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Evaluating default priors with a generalization of Eaton’s Markov chain

Brian P. Shea, Galin L. Jones (2014)

Annales de l'I.H.P. Probabilités et statistiques

We consider evaluating improper priors in a formal Bayes setting according to the consequences of their use. Let 𝛷 be a class of functions on the parameter space and consider estimating elements of 𝛷 under quadratic loss. If the formal Bayes estimator of every function in 𝛷 is admissible, then the prior is strongly admissible with respect to 𝛷 . Eaton’s method for establishing strong admissibility is based on studying the stability properties of a particular Markov chain associated with the inferential...

Evaluating improvements of records

Tomasz Rychlik (1997)

Applicationes Mathematicae

We evaluate the extreme differences between the consecutive expected record values appearing in an arbitrary i.i.d. sample in the standard deviation units. We also discuss the relevant estimates for parent distributions coming from restricted families and other scale units.

Evaluations of expected generalized order statistics in various scale units

Erhard Cramer, Udo Kamps, Tomasz Rychlik (2002)

Applicationes Mathematicae

We present sharp upper bounds for the deviations of expected generalized order statistics from the population mean in various scale units generated by central absolute moments. No restrictions are imposed on the parameters of the generalized order statistics model. The results are derived by combining the unimodality property of the uniform generalized order statistics with the Moriguti and Hölder inequalities. They generalize evaluations for specific models of ordered observations.

Evolutionary computation based on Bayesian classifiers

Teresa Miquélez, Endika Bengoetxea, Pedro Larrañaga (2004)

International Journal of Applied Mathematics and Computer Science

Evolutionary computation is a discipline that has been emerging for at least 40 or 50 years. All methods within this discipline are characterized by maintaining a set of possible solutions (individuals) to make them successively evolve to fitter solutions generation after generation. Examples of evolutionary computation paradigms are the broadly known Genetic Algorithms (GAs) and Estimation of Distribution Algorithms (EDAs). This paper contributes to the further development of this discipline by...

Evolutionary learning of rich neural networks in the Bayesian model selection framework

Matteo Matteucci, Dario Spadoni (2004)

International Journal of Applied Mathematics and Computer Science

In this paper we focus on the problem of using a genetic algorithm for model selection within a Bayesian framework. We propose to reduce the model selection problem to a search problem solved using evolutionary computation to explore a posterior distribution over the model space. As a case study, we introduce ELeaRNT (Evolutionary Learning of Rich Neural Network Topologies), a genetic algorithm which evolves a particular class of models, namely, Rich Neural Networks (RNN), in order to find an optimal...

Exact adaptive pointwise estimation on Sobolev classes of densities

Cristina Butucea (2001)

ESAIM: Probability and Statistics

The subject of this paper is to estimate adaptively the common probability density of n independent, identically distributed random variables. The estimation is done at a fixed point x 0 ∈ ℝ , over the density functions that belong to the Sobolev class W n ( β , L ) . We consider the adaptive problem setup, where the regularity parameter β is unknown and varies in a given set B n . A sharp adaptive estimator is obtained, and the explicit asymptotical constant, associated to its rate of convergence is found.

Exact adaptive pointwise estimation on Sobolev classes of densities

Cristina Butucea (2010)

ESAIM: Probability and Statistics

The subject of this paper is to estimate adaptively the common probability density of n independent, identically distributed random variables. The estimation is done at a fixed point x 0 ∈ ℝ , over the density functions that belong to the Sobolev class Wn(β,L). We consider the adaptive problem setup, where the regularity parameter β is unknown and varies in a given set Bn. A sharp adaptive estimator is obtained, and the explicit asymptotical constant, associated to its rate of convergence is found.

Exact and approximate distributions for the product of Dirichlet components

Saralees Nadarajah, Samuel Kotz (2004)

Kybernetika

It is well known that X / ( X + Y ) has the beta distribution when X and Y follow the Dirichlet distribution. Linear combinations of the form α X + β Y have also been studied in Provost and Cheong [S. B. Provost and Y.-H. Cheong: On the distribution of linear combinations of the components of a Dirichlet random vector. Canad. J. Statist. 28 (2000)]. In this paper, we derive the exact distribution of the product P = X Y (involving the Gauss hypergeometric function) and the corresponding moment properties. We also propose...

Exact distribution for the generalized F tests

Miguel Fonseca, Joao Tiago Mexia, Roman Zmyślony (2002)

Discussiones Mathematicae Probability and Statistics

Generalized F statistics are the quotients of convex combinations of central chi-squares divided by their degrees of freedom. Exact expressions are obtained for the distribution of these statistics when the degrees of freedom either in the numerator or in the denominator are even. An example is given to show how these expressions may be used to check the accuracy of Monte-Carlo methods in tabling these distributions. Moreover, when carrying out adaptative tests, these expressions enable us to estimate...

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