By Cayley A.
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Extra resources for Collected mathematical papers
The estimation of the potential consequences caused by the occurrence of the hazard. The product of the above three components constitutes the estimated risk, R; that is where: Hz = the result of a probabilistic hazard analysis; Vu = the result of a vulnerability analysis; may be in terms of the probability or fraction of damage to a city or a region; Cq = the estimated potential consequence resulting from the occurrence of the hazard. 46 As there are epistemic uncertainties in estimating or calculating each of the components in Eq.
1 θ2 X1 X2 … Xn (b) Exchangeable condition states θi with observable outputs Xi . 32 θ3 4 UPDATING OF CONDITION STATES When performing statistical inference in this model, we need to distinguish between updating one of the n systems, Fig. 6(a), or updating an “arbitrary” system as shown in Fig. 6(b). In the first case, suppose the system of interest is the system with index 0 which is an arbitrary system belonging to the n possible systems. This system possesses observed response variables X0 and a condition state θ0 .
2) Any random mixtures of exchangeable variables are also exchangeable. An important class identified in de Finetti (1974) is the case of partial exchangeability (exchange within different classes), and the Markov form of changeability. (3) iid random quantities are necessarily exchangeable. An infinite string of random quantities is exchangeable, if all finite segments θ1 , θ2 , . . , θn (2 < n) are exchangeable. θ1 θ2 (a) Figure 1. … θn α1 α2 … αn θ1 θ2 … (b) Independent random variables θi (i = 1, .
Collected mathematical papers by Cayley A.