Making sequential analysis of environmental monitoring data feasible by simplifying the covariance matrix structure

Abstract

As environmental monitoring data are collected successively in time, the data are suitable for sequential analysis. An earlier article proposed a refined sequential probability ratio test (SPRT) to test against a minimal relevanttrend, assuming no serial correlations and without modeling the spatial covariance matrix. As the model parameters are unknown in advance, a minimal number of observations(n _min) is required for estimation prior to analysis. Leaving the spatial covariance matrix unstructured, n _min increases if the number of sampling locations increases. Therefore, assumptions on the spatial covariance matrix are proposed, thereby reducing the number of nuisance parameters, thus reducingn _min. This article studies. three simple types of spatial covariance matrix structures and derives an adjusted SPRT for each of these types. Furthermore, we examine the robustness against deviations from the assumed spatial covariance matrix structure. Simulation studies show that adjusted SPRTs can be derived rather easily and that they are in general robust against deviations from the assumed type of spatial covariance matrix. Sequential analysis of simulated data, which are based on monitoring data of bats in the Netherlands, illustrates the use of one of the derived SPRTs.