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261. Since Px(w) is the probability of the outcome w, it follows that w supports the hypothesis that e* E Fx(w) to the degree Px(w). In other words, w is an argument in favor of the hypothesis Fx(w) and Px(w) is its weight. 37) It represents the knowledge about e inferred from the observation x in the generalized functional model. If we define then the degree of support of the hypothesis H is because every element in ux(H) is an argument of H. The value sp(H) measures the strength of the evidence represented by the observation x that speaks in favor of the hypothesis H.

Of course, this result is compatible with our intuition because if we keep observing living babies with the new treatment, then we are more and more inclined to believe that the new treatment will cure all babies. e. it is an absorbing state of the chain. 4 Evidence About a Survival Rate 53 If p1m,O denotes the plausibility function of Hm,o, then plm,o(B) = (BIN)m for all BEe. As Hm,o is consonant, it is easy to compute the degree of plausibility of any hypothesis H <:;; because e plm,o(H) = max {plm,o(B) ; B E H}.

H) = (vH(8),p ,rH ,8) l is not precise. Its corresponding support function is given by SPH (B 2 ) = (1 - PI)P2 PI + P2 - PIP2 On the other hand, if T is reported, then and the conditional distribution of P on vT(8) is the probability pi given by P I(( WI,w21))_PI(1-P2) 1 - PIP2 and P I((W2,W 2I)) -_ (1 - pI)(1- P2) . (T) = (vT(8),p l ,rT ,e) is also not precise. Its corresponding support function is given by SPT (1 - PI)P2 (0) I = 1 - PIP2 SPT (B) 2 = PI(l - P2) . 8 Prior Information 33 Now let us analyze the situation where n reports are made, k of which being Hand n - k being T.

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A Mathematical Theory of Arguments for Statistical Evidence by Paul-Andre Monney


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