Modeling Nonstationary Processes Through Dimension Expansion

LAND-USE FILTERING FOR NONSTATIONARY SPATIAL PREDICTION OF COLLECTIVE EFFICACY IN AN URBAN ENVIRONMENT

Collective efficacy-the capacity of communities to exert social control toward the realization of their shared goals-is a foundational concept in the urban sociology and neighborhood effects literature. Traditionally, empirical studies of collective efficacy use large sample surveys to estimate collective efficacy of different neighborhoods within an urban setting. Such studies have demonstrated an association between collective efficacy and local variation in community violence, educational achievement, and health. Unlike traditional collective efficacy measurement strategies, the Adolescent Health and Development in Context (AHDC) Study implemented a new approach, obtaining spatially-referenced, place-based ratings of collective efficacy from a representative sample of individuals residing in Columbus, OH. In this paper we introduce a novel nonstationary spatial model for interpolation of the AHDC collective efficacy ratings across the study area, which leverages administrative data on land use. Our constructive model specification strategy involves dimension expansion of a latent spatial process and the use of a filter defined by the land-use partition of the study region to connect the latent multivariate spatial process to the observed ordinal ratings of collective efficacy. Careful consideration is given to the issues of parameter identifiability, computational efficiency of an MCMC algorithm for model fitting, and fine-scale spatial prediction of collective efficacy.

Estimation of the Covariance Matrix in Hierarchical Bayesian Spatio-Temporal Modeling via Dimension Expansion

Ozone concentrations are key indicators of air quality. Modeling ozone concentrations is challenging because they change both spatially and temporally with complicated structures. Missing data bring even more difficulties. One of our interests in this paper is to model ozone concentrations in a region in the presence of missing data. We propose a method without any assumptions on the correlation structure to estimate the covariance matrix through a dimension expansion method for modeling the semivariograms in nonstationary fields based on the estimations from the hierarchical Bayesian spatio-temporal modeling technique (Le and Zidek). Further, we apply an entropy criterion (Jin et al.) based on a predictive model to decide if new stations need to be added. This entropy criterion helps to solve the environmental network design problem. For demonstration, we apply the method to the ozone concentrations at 25 stations in the Pittsburgh region studied. The comparison of the proposed method and the one is provided through leave-one-out cross-validation, which shows that the proposed method is more general and applicable.

Modeling Spatiotemporal Distribution of Mosquitoes Abundance With Unobservable Environmental Factors

Mosquito trap counts are heavily influenced by environmental factors such as temperature and precipitation. However, some important geographic factors, such as land use and elevation of a particular site, are often either not recorded or simplify not observable. This is a major issue in building a predictive model for the mosquito trap counts over time across a particular region. The collective impact of all unobservable factors for one particular site is estimated by a hidden dimension method. Application to mosquito trap counts in Peel Region has shown that our model can significantly improve the modeling accuracy of the generalized linear model. This method may provide a significantly better characterization of the spatiotemporal distribution of mosquito (Diptera: Culicidae) abundance in areas with green lands or open spaces.

PHENOMENOLOGICAL FORECASTING OF DISEASE INCIDENCE USING HETEROSKEDASTIC GAUSSIAN PROCESSES: A DENGUE CASE STUDY

In 2015 the US federal government sponsored a dengue forecasting competition using historical case data from Iquitos, Peru and San Juan, Puerto Rico. Competitors were evaluated on several aspects of out-of-sample forecasts including the targets of peak week, peak incidence during that week, and total season incidence across each of several seasons. our team was one of the winners of that competition, outperforming other teams in multiple targets/locales. In this paper we report on our methodology, a large component of which, surprisingly, ignores the known biology of epidemics at large-for example, relationships between dengue transmission and environmental factors-and instead relies on flexible nonparametric nonlinear Gaussian process (GP) regression fits that "memorize" the trajectories of past seasons, and then "match" the dynamics of the unfolding season to past ones in real-time. Our phenomenological approach has advantages in situations where disease dynamics are less well understood, or where measurements and forecasts of ancillary covariates like precipitation are unavailable, and/or where the strength of association with cases are as yet unknown. In particular, we show that the GP approach generally outperforms a more classical generalized linear (autoregressive) model (GLM) that we developed to utilize abundant covariate information. We illustrate variations of our method(s) on the two benchmark locales alongside a full summary of results submitted by other contest competitors.

Modeling nonstationarity in space and time

We propose to model a spatio-temporal random field that has nonstationary covariance structure in both space and time domains by applying the concept of the dimension expansion method in Bornn et al. (2012). Simulations are conducted for both separable and nonseparable space-time covariance models, and the model is also illustrated with a streamflow dataset. Both simulation and data analyses show that modeling nonstationarity in both space and time can improve the predictive performance over stationary covariance models or models that are nonstationary in space but stationary in time.

Incorporating High-Dimensional Exposure Modelling into Studies of Air Pollution and Health

Performing studies on the risks of environmental hazards on human health requires accurate estimates of exposures that might be experienced by the populations at risk. Often there will be missing data and in many epidemiological studies, the locations and times of exposure measurements and health data do not match. To a large extent this will be due to the health and exposure data having arisen from completely different data sources and not as the result of a carefully designed study, leading to problems of both ‘change of support’ and ‘misaligned data’. In such cases, a direct comparison of the exposure and health outcome is often not possible without an underlying model to align the two in the spatial and temporal domains. The Bayesian approach provides the natural framework for such models; however, the large amounts of data that can arise from environmental networks means that inference using Markov Chain Monte Carlo might not be computationally feasible in this setting. Here we adapt the integrated nested Laplace approximation to implement spatio–temporal exposure models. We also propose methods for the integration of large-scale exposure models and health analyses. It is important that any model structure allows the correct propagation of uncertainty from the predictions of the exposure model through to the estimates of risk and associated confidence intervals. The methods are demonstrated using a case study of the levels of black smoke in the UK, measured over several decades, and respiratory mortality.

Non-stationary spatio-temporal modeling of traffic-related pollutants in near-road environments

A problem often encountered in environmental epidemiological studies assessing the health effects associated with ambient exposure to air pollution is the spatial misalignment between monitors' locations and subjects' actual residential locations. Several strategies have been adopted to circumvent this problem and estimate pollutants concentrations at unsampled sites, including spatial statistical or geostatistical models that rely on the assumption of stationarity to model the spatial dependence in pollution levels. Although computationally convenient, the assumption of stationarity is often untenable for pollutants concentration, particularly in the near-road environment. Building upon the work of Fuentes (2001) and Schmidt et al. (2011), in this paper we present a non-stationary spatio-temporal model for three traffic-related pollutants in a localized near-road environment. Modeling each pollutant separately and independently, we express each pollutant's concentration as a mixture of two independent spatial processes, each equipped with a non-stationary covariance function with covariates driving the non-stationarity and the mixture weights.