Detection error exponent for spatially dependent samples in random networks

The problem of binary hypothesis testing is considered when the measurements are drawn from a Markov random field (MRF) under each hypothesis. Spatial dependence of the measurements is incorporated by explicitly modeling the influence of sensor node locations on the clique potential functions of each MRF hypothesis. The nodes are placed i.i.d. in expanding areas with increasing sample size. Asymptotic performance of hypothesis testing is analyzed through the Neyman-Pearson type-II error exponent. The error exponent is expressed as the limit of a functional over dependency edges of the MRF hypotheses for acyclic graphs. Using the law of large numbers for graph functionals, the error exponent is derived.