Geostatistical estimation and prediction for censored responses

Abstract

Spatially-referenced geostatistical responses that are collected in environmental sciences research are often subject to detection limits, where the measures are not fully quantifiable. This leads to censoring (left, right, interval, etc), and various ad hoc statistical methods (such as choosing arbitrary detection limits, or data augmentation) are routinely employed during subsequent statistical analysis for inference and prediction. However, inference may be imprecise and sensitive to the assumptions and approximations involved in those arbitrary choices. To circumvent this, we propose an maximum likelihood estimation framework of the fixed effects and variance components and related prediction via a novel application of the Stochastic Approximation of the Expectation Maximization (SAEM) algorithm, allowing for easy and elegant estimation of model parameters under censoring. Both simulation studies and application to a real dataset on arsenic concentration collected by the Michigan Department of Environmental Quality demonstrate the advantages of our method over the available naïve techniques in terms of finite sample properties of the estimates, prediction, and robustness. The proposed methods can be implemented using the R package CensSpatial.

Comparison of different interpolation methods and sequential Gaussian simulation to estimate volumes of soil contaminated by As, Cr, Cu, PCP and dioxins/furans

“…Goovaerts (1999) reported that when the phenomena studied is complex, classical statistics are quickly abandoned in favor of the geostatistical models. Geostatistical data modeling has now virtually permeated all areas of oceanography, cartography, meteorology, agriculture, fisheries resources, civil engineering, finance (Ordoñez et al, 2018) as well as the environment, especially for the rehabilitation of contaminated soils (Lin et al, 2016, Shen et al, 2017, Xie et al, 2011. During the past years, significant effort have been invested to improve the characterization of contaminated soils and to reduce the costs related to the rehabilitation of these sites by applying geostatistical techniques within the characterization phase.…”

Likelihood‐based inference for spatiotemporal data with censored and missing responses

“…In this paper, we introduced a spatiotemporal linear model for censored and missing responses, extending the recent proposals by Lachos et al (2017) and Ordoñez et al (2018), which consider the estimation and diagnostics of spatial censored linear models. To obtain the ML estimates of model parameters, we developed a stochastic approximation of the EM algorithm, called the SAEM algorithm, leading to more efficient ML estimation than in the MCEM algorithm.…”

A hierarchical bi-resolution spatial skew-tmodel

“…However, full conditionals for u 0,t , u 1,t are available and full MCMC is necessary only for z t . In order to fit larger data sets with this model, a promising direction of research to achieve approximate but faster computation is the use of Stochastic Approximation EM (SAEM, Jank (2006), Ordoez et al (2018)), which relies on a Taylor approximation of the Q function.…”