Geostatistics under preferential sampling in the presence of local repulsion effects
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Geostatistics under preferential sampling in the presence of local repulsion effects Gustavo da Silva Ferreira1 Received: 9 December 2019 / Revised: 22 June 2020 / Accepted: 9 July 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract This paper presents an extension of the Geostatistical model under preferential sampling in order to accommodate possible local repulsion effects. This local repulsion can be caused by the researcher in charge of collecting data who, after observing the stochastic process of interest in a specific location, avoids collecting new samples near this place. Proceeding in this way, the resulting sampling design would in practice include a repulsion window centered on each sampling location, even though the researcher was planning the sample preferentially. This perturbation in the Geostatistical model under preferential sampling can be modeled through a discrete nonhomogeneous stochastic process over a partition composed of M subregions of the study area, where only one sample lies in each subregion. Simulations and an application to real data are performed under the Bayesian approach and the effects of this perturbation on estimation and prediction are then discussed. The results obtained corroborate the idea that the proposed methodology corrects the distortions caused by this perturbation, thus mitigating the effects on inference and spatial prediction. Keywords Bayesian inference · Point Processes · Preferential sampling · Spatial processes Mathematics Subject Classification 62M30 · 62D99
Handling Editor: Bryan F. J. Manly
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Gustavo da Silva Ferreira [email protected] National School of Statistical Sciences, Brazilian Institute of Geography and Statistics, 106 Andre Cavalcanti St, Rio de Janeiro, RJ 20231-050, Brazil
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Environmental and Ecological Statistics
1 Introduction Geostatistics is the sub-area of spatial statistics in which data are obtained through a partial observation of a continuous stochastic process S = S(x) : x ∈ d . In general, data Y = (Y1 , . . . , Yn ) are observed in a finite set of locations x = (x1 , . . . , xn ) distributed over a region of interest D ⊂ d . Using the observed sample, the main goal of Geostatistics is to perform inference about the parameters of the underlying stochastic process and make predictions in unobserved locations x0 ∈ D. Traditional approaches to performing inference in Geostatistics consider the sample points x as fixed or, if they come from a stochastic process, independent of the process S(x) (see Cressie 1993; Diggle et al. 1998; Banerjee et al. 2004). However, when the sampling design is stochastic, it is necessary to specify the joint distribution of [Y , S, X ] and we will have a process under preferential sampling if S ⊥ X , i.e., if the sample design is dependent on the underlying stochastic process. Although most approaches to obtaining optimal sample plans assume independence between S and X (see Diggle and Lophaven 2006), in many practical situations the spatial co
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