Detection of Gauss-Markov Random Fields with Nearest-Neighbor Dependency
arXiv:0706.1588 · doi:10.1109/TIT.2008.2009855
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.
Information Theory, IEEE Transactions
References in corpus (2)
Cited by in corpus (11)
- Detection of Gauss-Markov Random Fields with Nearest-Neighbor Dependency
- Covariance estimation in decomposable Gaussian graphical models
- Graph Laplacian for Image Anomaly Detection
- Detection of correlations
- Diffusion Adaptation Strategies for Distributed Estimation over Gaussian Markov Random Fields
- Energy Scaling Laws for Distributed Inference in Random Fusion Networks
- Learning from Complex Systems: On the Roles of Entropy and Fisher Information in Pairwise Isotropic Gaussian Markov Random Fields
- Exploiting Spatial Correlation in Energy Constrained Distributed Detection
- Active Sampling for the Quickest Detection of Markov Networks
- Distributed Detection of a Random Process over a Multiple Access Channel under Energy and Bandwidth Constraints
- Design and performance analysis of a fully distributed source detection algorithm for WSNs