Research Reports from the Department of Operations
Document Type
Dissertation
Publication Date
5-1-1989
Abstract
This dissertation addresses the problem of optimal decentralized detection or decision-making about some binary states of the world. In the centralized case, the solutions are well known and easily obtained using the classical theory of statistical hypothesis testing. The decentralized case has an additional degree of complexity due to the interrelationships and the dependence between the decision-makers. As formulated here, the model has applications to any problem in which stochastically independent observations are abstracted to inform a central decision-maker, or are used to determine a team action. Examples include: a strategic defense system, a battery of medical tests, or an array of independent expert judges or advisers. We study different detection networks. All decision-makers of the network make conditionally independent observations about some underlying binary hypothesis. The agents seek to minimize a team cost function (Bayes optimality criterion) or maximize the overall probability of detection at fixed overall false alarm rate (Neyman-Pearson optimality criterion) by making binary decisions. These decisions are conveyed to other decision-makers over binary links according to the topology of the underlying network. It is shown that the optimal decisions can be reduced to most powerful tests where the optimal false alarm rates are determined by solving a nonlinear program depending on the ROC (Receiver Operating Characteristic) functions. For the fusion network, we show that the peripheral decisions and the fusion rule must be optimized jointly. We derive dominance rules that restrict the class of possible optimal fusion rules and derive some interesting combinatorial results. We propose two important conjectures for decision-makers the fusion (detectors) efficient heuristic solutions. and topology give some with identical computationally Some conjectures that would further simplify the decentralized decision problem have been studied and refuted. Some specific numeric counterexamples are given.
Keywords
Operations research, Decision making--Mathematical models, Decentralization in management--Mathematical models, Statistical decision, Statistical hypothesis testing, Receiver operating characteristic curves, Mathematical optimization, Systems engineering--Mathematical models, Algorithms
Publication Title
Dissertation/Technical Memorandums from the Department of Operations, School of Management, Case Western Reserve University
Issue
Technical memorandum no. 666 ; Submitted in partial fulfillment of the requirements for the Degree of Doctor of Philosophy.
Rights
This work is in the public domain and may be freely downloaded for personal or academic use
Recommended Citation
Cherikh, Moula, "Optimal Decision and Detection in the Decentralized Case" (1989). Research Reports from the Department of Operations. 383.
https://commons.case.edu/wsom-ops-reports/383
