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. Index Terms-Detection and Estimation, Error exponent, GaussMarkov random fields, Law of large numbers.
In REF , we considered a special case of the problem here, viz., of testing a Gauss-Markov random field (GMRF) with nearest-neighbor dependency graph against independence when the nodes are uniformly distributed.
Detection of Gauss-Markov Random Fields with Nearest-Neighbor Dependency
vol. 55, no. 2, Feb. 2009
Computer Science Mathematics