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Vladimir_Nesov comments on Bayesian Utility: Representing Preference by Probability Measures - Less Wrong

10 Post author: Vladimir_Nesov 27 July 2009 02:28PM

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Comment author: Vladimir_Nesov 27 July 2009 11:58:10PM *  0 points [-]

P(x|A) = P(x,A)/P(A) is by definition of conditional probability. You are trying to interpret x1 and x2 as events, while in grandparent comment x are elements of the sample space. If you want to consider non-concrete outcomes, compose them from smaller elements. For example, you can have P(O1)=P(O2)=.5, P(O1|A)=.2, P(O2|A)=.8, if O1={x1,x2}, O2={x3,x4}, A={x1,x3}, and p(x1)=.1, p(x2)=.4, p(x3)=.4, p(x4)=.1.