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

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.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2010
Accession Number
ADA536158

Entities

People

  • Ananthram Swami
  • Anima Anandkumar
  • Lang Tong

Organizations

  • United States Army Research Laboratory

Tags

Communities of Interest

  • Materials and Manufacturing Processes
  • Sensors

DTIC Thesaurus Topics

  • Computational Science
  • Data Mining
  • Detection
  • Detectors
  • Electrical Engineering
  • Engineering
  • Information Processing
  • Information Science
  • Information Theory
  • Military Research
  • Probability
  • Random Variables
  • Sensor Networks
  • Signal Processing
  • Warning Systems
  • Wireless Communications
  • Wireless Sensor Networks

Readers

  • Graph Algorithms and Convex Optimization.
  • Statistical inference.