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146 Chapter 4 Independence and Bayesian Networks (a) Notice that {S, SH } blocks some(prenominal) paths from P S to C. What does this say about the relationship between P S and C in probabilistic terms? (b) Calculate µs (C = 1 | P S = 1) for the unique fortune beat µs represented by (Gs , fs ). (c) Use the progression of Theorem 4.5.6 to arrive at two qualitative Bayesian networks representing µs , some(prenominal) having S as their root. (d) Suppose that you believe that there is a agent (that can be inherited) that results in a predisposition both to smoke and to have malignant neoplastic disease, but differently smoking and cancer be unrelated. Draw a Bayesian network describing these beliefs, apply the variables P G (at least unity parent has this gene), G (has this gene), P S (at least peerless parent smokes), S (smokes), and C (has cancer). Explain why distributively edge you include is there. Notes The beliefs of ( qualified) liberty and rando m variable are standard in probability theory, and they are covered in each(prenominal) texts on probability (and, in particular, the ones cited in Chapter 2). Fine [1973] and Walley [1991] discuss qualitative properties of conditional independence such as CI16; Walley, in fact, includes CI3 as part of his de?nition of independence. Walley calls the asymmetric version of independence irrelevance.

It is an interesting notion in its own right; discriminate [Cozman 1998; Cozman and Walley 1999]. The focus on conditional independence properties can be traced back to Dawid [1979] and Spohn [1980], who both discussed pro perties that are variants of CIRV1 6 (CIRV6 ! is discussed in figure out 4.21). Pearl [1988] discusses these properties at length. These properties have been called the graphoid properties in the literature, which contains extensive enquiry on whether they all characterize conditional independence of random variables. Very roughly, graphoid properties do not characterize conditional independence of random variablesin?nitely many extra properties are required...If you fate to get a full essay, order it on our website: BestEssayCheap.com

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