Detection of Gauss-Markov Random Fields with Nearest-Neighbor Dependency

TL;DR

This paper analyzes hypothesis testing for Gauss-Markov random fields with nearest-neighbor dependency, deriving error exponents and revealing how correlation affects detection performance under different variance ratios.

Contribution

It provides a novel analytical framework for the error exponent of GMRF detection using large deviations and stabilizing graph functionals, considering random node placement.

Findings

Higher correlation increases error exponent at low variance ratios.

Error exponent behavior reverses at high variance ratios.

Analytical expressions for detection performance are derived.

Abstract

The problem of hypothesis testing against independence for a Gauss-Markov random field (GMRF) is analyzed. Assuming an acyclic dependency graph, an expression for the log-likelihood ratio of detection is derived. Assuming random placement of nodes over a large region according to the Poisson or uniform distribution and nearest-neighbor dependency graph, the error exponent of the Neyman-Pearson detector is derived using large-deviations theory. The error exponent is expressed as a dependency-graph functional and the limit is evaluated through a special law of large numbers for stabilizing graph functionals. The exponent is analyzed for different values of the variance ratio and correlation. It is found that a more correlated GMRF has a higher exponent at low values of the variance ratio whereas the situation is reversed at high values of the variance ratio.