Modeling Non-Stationary Processes Through Dimension Expansion

In this paper, we propose a novel approach to modeling nonstationary spatial fields. The proposed method works by expanding the geographic plane over which these processes evolve into higher dimensional spaces, transforming and clarifying complex patterns in the physical plane. By combining aspects of multi-dimensional scaling, group lasso, and latent variables models, a dimensionally sparse projection is found in which the originally nonstationary field exhibits stationarity. Following a comparison with existing methods in a simulated environment, dimension expansion is studied on a classic test-bed data set historically used to study nonstationary models. Following this, we explore the use of dimension expansion in modeling air pollution in the United Kingdom, a process known to be strongly influenced by rural/urban effects, amongst others, which gives rise to a nonstationary field

Health-Exposure Modelling and the Ecological Fallacy

Recently there has been increased interest in modelling the association between aggregate disease counts and environmental exposures measured, for example via air pollution monitors, at point locations. This paper has two aims: first we develop a model for such data in order to avoid ecological bias; second we illustrate that modelling the exposure surface and estimating exposures may lead to bias in estimation of health effects. Design issues are also briefly considered, in particular the loss of information in moving from individual to ecological data, and the at-risk populations to consider in relation to the pollution monitor locations. The approach is investigated initially through simulations, and is then applied to a study of the association between mortality in the over 65’s in the year 2000, and the previous year’s SO2, in London. We conclude that the use of the proposed model can provide valid inference, but the use of estimated exposures should be carried out with great caution

Estimating exposure response functions using ambient pollution concentrations

This paper presents an approach to estimating the health effects of an environmental hazard. The approach is general in nature, but is applied here to the case of air pollution. It uses a computer model involving ambient pollution and temperature input to simulate the exposures experienced by individuals in an urban area, while incorporating the mechanisms that determine exposures. The output from the model comprises a set of daily exposures for a sample of individuals from the population of interest. These daily exposures are approximated by parametric distributions so that the predictive exposure distribution of a randomly selected individual can be generated. These distributions are then incorporated into a hierarchical Bayesian framework (with inference using Markov chain Monte Carlo simulation) in order to examine the relationship between short-term changes in exposures and health outcomes, while making allowance for long-term trends, seasonality, the effect of potential confounders and the possibility of ecological bias. The paper applies this approach to particulate pollution (PM10) and respiratory mortality counts for seniors in greater London (≥65 years) during 1997. Within this substantive epidemiological study, the effects on health of ambient concentrations and (estimated) personal exposures are compared. The proposed model incorporates within day (or between individual) variability in personal exposures, which is compared to the more traditional approach of assuming a single pollution level applies to the entire population for each day. Effects were estimated using single lags and distributed lag models, with the highest relative risk, RR=1.02 (1.01–1.04), being associated with a lag of two days ambient concentrations of PM10. Individual exposures to PM10 for this group (seniors) were lower than the measured ambient concentrations with the corresponding risk, RR=1.05 (1.01–1.09), being higher than would be suggested by the traditional approach using ambient concentrations

Bayesian inferencing for wind resource characterisation

The growing role of wind power in power systems has motivated R&D on methodologies to characterise the wind resource at sites for which no wind speed data is available. Applications such as feasibility assessment of prospective installations and system integration analysis of future scenarios, amongst others, can greatly benefit from such methodologies. This paper focuses on the inference of wind speeds for such potential sites using a Bayesian approach to characterise the spatial distribution of the resource. To test the approach, one year of wind speed data from four weather stations was modelled and used to derive inferences for a fifth site. The methodology used is described together with the model employed and simulation results are presented and compared to the data available for the fifth site. The results obtained indicate that Bayesian inference can be a useful tool in spatial characterisation of wind

Ecological bias in studies of the short–term effects of air pollution on health.

Recently there has been great interest in modelling the association between aggregate disease counts and environmental exposures measured at point locations, for example via air pollution monitors. In such cases, the standard approach is to average the observed measurements from the individual monitors and use this in a log-linear health model. Hence such studies are ecological in nature being based on spatially aggregated health and exposure data. Here we investigate the potential for biases in the estimates of the effects on health in such settings. Such ecological bias may occur if a simple summary measure, such as a daily mean, is not a suitable summary of a spatially variable pollution surface. We assess the performance of commonly used models when confronted with such issues using simulation studies and compare their performance with a model specifically designed to acknowledge the effects of exposure aggregation. In addition to simulation studies, we apply the models to a case study of the short–term effects of particulate matter on respiratory mortality using data from Greater London for the period 2002–2005

Generalized Additive Models for Gigadata:Modeling the U.K. Black Smoke Network Daily Data

<p>We develop scalable methods for fitting penalized regression spline based generalized additive models with of the order of 10⁴ coefficients to up to 10⁸ data. Computational feasibility rests on: (i) a new iteration scheme for estimation of model coefficients and smoothing parameters, avoiding poorly scaling matrix operations; (ii) parallelization of the iteration’s pivoted block Cholesky and basic matrix operations; (iii) the marginal discretization of model covariates to reduce memory footprint, with efficient scalable methods for computing required crossproducts directly from the discrete representation. Marginal discretization enables much finer discretization than joint discretization would permit. We were motivated by the need to model four decades worth of daily particulate data from the U.K. Black Smoke and Sulphur Dioxide Monitoring Network. Although reduced in size recently, over 2000 stations have at some time been part of the network, resulting in some 10 million measurements. Modeling at a daily scale is desirable for accurate trend estimation and mapping, and to provide daily exposure estimates for epidemiological cohort studies. Because of the dataset size, previous work has focused on modeling time or space averaged pollution levels, but this is unsatisfactory from a health perspective, since it is often acute exposure locally and on the time scale of days that is of most importance in driving adverse health outcomes. If computed by conventional means our black smoke model would require a half terabyte of storage just for the model matrix, whereas we are able to compute with it on a desktop workstation. The best previously available reduced memory footprint method would have required three orders of magnitude more computing time than our new method. Supplementary materials for this article are available online.</p