Default Bayesian analysis of the Behrens–Fisher problem

Moreno, Elı́as; Bertolino, Francesco; Racugno, Walter

doi:10.1016/s0378-3758(99)00070-1

Cited by 29 publications

(18 citation statements)

References 13 publications

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“…The separate variance SD test tends to favor the null hypothesis more than does the shared variance SD test, although the difference is small. The intrinsic Bayes factor (i.e., a default Bayes factor that uses minimal training samples and uninformative priors; Berger & Pericchi, 1996;Moreno et al, 1999) supports the null hypothesis the most. A more detailed treatment of the Behrens-Fisher problem is beyond the scope of the present article; we include it here only to highlight the flexibility of the SD test.…”

Section: Discussionmentioning

confidence: 99%

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How to quantify support for and against the null hypothesis: A flexible WinBUGS implementation of a default Bayesian t test

Wetzels

Raaijmakers

Jakab

et al. 2009

Psychonomic Bulletin & Review

136

158

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Section: Discussionmentioning

confidence: 99%

“…To illustrate the behavior of the separate variance SD Bayes factors, we follow Moreno, Bertolino, and Racugno (1999) and apply the tests to hypothetical data from Box and Tiao (1973, p. 107). These data have the following properties: n 1 20, var 1 12, n 2 12, and var 2 40.…”

Section: Extension 1: Order Restrictionsmentioning

confidence: 99%

How to quantify support for and against the null hypothesis: A flexible WinBUGS implementation of a default Bayesian t test

Wetzels

Raaijmakers

Jakab

et al. 2009

Psychonomic Bulletin & Review

136

158

View full text Add to dashboard Cite

show abstract

“…Furthermore, reasons for using intrinsic priors include (a) they are free of hyperparameters, (b) they provide a well-defined Bayesian solution for testing problems, and (c) under the intrinsic prior distribution, the parameters in the alternative model are not independent and they are ''centered'' at the null, a condition widely required in testing scenarios (Jeffreys 1961;Berger and Sellke 1987;Casella and Berger 1987;Morris 1987). Moreover, intrinsic priors have proved to behave extremely well for a wide variety of problems (see, for instance, Moreno et al 1999Moreno et al , 2000Moreno and Liseo 2003;Kim and Sun 2000;Casella and Moreno 2002, 2005. The main inconvenient of the intrinsic priors for complex models is that they are difficult to compute.…”

Section: Objective Bayesian Methodsmentioning

confidence: 99%

An objective Bayesian analysis of the change point problem

Moreno

Casella

Garcı́a-Ferrer

2005

Stoch Environ Res Ris Assess

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The Bayesian literature on the change point problem deals with the inference of a change in the distribution of a set of time-ordered data based on a sample of fixed size. This is the so-called ''retrospective or off-line'' analysis of the change point problem. A related but different problem is that of the ''sequential'' change point detection, mainly analyzed from a frequentist viewpoint. While the former typically focuses on the estimation of the position in which the change point occurs, the latter is a testing problem which has a natural formulation as a Bayesian model selection problem. In this paper we provide such a Bayesian formulation, which generalizes previous formulations such as the well-known CUSUM stopping rule. We show that the conventional improper priors (also called non-informative, objective or default), cannot be used either for sequential detection of the change or for retrospective estimation. Then, we propose objective intrinsic prior distributions for the unknown model parameters. The normal and Poisson cases are studied in detail and examples with simulated and real data are provided.

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“…Some Bayesian solutions, in the univariate case, were illustrated by Box and Tiao [3], Girón et al [16] and Moreno et al [22].…”

Section: Introductionmentioning

confidence: 99%

The multivariate Behrens–Fisher distribution

Girón

Castillo

2010

Journal of Multivariate Analysis

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a b s t r a c tThe main purpose of this paper is the study of the multivariate Behrens-Fisher distribution. It is defined as the convolution of two independent multivariate Student t distributions. Some representations of this distribution as the mixture of known distributions are shown. An important result presented in the paper is the elliptical condition of this distribution in the special case of proportional scale matrices of the Student t distributions in the defining convolution. For the bivariate Behrens-Fisher problem, the authors propose a non-informative prior distribution leading to highest posterior density (H.P.D.) regions for the difference of the mean vectors whose coverage probability matches the frequentist coverage probability more accurately than that obtained using the independence-Jeffreys prior distribution, even with small samples.

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Default Bayesian analysis of the Behrens–Fisher problem

Cited by 29 publications

References 13 publications

How to quantify support for and against the null hypothesis: A flexible WinBUGS implementation of a default Bayesian t test

How to quantify support for and against the null hypothesis: A flexible WinBUGS implementation of a default Bayesian t test

An objective Bayesian analysis of the change point problem

The multivariate Behrens–Fisher distribution

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