Wednesday, June 19, 2019

Bayesian Networks Essay Example | Topics and Well Written Essays - 4750 words

Bayesian Networks - Essay ExampleBNs are graphical models that set probabilistic relationships among variables of interest. They depict the relationships between causes and effects. The BNs are strong knowledge federal agency and reasoning tool under conditions of uncertainty. The BNs are a directed acyclic graph having nodes and arcs with a conditional probability distribution linked for each node. Nodes plump for for domain variables, and arcs between nodes stand for probabilistic dependencies. Set of nodes and a set of directed links between them must not form a cycle. apiece node represents a random variable that can take discrete or continuous finite, mutually exclusive values. These values depend on a probability distribution, which can be unalike for each node. Each link states probabilistic cause-effect relations among the linked variables. A link is shown by an arc startle from the affecting variable (parent node) and ending on the affected variable (child node).We will use BNs to represent risk. For example, Figure 3.1 shows BN for Decreased profits risk. By linking together different risks we can model multiple risks in a project and we will look at this property in Chapter 5.Bayes Theorem was developed after Rev. Thomas Bayes, an eighteenth century mathematician and theologian. Bayes set out his theory of probability in Essay towards solving a problem in the doctrine of chances published in the Philosophical Transactions of the Royal Society of London in 1764. Richard Price, a friend of Bayes sent the paper to the Royal Society and wroteI now get out you an essay which I have found among the papers of our deceased friend Mr Bayes, and which, in my opinion, has great merit... In an introduction which he has writ to this Essay, he says, that his de shapeination at first in thinking on the subject of it was, to find out a regularity by which we might judge concerning the probability that an government issue has to happen, in given circumstance s, upon supposition that we know nothing concerning it but that, under the same circumstances, it has happened a certain hail of times, and failed a certain other number of times. (Hogben 1970)Laplace accepted Bayess results in a 1781 memoir and Condorcet rediscovered them (as Laplace mentions). They stayed accepted until Boole doubted them in the Laws of Thought . Mathematically Bayes theorem is stated asWhere it is possible to update our belief in hypothesis H given the additional evidence E. The left-hand term, P(HE) is known as the posterior probability, or the probability of H after considering the effect of E. The term P(H) is called the prior probability of H. The term P(EH) is called the likelihood and gives the probability of the evidence assuming the hypothesis H is true. Finally, the last term P(E) is free of H and can be viewed as a normalizing or scaling factor.The power of Bayes theorem is that in many situations where we actually want to calculate p(HE) it turns out that it is hard to do so directly, barely we might have direct information about the likelihood, p(EH). Bayes theorem allows us to calculate p(HE) in terms of p(EH). 1.3 The Bayesian Approach to Probability and StatisticsUnderstanding of the Bayesian method to probability and statistics helps to know BNs and related learning techniques. The