State estimation in stochastic decision theory

This dissertation addresses the problem of state estimation by viewing it as a decision-making process under uncertainty. An efficient structure for knowledge representation, in an uncertain environment, is introduced in the framework of stochastic decision theory. Compared to some alternate representations, this structure unifies the uncertain character of the knowledge with the representation. Furthermore, this structure is exclusively armed with manipulation capabilities which regulate information storage and retrieval.

The problem of incomplete information is also addressed in the context of stochastic decision theory using the maximum entropy principle. A second important problem which arises in any uncertain knowledge representation structure is the problem of statistical independence/dependence between the propositions of the knowledge.

The dissertation provides an algorithm which simultaneously uncovers, for a given stochastic term, all the independence and dependence classes. The dissertation explores how this structure can be used to approach some classical problems in state estimation. This provides a new visualization of the state estimation procedure in terms of syntactic manipulation. The results of the entailment and the statistical independence problem are used to devise a cluster decomposition scheme for stochastic terms, similar to machine decomposition in automata theory, which allows the decomposition of the state estimation problem into smaller sub-problems. This finding helps avoid the crucial storage and computational explosion encountered in large scale svstems.