Algorithm AS 63: The Incomplete Beta Integral

“…The numerical approximation specified in Algorithm AS 63 (Majumdar and Bhattacharjee 1985a) is used. This algorithm is based on the reduction method first published by (Soper 1921).…”

Section: Algorithms For the Beta Distributionmentioning

confidence: 99%

User Instructions for the CiderF Individual Dose Code and Associated Utility Codes

Eslinger¹,

Napier²

2013

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SUMMARYHistorical activities at facilities producing nuclear materials for weapons released radioactivity into the air and water. Past studies in the United States have evaluated the release, atmospheric transport and environmental accumulation of 131 I from the nuclear facilities at Hanford in Washington State and the resulting dose to members of the public . A multi-year dose reconstruction effort (Mokrov et al. 2004) is also being conducted to produce representative dose estimates for members of the public living near Mayak, Russia, from atmospheric releases of 131

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“…For a confidence level R, between zero and one, we then want to find (a, b) such that R = Pr(a ≤ p i ≤ b). The incomplete Beta integral and its inverse can be found using computational methods, see [26,27,28,29] for details.…”

Section: Dirichlet Distributionmentioning

confidence: 99%

Inferring Markov chains: Bayesian estimation, model comparison, entropy rate, and out-of-class modeling

2007

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Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer k-th order Markov chains, for arbitrary k, from finite data by applying Bayesian methods to both parameter estimation and model-order selection. Extending existing results for multinomial models of discrete data, we connect inference to statistical mechanics through information-theoretic (type theory) techniques. We establish a direct relationship between Bayesian evidence and the partition function which allows for straightforward calculation of the expectation and variance of the conditional relative entropy and the source entropy rate. Finally, we introduce a novel method that uses finite data-size scaling with model-order comparison to infer the structure of out-of-class processes.

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Algorithm AS 63: The Incomplete Beta Integral

Cited by 87 publications

References 0 publications

Effective non-universality of the quorum percolation model on directed graphs with Gaussian in-degree

Effective non-universality of the quorum percolation model on directed graphs with Gaussian in-degree

User Instructions for the CiderF Individual Dose Code and Associated Utility Codes

Inferring Markov chains: Bayesian estimation, model comparison, entropy rate, and out-of-class modeling

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