuentes M, Richardson DB, Aylsworth AS, Herring AH, Anderka M, Botto L, Correa A, Gilboa SM, Langlois PH, Mosley B, Shaw GM, Siffel C, Olshan AF, National Birth Defects Prevention Study. 2014. Maternal exposure to criteria air pollutants and congenital heart defects in offspring: results from the National Birth Defects Prevention Study. Environ Health Perspect 122:863–872; http://dx.doi.org/10.1289/ehp.1307289

Spatial‐Temporal Modeling of the Association between Air Pollution Exposure and Preterm Birth: Identifying Critical Windows of Exposure

Exposure to high levels of air pollution during the pregnancy is associated with increased probability of preterm birth (PTB), a major cause of infant morbidity and mortality. New statistical methodology is required to specifically determine when a particular pollutant impacts the PTB outcome, to determine the role of different pollutants, and to characterize the spatial variability in these results. We develop a new Bayesian spatial model for PTB which identifies susceptible windows throughout the pregnancy jointly for multiple pollutants (PM(2.5) , ozone) while allowing these windows to vary continuously across space and time. We geo-code vital record birth data from Texas (2002-2004) and link them with standard pollution monitoring data and a newly introduced EPA product of calibrated air pollution model output. We apply the fully spatial model to a region of 13 counties in eastern Texas consisting of highly urban as well as rural areas. Our results indicate significant signal in the first two trimesters of pregnancy with different pollutants leading to different critical windows. Introducing the spatial aspect uncovers critical windows previously unidentified when space is ignored. A proper inference procedure is introduced to correctly analyze these windows.