Properties of Binary Data Generated from a Truncated Gaussian Random Field

Abstract

Let Y*(s) represent a Gaussian random field with location index s ∈ D ⊂ R 2, and let Y(s) represent a binary random field on the same locations. We suppose that Y(s) is the indicator variable of the event Y*(s) > c for some cutoff value c. Moreover, we assume that Y(s), but not Y*(s), is observable. This could model, for example, trees in a plantation that are observed to be alive or dead as a result of the latent build-up of a toxin. The purpose of this article is to evaluate the relationship between the correlation structure of the latent Y*(s) and the observable Y(s). The results that we derive are relevant to the computer simulation of binary random fields.