24.5 PROTOTYPE DECISION-MAKING SUPPORT ASSISTANT DESIGN

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Different decision strategies can provide distinguished for varying decisions because of their different philosophies for dealing with uncertainty.

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24.5.1 Bayesian Decision Strategy and Belief Networks

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Our motivation in the application of Bayesian belief networks is driven by the following: (a) decision-making in biometric-based systems in the presence of random factors can be described in causal form and (b) the Bayesian (probabilistic) interpretation of uncertainty provides an acceptable reliability for decision-making. Traditionally, the semantics of Bayesian decision-making are not the focus of interest [49]. In our design concept, we extensively utilize the semantic properties of Bayesian networks in the representation and manipulation of biometric data. For this reason, we introduce a technique for computing based on belief decision trees. We assume that biometric data structure can be expressed as a causal network with appropriate conditional probabilities. Causal knowledge is modeled as causal networks in which the nodes represent propositions (or variables), the arcs signify direct dependencies between linked propositions, and the strengths of these dependencies are quanti ed by conditional probabilities. Bayesian decision-making is based

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24.5 Prototype Decision-Making Support Assistant Design

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Figure 24.15. Belief tree (a), corresponding probability tables (b), and causal network (c).

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on the evaluation of a prior probability given a posterior probability and likelihood (of an event happening given some history of previous events)

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Prior Likelihood Posterior

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P(Hypothesis|Data) = P(Data|Hypothesis) P(Hypothesis)

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The posterior probability of A is called the belief for A, Bel(A). The probability P(a|b) is called the likelihood of b given a. In our design concept, a causal network is mapped into a belief tree (Figure 24.15). The belief tree is designed based on the rules for binary linguistic variables. An arbitrary causal network can be transformed into a belief tree. An arbitrary complete belief tree with binary linguistic variables can be decomposed into two trees using evidence criteria: a tree characterized by ignorance (prior data are not available) and a tree of evidence (prior data are available). The main advantage of the belief trees is the possibility they provide for detailed description of the problem. However, belief trees can be applied only to small-size problems. Causal knowledge can be represented in the following forms: (a) linguistic description, (b) algebraic (probabilistic) description, (c) decision tree, and (d) causal network. These data structures are useful for the representation of causal knowledge at a high level of abstraction. For the implementation of these data structures, the logic level of abstraction should be used that is, logic networks. A causal network is a DAG in which each arc is interpreted as a direct causal in uence between a parent node and a child node, relative to the other nodes in the network, so that this causal network s structure describes the dependence between associate variables and gives a concise speci cation of the joint probability distributions. A node in a causal network denotes a variable that models a feature of a process, event, state, object, agent, and so on. The causal network may contain both measured and hidden variables. Hidden variables are variables for which there are have no data. For each node, there is a probability distribution on that node given the state of its parents. In a causal network, this distribution shows how the node probabilities factor to affect a joint probability distribution over all the node. Directed edges represent causality between two nodes.

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24

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Decision-Making Support

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Figure 24.16. Graphical, linguistic, and probabilistic descriptions of the independent (a) and dependent (b,c) events A and B.

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Figure 24.16 illustrates various relationships between two nodes in graphical and probabilistic forms. Consider two nodes A and B, interpreted as propositions. It is judged that: propositions A and B are not relevant (a); A is relevant for B, so a directed link is drawn from A to B (b); and B is relevant for A (c). Another graphical representation of a causal relationship is the belief tree. In Figure 24.15, the belief tree represents the case that A is relevant for B. For example, given the measured temperature, M C temp, the posterior probability of Abnormal condition upon the evidence of M C temp is computed as follows:

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p(ABNORMAL|M C TEMP) = p(ABNORMAL)

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