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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 heartbeat µs represented by (Gs , fs ). (c) Use the progression of Theorem 4.5.6 to get to two qualitative Bayesian networks representing µs , both having S as their root. (d) Suppose that you believe that there is a gene (that can be inherited) that results in a predisposition both to smoke and to have malignant neoplastic disease, but other smoking and cancer atomic number 18 unrelated. Draw a Bayesian network describing these beliefs, apply the variables P G (at least iodine parent has this gene), G (has this gene), P S (at least mavin parent smokes), S (smokes), and C (has cancer). Explain why to each one edge you include is there. Notes The beliefs of ( qualified) emancipation and stochasti c variable are standard in probability theory, and they are treated in each 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; go for [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 properties that are variants of CIRV1 6 (CIRV6 is discussed in put to work 4.21). Pearl [1988] discusses these properties at length. These properties have been called the graphoid properties in the literature, which contains extensive investigate on whether they all characterize conditional independence of random variables. Very roughly, graphoid properties do not characterize condition al independence of random variablesin?nitely! many extra properties are required...If you fatality to get a full essay, order it on our website: BestEssayCheap.com

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