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It has to be admitted, though, that for the probabilistic setting there is a well-known principle, namely the so-called insufficient reason principle, which prescribes a specific way of fixing the conditional probabilities within the contexts and for which a very strong case can be made The insufficient reason principle states that if you can specify neither probabilities (quantitative information) nor preferences (comparative information) for a given set of (mutually exclusive) events, then you should assign equal probabilities to the events in the set, because you have insufficient reasons to assign to one event a higher probability than to another Hence the conditional probabilities of the events possible in a context should be the same.



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with PQ IRm m is any permutation matrix. The result indicates that the natural gradient for under-complete mixture (m > n) is not unique, which depends on the permutation matrix PQ . Assume that m > n. For W Gl(n, m), there exists a permutation matrix PQ IRm m such that W = [W1 , W2 ]PQ , (G.4)





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Surgery for ovarian malignancies serves two important functions: diagnostic staging and therapeutic tumor reduction. In order to accomplish the former, surgery for ovarian malignancies usually includes removal of both ovaries, the uterus, biopsies of pelvic and peri-aortic lymph nodes, biopsies of the omentum, biopsies of the peritoneum, consideration for an appendectomy, and cytology from both peritoneal washings and the diaphragm. Without evaluation of all of these tissues, a physician cannot assign the tumor a surgical stage, and discussions about prognosis and future therapies become more speculative. Ovarian granulosa cell tumors are staged according to the guidelines created by FIGO to stage ovarian malignancies (Table 11.2). Among sex cord-stromal tumors that have been completely staged, 80% of granulosa theca cell tumors were stage IA. However, within that same study population, 58% of granulosa cell tumors were stage IA de ned at comprehensive staging but only 8% were stage III, and most advanced-stage patients had grossly apparent disease.1 These ndings once again raise the

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A standard argument in favor of the insufficient reason principle is the permutation invariance argument: in the absence of any information about the (relative) probability of a given set of (mutually exclusive) events, permuting the event labels should not change anything However, the only assignment of probabilities that remains unchanged under such a permutation is the uniform assignment (that is, all events are assigned the same probability) Note that the structure of the permutation invariance argument is the same as the structure of the argument by which we usually convince ourselves that the probability of an ace when rolling a (normal, ie cube-shaped) die is 1 We argue that the die is symmetric and thus permuting the numbers 6 should not change the probabilities of the numbers This structural equivalence is the basis for the persuasiveness of the insufficient reason principle.

Now that the fundamentals have been addressed, it s time to get down to work. Phase 2 retouching is where the rubber meets the road. Here s a list of the things we need to address during Phase 2: n Remove blemishes and soften wrinkles. n Do some preliminary smoothing on the skin on her forehead and chest. n Tone down the shine on her lips. n Enhance the eyes by cleaning the whites, brightening the irises, and removing one of the catch lights. n Lighten and whiten the teeth. Also tone down or remove bright reflections on them. n Remove all the fly-away hair around the outer edges of her head. n Do final skin smoothing. With the exception of final skin smoothing, these steps don t necessarily need to be carried out in this exact order. I tend to take care of some of the bigger issues and then move around the image,

Let I be a set of items and T : {1, . . . , n} P(I) be a transaction data set. Denote by D the set of transaction identi ers, D = {1, . . . , n}. The functions itemsT : P(D) P(I) and tidsT : P(I) P(D) are de ned by itemsT (E) = {T (k)|k E},

However, it should be noted that the two situations are fundamentally different In the case of the die we consider the physical parameters that influence the probability of the outcomes and find them to be invariant under a per-.

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