2,137 research outputs found

    Analysis of the Behrens-Fisher Problem Based on Bayesian Evidence

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    The Behrens-Fisher problem concerns the inferences for the difference between the means of two normal populations without making any assumption about the variances. Although the problem has been extensively studied in the literature, researchers cannot agree on its solution at present. In this paper, we propose a new method for dealing with the Behrens-Fisher problem in the Bayesian framework. The Bayesian evidence for testing the equality of two normal means and a credible interval at a specified level for the difference between the means are derived. Simulation studies are carried out to evaluate the performance of the provided Bayesian evidence

    Reference priors in non-normal location problems

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    Bayesian Statistics;Statistical Distribution

    "Magnitude-based inference": a statistical review

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    Purpose: We consider ‘‘magnitude-based inference’’ and its interpretation by examining in detail its use in the problem of comparing two means. Methods: We extract from the spreadsheets, which are provided to users of the analysis (http:// www.sportsci.org/), a precise description of how ‘‘magnitude-based inference’’ is implemented.We compare the implemented version of the method with general descriptions of it and interpret the method in familiar statistical terms. Results and Conclusions: We show that ‘‘magnitude-based inference’’ is not a progressive improvement on modern statistics. The additional probabilities introduced are not directly related to the confidence interval but, rather, are interpretable either as P values for two different nonstandard tests (for different null hypotheses) or as approximate Bayesian calculations, which also lead to a type of test. We also discuss sample size calculations associated with ‘‘magnitude-based inference’’ and show that the substantial reduction in sample sizes claimed for the method (30% of the sample size obtained from standard frequentist calculations) is not justifiable so the sample size calculations should not be used. Rather than using ‘‘magnitude-based inference,’’ a better solution is to be realistic about the limitations of the data and use either confidence intervals or a fully Bayesian analysis.Alan H. Welsh, Emma J. Knigh

    On the frequentist and Bayesian approaches to hypothesis testing

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    Hypothesis testing is a model selection problem for which the solution proposed by the two main statistical streams of thought, frequentists and Bayesians, substantially differ. One may think that this fact might be due to the prior chosen in the Bayesian analysis and that a convenient prior selection may reconcile both approaches. However, the Bayesian robustness viewpoint has shown that, in general, this is not so and hence a profound disagreement between both approaches exists. In this paper we briefly revise the basic aspects of hypothesis testing for both the frequentist and Bayesian procedures and discuss the variable selection problem in normal linear regression for which the discrepancies are more apparent. Illustrations on simulated and real data are given

    An Exposition on Bayesian Inference

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    The Bayesian approach to probability and statistics is described, a brief history of Bayesianism is related, differences between Bayesian and Frequentist schools of statistics are defined, protential applications are investigated, and a literature survey is presented in the form of a machine-sort card file. Bayesian thought is increasing in favor among statisticians because of its ability to attack problems that are unassailable from the Frequentist approach. It should become more popular among practitioners because of the flexibility it allows experimenters and the ease with which prior knowledge can be combined with experimental data. (82 pages
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