UNIVERSITY OF WEST BOHEMIA FACULTY OF APPLIED SCIENCES Software Analysis of Bayesian Distributed Dynamic Decision Making

Decision making is an active and purposeful selection of actions among several alternative options. For humans, DM is a natural part of everyday life. The Bayesian theory provides a rigorous and consistent tool to help the decision maker to select the best action to achieve his aim. A significant application area of the decision-making theory is the control theory. Most of the applications of the theory are based on two assumptions: (i) the optimal decision is the only action that intentionally influences the response, (ii) the decision-maker pursue only one aim which is known a priori. A theory of distributed Bayesian decision-making—which relax the above mentioned assumption—is still under development. This thesis is a contribution to a wider project in creation of consistent theory of distributed Bayesian decision-making, using the concept of multiple-participant decision-making. The main concern of this work is preparation of a new software framework for development and application of the Bayesian distributed decision making theory. In order to achieve this aim we have done the following: Chapter 2: the requirements on the resulting software were formalized, and the most prominent freely available software packages were reviewed in the light of our requirements. It was concluded that none of the packages is suitable for our needs and that it is necessary to create a new one. We have chosen the object-oriented (OO) approach as a design method of the toolbox. Since the main development platform for the project is Matlab and ANSI C, we have proposed a novel approach of implementation of OO software in these tools. Chapter 3: the basics of Bayesian decision-making theory were reviewed in this Chapter. We have presented well known results, as well as new emerging methods and translated them into a sequence of basic probabilistic operations, which are suitable for software implementation. Chapter 4: it is well known that the Bayesian theory of decision making is computationally tractable only under certain assumptions. Many approximate techniques were developed for model families for which the general Bayesian DM is not analytically tractable. These techniques were also reviewed in this Chapter. Special attention was paid to the Variational Bayes technique, which is based on the assumption of conditional independence. The basic tasks of decision-making for this approximation were introduced. Chapter 5: the basic steps of implementing DM theory in practice—gained from the experience i Summary with single participant DM—were reviewed in this Chapter. Majority of …