This paper presents a general model framework for detecting the preferential sampling of environmental monitors recording an environmental process across space and/or time. This is achieved by considering the joint distribution of an environmental process with a site--selection process that considers where and when sites are placed to measure the process. The environmental process may be spatial, temporal or spatio--temporal in nature. By sharing random effects between the two processes, the joint model is able to establish whether site placement was stochastically dependent of the environmental process under study. The embedding into a spatio--temporal framework also allows for the modelling of the dynamic site---selection process itself. Real--world factors affecting both the size and location of the network can be easily modelled and quantified. Depending upon the choice of population of locations to consider for selection across space and time under the site--selection process, different insights about the precise nature of preferential sampling can be obtained. The general framework developed in the paper is designed to be easily and quickly fit using the R-INLA package. We apply this framework to a case study involving particulate air pollution over the UK where a major reduction in the size of a monitoring network through time occurred. It is demonstrated that a significant response--biased reduction in the air quality monitoring network occurred. We also show that the network was consistently unrepresentative of the levels of particulate matter seen across much of GB throughout the operating life of the network. Finally we show that this may have led to a severe over-reporting of the population--average exposure levels experienced across GB. This could have great impacts on estimates of the health effects of black smoke levels.
On Ignorability of Preferential Sampling in Geostatistics
Centrum Wiskunde & Informatica（荷兰数学与计算机科学研究中心）；University of Miami（迈阿密大学）；Academia Sinica（中央研究院）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））
Accounting for Preferential Sampling Using a Constructed Covariate
Centre of Mathematics of the University of Minho (CMAT)（米尼奥大学数学中心）；Department of Mathematics of the Nova School of Science and Technology（新大学科学技术学院数学系）；Center for Mathematics and Applications (NOVA Math)（数学与应用研究中心）；NOVA University of Lisbon, Caparica, Portugal（里斯本新大学）；Portuguese Institute for Sea and Atmosphere (IPMA)（葡萄牙海洋与大气研究所）；Center of Statistics and its Applications (CEAUL)（统计学及其应用中心）；Military Academy Research Center - Military University Institute (CINAMIL)（军事学院研究中心）；Engineering Superior Institute of Lisbon (ISEL), Polytechnic Institute of Lisbon（里斯本高等工程学院）；NOVA University of Lisbon, Portugal（里斯本新大学）
Department of Mathematics of the Nova School of Science and Technology（新理工大学数学系）；Center for Mathematics and Applications (NOVA Math)（应用数学中心（NOVA Math））；NOVA University of Lisbon, Caparica, Portugal（里斯本诺瓦大学）；Instituto Politécnico do Cávado e Ave (IPCA)（卡瓦多和阿韦理工学院）
