General Multidecision Theory: Hypothesis Testing and Changepoint Detection with Applications to Homeland Security
Abstract
We have addressed all objectives planned in the proposal. First, we proved asymptotic optimality of the Generalized SLRT and the Adaptive SLRT for testing multiple composite hypotheses and very general non-iid stochastic models as the probabilities of errors become small. The results are indeed very general and include Markov, hidden Markov, state-space, and auto regression models as particular cases. Second, we developed computationally efficient and nearly optimal tests for detecting unstructured and structured patterns in multi-stream (sensor, channel) systems assuming that data between channels are mutually independent but may be of a very general non-iid structure in channels, and that the number of affected channels is unknown and may vary from small to large. Third, we developed a general Bayesian theory of quickest changepoint detection for general non-iid stochastic models assuming a certain stability of the log-likelihood ratio (LLR) process expressed via the r-complete convergence of the LLR to a finite and positive number which can be regarded as the KullbackLeibler information number. Fourth, we developed a similar minimax change detection theory modifying and relaxing previous results of Lai (1998) to complete convergence of the LLR and considering novel classes of detection procedures that confine local maximal conditional probability of a false alarm.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 19, 2016
- Accession Number
- AD1008619
Entities
People
- Alexander G. Tartakovsky
Organizations
- University of Connecticut