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Chapter 5:
Bayesian Inference
Abstract
Bayesian inference is a probability-based reasoning discipline grounded in Bayes' rule. When used to support data fusion, Bayesian inference belongs to the class of data fusion algorithms that use a priori knowledge about events or objects in an observation space to make inferences about the identity of events or objects in that space. Bayesian inference provides a method for calculating the conditional a posteriori probability of a hypothesis being true given supporting evidence. Thus, Bayes' rule offers a technique for updating beliefs in response to information or evidence that would cause the belief to change. 5.1 Bayes' rule Bayes' rule may be derived by evaluating the probability of occurrence of an arbitrary event E assuming that another event H has occurred. The probability is given by P(E|H)=P(EH) P(H) , where H is an event with positive probability. The quantity P(E|H) is the probability of E conditioned on the occurrence of H. The conditional probability is not defined when H has zero probability. The factor P(EH) represents the probability of the intersection of events E and H. To illustrate the meaning of Eq. (5-1), consider a population of N people that includes NE left-handed people and NH females as shown in the Venn diagram of Figure 5.1. Let E and H represent the events that a person chosen at random is left-handed or female, respectively. then P(E)=N E âN and P(H)=N H âN.