Sequential Hypothesis Testing With Spatially Correlated Presence-Absence Data

Abstract

A pest management decision to initiate a control treatment depends upon an accurate estimate of mean pest density. Presence-absence sampling plans significantly reduce sampling efforts to make treatment decisions by using the proportion of infested leaves to estimate mean pest density in lieu of counting individual pests. The use of sequential hypothesis testing procedures can significantly reduce the number of samples required to make a treatment decision. Here we construct a mean-proportion relationship for Oligonychus perseae Tuttle, Baker, and Abatiello, a mite pest of avocados, from empirical data, and develop a sequential presence-absence sampling plan using Bartlett's sequential test procedure. Bartlett's test can accommodate pest population models that contain nuisance parameters that are not of primary interest. However, it requires that population measurements be independent, which may not be realistic because of spatial correlation of pest densities across trees within an orchard. We propose to mitigate the effect of spatial correlation in a sequential sampling procedure by using a tree-selection rule (i.e., maximin) that sequentially selects each newly sampled tree to be maximally spaced from all other previously sampled trees. Our proposed presence-absence sampling methodology applies Bartlett's test to a hypothesis test developed using an empirical mean-proportion relationship coupled with a spatial, statistical model of pest populations, with spatial correlation mitigated via the aforementioned tree-selection rule. We demonstrate the effectiveness of our proposed methodology over a range of parameter estimates appropriate for densities of O. perseae that would be observed in avocado orchards in California.