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Cryptic variation fuels plant phenotypic change through hierarchical epistasis. [PDF]

Nature
Zebell SG, Martí-Gómez C, Fitzgerald B, Cunha CP, Lach M, Seman BM, Hendelman A, Sretenovic S, Qi Y, Bartlett M, Eshed Y, McCandlish DM, Lippman ZB.   +12 more
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Cuts in Natural Exponential Families

Theory of Probability & Its Applications, 1996
The concept of cuts [\textit{O. E. Barndorff-Nielsen}, Exponential families and conditioning. Sc. D. Thesis, Univ. Copenhagen (1973; Zbl 0297.62001)], which is intimately connected to the concepts of \(S\)-ancillarity and \(S\)-sufficiency, has been studied in the context of general exponential families.
Barndorff-Nielsen, O. E., Koudou, A. E.
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Natural exponential families and self-decomposability

Statistics & Probability Letters, 1992
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Bar-Lev, Shaul K., Bshouty, Daoud, Letac, Gérard   +2 more
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Conjugate Parameterizations for Natural Exponential Families

Journal of the American Statistical Association, 1995
Abstract Recently, Consonni and Veronese have shown that the form of the standard conjugate distribution for the mean parameter μ of a univariate natural exponential family F coincides with that of the distribution induced on μ by the standard conjugate distribution for the canonical parameter if and only if F has a quadratic variance function. In this
E. Gutiérrez-Peña, A. F. M. Smith
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Conditional natural exponential families

Statistics & Probability Letters, 2006
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Laplace Approximations for Natural Exponential Families with Cuts

Scandinavian Journal of Statistics, 1998
Standard and fully exponential form Laplace approximations to marginal densities are described and conditions under which these give exact answers are investigated. A general result is obtained and is subsequently applied in the case of natural exponential families with cuts, in order to derive the marginal posterior density of the mean parameter ...
Efstathiou, M., Gutiérrez-Peña, E., Smith, A. F. M.   +2 more
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Natural Exponential Families and Umbral Calculus

1998
We use the Umbral Calculus to investigate the relation between natural exponential families and Sheffer polynomials. As a corollary, we obtain a new transparent proof of Feinsilver’s theorem which says that natural exponential families have a quadratic variance function if and only if their associated Sheffer polynomials are orthogonal.
Di Bucchianico, A., Loeb, D.E.
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A note on natural exponential families with cuts

Statistics & Probability Letters, 2003
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Bar-Lev, Shaul K., Pommeret, Denys
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Predictive Fit for Natural Exponential Families

Biometrika, 1989
The basic problem considered is where the observed data are all realizations of a random variable X and some probability statement about a future variable from the same distribution is desired. The paper examines such predictions with regard to a particular measure of prediction fit, the average Kullback-Leibler divergence between distributions.
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Natural exponential families of probability distributions and exponential-polynomial approximation

Applied Mathematics and Computation, 1993
A Dirichlet polynomial in a finite linear combination of the functions \(e^{\lambda_ k x}, e^{\lambda_ k x},\dots, x^{m_ k-1} e^{\lambda_ k x}\), \(k=1,2,3,\dots\), where \(\{\lambda_ k\}\) is a sequence of complex numbers and \(\{m_ k\}\) is a sequence of positive integers. The authors [Appl. Math. Comput. 53, No.
Martin, Clyde, Shubov, Victor
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