Detection error exponent for spatially dependent samples in random networks

Creators: Anandkumar, Animashree; Tong, Lang; Willsky, Alan

Abstract

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.

Additional Information

© 2009 IEEE. This work was supported in part by collaborative participation in Communications and Networks Consortium sponsored by U. S. Army Research Laboratory under Collaborative Technology Alliance Program, Cooperative Agreement DAAD19-01-2-0011 and by Army Research Office under Grant ARO-W911NF-06-1-0346. The first author is supported by the IBM Ph.D Fellowship 2008-09 and is currently a visiting student at MIT, Cambridge, MA 02139. The third author is supported in part by ARO Grant W911NF-06-1-0076, in part by AFOSR through Grant FA9550-08-1-1080, in part under a MURI through AFOSR Grant FA9550-06-1-0324 and in part by Shell International Exploration and Production, Inc. The U. S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation thereon.

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