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Representing uncertainties using Bayesian networks

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Abstract

This demonstrates demonstrates the application of Bayesian networks for modelling and reasoning about uncertainties. A scenario for naval anti-surface warfare is constructed and bayesian networks are used to represent and updat uncertainties encountered in the process of 'situation assessment'. Concepts from information theory are used to procide a measure of uncertainty and understand its flow in a Bayesian network. This in turn yields analytical methods to formulate various effectiveness measures.

Executive Summary

The work reported here was undertaken in relation to a broader task which is aimed at providing better tools and techniques in aid of command, control, communications and intelligence (C3I). The task plan places major emphasis on using the techniques of modelling and simulation in the analysis and resolution of C3I problems. A crucial problem that decision makers face in any C3I process is the problem of uncertainty. Here we use Bayesian networks to model uncertainty and reason about it in both a qualitative and a quantitative manner. It is hoped that the tools developed here would be integrated with other existing simulation tools to provide a refined and more versatile modelling environment and decision aid package. The central features of the Bayesian network approach are: • Qualitative: Given a scenario, a Bayesian network depicts graphically the cause and effect relationship between various elements of the scenario. In doing so it also demonstrates conditional independence i.e., which factors are relevant and directly affect a given event and which factors are irrelevant – irrelevant in the sense that knowledge regarding these factors become redundant once the direct causes are known. • Quantitative: It updates probability distributions. Given a battlefield situation and a prior probability distribution over a hypothesis variable that represents possible enemy courses of action, Bayesian network provides the capability to update this probability distribution when fresh reconnaissance and surveillance data are obtained. The pictorial display of the model as a graph facilitates easy understanding and is therefore of great help in rapid model development. To make the analysis specific we construct a scenario of naval anti-surface warfare. The scenario has the advantage of being based upon an approved naval exercise called Operation Dardanelles. Bayesian networks are constructed to represent the uncertainties in the process of situation assessment. A temporal development of the scenario is considered, which evolves through a number of stages starting from the initial detection of the enemy to a major engagement between Blue and Orange forces. Bayesian networks are used at every stage to update knowledge and decide upon a course of action (COA). These networks have been implemented through the commercially available product Netica. After demonstrating the applicability of Bayesian networks to command and control problems, we turn our attention towards developing analytical tools to investigate the flow of information and uncertainty in the network. Concepts from information theory are used to provide a measure of uncertainty, a measure of sensor effectiveness, a measure of the effectiveness of belief updating and finally a measure of the effectiveness of any particular Bayesian network considered as a decision aid tool. A number of examples related to the scenario are considered and numerical effectiveness measures obtained.

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