scholarly journals Bayesian Nonparametric Modeling and the Ubiquitous Ewens Sampling Formula

2016 ◽  
Vol 31 (1) ◽  
pp. 34-36
Author(s):  
Yee Whye Teh
Keyword(s):  
Bayesian Nonparametric ◽  
Nonparametric Modeling ◽  
Ewens Sampling Formula ◽  
Sampling Formula

The infinitely-many-neutral-alleles diffusion model by ages

1990 ◽  
Vol 22 (01) ◽  
pp. 1-24 ◽  
Author(s):  
S. N. Ethier
Keyword(s):  
Diffusion Model ◽  
Probability Distributions ◽  
Ewens Sampling Formula ◽  
Sample Paths ◽  
Sampling Formula ◽  
Frequent Allele

We discuss two formulations of the infinitely-many-neutral-alleles diffusion model that can be used to study the ages of alleles. The first one, which was introduced elsewhere, assumes values in the set of probability distributions on the set of alleles, and the ages of the alleles can be inferred from its sample paths. We illustrate this approach by proving a result of Watterson and Guess regarding the probability that the most frequent allele is oldest. The second diffusion model, which is new, assumes values in the set of probability distributions on the set of pairs (x, a), where x is an allele and a is its age. We illustrate this second approach by proving an extension of the Ewens sampling formula to age-ordered samples due to Donnelly and Tavaré.

A stability property of the Ewens sampling formula

1983 ◽  
Vol 20 (03) ◽  
pp. 449-459
Author(s):  
Stanley Sawyer
Keyword(s):  
Population Size ◽  
Error Bound ◽  
Mutation Rate ◽  
Stability Property ◽  
Ewens Sampling Formula ◽  
Sampling Formula ◽  
Deleterious Alleles

An error bound for convergence to the Ewens sampling formula is given where the population size or mutation rate may vary from generation to generation, or the population is not yet at equilibrium. An application is given to a model of Hartl and Campbell about selectively-equivalent subtypes within a class of deleterious alleles, and a theorem is proven showing that the size of the deleterious class stays within bounds sufficient to apply the first result. Generalizations are discussed.

scholarly journals Bayesian Nonparametric Modeling for Rapid Design of Metamaterial Microstructures

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Bin Liu ◽  
Chunlin Ji
Keyword(s):  
Geometric Dimension ◽  
Mapping Function ◽  
Point Of View ◽  
Electromagnetic Response ◽  
Type Model ◽  
Nonparametric Model ◽  
Bayesian Nonparametric ◽  
Nonparametric Modeling ◽  
Statistical Point ◽  
Rapid Design

We consider the problem of rapid design of massive metamaterial (MTM) microstructures from a statistical point of view. A Bayesian nonparametric model, namely, Gaussian Process (GP) mixture, is developed to generate the mapping relationship from the microstructure’s geometric dimension to the electromagnetic response, which is approximately expressed in a closed form of Drude-Lorentz type model. This GP mixture model is neatly able to tackle nonstationarity, discontinuities in the mapping function. The inference is performed using a Markov chain relying on Gibbs sampling. Experimental results demonstrate that the proposed approach is highly efficient in facilitating rapid design of MTM with accuracy.

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