منابع مشابه
Exchangeable random variables
If Equation (1) be satisfied, then all sets S are equally likely under the null hypothesis. To obtain a permutation test that is both unbiased and most powerful, one need only select the set S so that its probability under the alternative >0 is a maximum. This is accomplished in most cases by rejecting the hypothesis for all values of the test statistic that lie in the upper tail of the permuta...
متن کاملRepresentation theorems for partially exchangeable random variables
We provide representation theorems for both finite and countable sequences of finite-valued random variables that are considered to be partially exchangeable. In their most general form, our results are presented in terms of sets of desirable gambles, a very general framework for modelling uncertainty. Its key advantages are that it allows for imprecision, is more expressive than almost every o...
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In this article, we derive the distribution of partially exchangeable binary random variables, generalizing the distribution of exchangeable binary random variables and hence the binomial distribution. The distribution can also be viewed as a mixture of Markov chains. We introduce rectangular complete monotonicity and show that partial exchangebility can be characterized by rectangular complete...
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We discuss the implications of Bayes’ postulate in the setting of exchangeable Bernoulli random variables. Bayes’ postulate, here, stipulates a uniform distribution on the total number of successes in any number of trials. For an infinite sequence of exchangeable Bernoulli variables the conditions of Bayes’ postulate are equivalent to a uniform (prior) distribution on the underlying mixing vari...
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Call a random partition of the positive integers partially exchangeable if for each finite sequence of positive integers n l , . . . , nk, the probability that the partition breaks the first nl + . . . § nk integers into k particular classes, of sizes nl . . . . , nk in order of their first elements, has the same value p(na . . . . . nk) for every possible choice of classes subject to the sizes...
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ژورنال
عنوان ژورنال: Bioinformatics
سال: 2010
ISSN: 1367-4803,1460-2059
DOI: 10.1093/bioinformatics/btq297