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Second and higher-order probabilities

  1. Jun 4, 2009 #1
    Why do I never hear of "second-order probabilities" (probability that the probability of an event is x. for example, you pick a box at random out of 3 boxes, and each box can have either 1, 3 or 5 red marbles out of six marbles)? can measurement or calculation of probability not be affected by random and inaccurate data?
     
  2. jcsd
  3. Jun 5, 2009 #2

    EnumaElish

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    How is your concept different from joint probability? How is it different from conditional probability?

    Alternatively, you can define higher-order probability as follows. Let P = Prob{X < x} = CDF(x). Since X is a random variable, so is P (because it is a function of a random variable, with CDF of X as the link function). As a random variable, P is distributed uniformly over [0,1]. Defined this way, higher-order probabilities are not interesting: they are all distributed uniformly over [0,1].
     
    Last edited: Jun 6, 2009
  4. Jun 5, 2009 #3
    Decision theory does sometimes use second-order probabilities, although they are distrusted by some.

    google has the answers.
     
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