Distributions Determined by Cutting a Simplex with Hyperplanes

Dempster, A. P.; Kleyle, R.

doi:10.1214/aoms/1177698126

Cited by 28 publications

(17 citation statements)

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“…random variables [we indicate by n F the size of a set F], the sum of the t largest variables is less than S t . The solution for this problem can be found in [32,39]. The cumulative probability distribution is given by the expression P r < S t C t , B t , r wt+1 = 1 − θt j=1 (−1)…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Statistical significance of communities in networks

2010

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Nodes in real-world networks are usually organized in local modules. These groups, called communities, are intuitively defined as sub-graphs with a larger density of internal connections than of external links. In this work, we introduce a new measure aimed at quantifying the statistical significance of single communities. Extreme and Order Statistics are used to predict the statistics associated with individual clusters in random graphs. These distributions allows us to define one community significance as the probability that a generic clustering algorithm finds such a group in a random graph. The method is successfully applied in the case of real-world networks for the evaluation of the significance of their communities.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Statistical significance of communities in networks

2010

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“…For the generic expression for the test statistic ∆ n = n i=1 l i U (i) , the following Theorem from Dempster and Kleyle (1968) gives the exact null distribution of the statistic.…”

Section: Exact Null Distributionmentioning

confidence: 99%

A distribution free goodness of fit test for a stochastically ordered alternative

Banerjee

2008

Statistics & Probability Letters

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“…In the likelihood approach, the appropriate estimator of ψ is the maximiser of p(y|ψ), and the interpretation of the problem as a missing-data problem, with the true scene x being missing, makes available the general iterative EM algorithm of Dempster et al 12 Let L(x, y|ψ) denote the complete-data loglikelihood, given by…”

Section: Bayesian Image Analysismentioning

confidence: 99%

Some Aspects of Statistical Image Modelling and Restoration

Titterington¹

2006

Statistical Problems in Particle Physics, Astrophysics and Cosmology

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A review is provided of some ways in which statistical ideas have influenced research into image analysis, in particular the problems involved in making inferences about the true scene and any parameters in the underlying model. The emphasis will be on the application of general statistical paradigms such as maximum likelihood, implemented using tools such as the EM algorithm, and Bayes' Theorem. The resulting procedures can be regarded as particular recipes for regularisation or deconvolution, according to the context.

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Distributions Determined by Cutting a Simplex with Hyperplanes

Cited by 28 publications

References 0 publications

Statistical significance of communities in networks

Statistical significance of communities in networks

A distribution free goodness of fit test for a stochastically ordered alternative

Some Aspects of Statistical Image Modelling and Restoration

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