Distribution of the maximum in air pollution fields

Abstract

Air quality standards are set to protect public health. The values of the standards are often based on health effect studies, without any statistical considerations. In order to judge if a standard is met measurements of ambient air quality are taken at monitoring stations, and these measured values are used to decide whether or not the standard has been violated. In this paper we examine the statistical quality of some air quality standards by taking both measurement error and variability of the ambient field away from the monitoring sites into account. In particular we study the distribution of the maximum of the ambient field conditional on a measured monitoring value at the value prescribed by the standard. The distribution of the maximum is computed using Rice's method and relies on a generalization of upcrossings of a level in one dimension to two dimensions.

On the conditional distributions and the efficient simulations of exponential integrals of Gaussian random fields

“…The latent intensity λ(t) [or equivalently f (t)] represents the unobserved (and appropriately transformed) metric of the pollution severity at location t. The mean function can be written as a linear combination of the observed covariates that may affect the pollution level, that is, µ(t) = β ⊤ x(t) is treated as a deterministic function. It is well understood that λ(t) is a smooth function of the spatial parameter t at the macro level as the atmosphere mixes well; see, for example, [1]. One natural question in epidemiology is the following: upon observing an unusually high number of asthma cases, what is their geographical distribution, that is, the conditional distribution of the point process N (•) given that N (T ) > b for some large b?…”

“…Note that Therefore at least one of (A * ) c ∩ D and A * ∩ D is nonempty. If mes((A * ) c ∩ D) ≥ 1 2 mes(D), we have the bound…”

Statistics and Climate

“…In the context of climate data, this average distribution becomes our statistical estimate of climate. Developing simultaneous confidence bands for the average distribution function or for the marginal density of time series data entails finding computational approaches to suprema for Gaussian processes [using tools such as in Cierco-Aroylle et al (2003) and Åberg & Guttorp (2008)] or Rosenblatt processes (Veillette & Taqqu 2010, Taqqu 2011, depending on the degree of dependence in the data. For multivariate extensions, the standard theory leads to approximations by a Kiefer process (Philipp & Pinzur 1980), and extensions of this theory to dependent situations exist (e.g., R üschendorf 1974).…”

The role of statisticians in international science policy

“…While the Palestine Statistics Office example has a very clear political aspect, albeit still being an international policy issue, there are many less obvious situations where the choice of research approach in itself has consequences that may be considered political. I have done some research on the statistical aspects of air quality standards (Guttorp, 2006; Åberg and Guttorp, 2008), where the approach has been to try to protect vulnerable members of society (e.g., asthmatic children or the elderly) by reducing their exposure to harmful air pollutants. The research, therefore, focuses on the risk that an individual living near a measurement site that does not violate the standard may, in spite of this, be exposed to harmful levels.…”