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Cognitive Constructivism, EigenSolutions, and Sharp Statistical Hypotheses
 Cybernetics & Human Knowing
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Testing and estimating the nondisjunction fraction in meiosis I using reference priors
 Biom. J. 2007
"... In this paper we analyze the fraction of nondisjunction in Meiosis I assuming reference (noninformative) priors. We consider Jeffreys’s approach to built a noninformative prior (Jeffreys’s prior) for the fraction of nondisjunction in Meiosis I. We prove that Jeffreys’s prior is a proper distribu ..."
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In this paper we analyze the fraction of nondisjunction in Meiosis I assuming reference (noninformative) priors. We consider Jeffreys’s approach to built a noninformative prior (Jeffreys’s prior) for the fraction of nondisjunction in Meiosis I. We prove that Jeffreys’s prior is a proper distribution. We perform Monte Carlo studies in order to compare Bayes estimates obtained assuming Jeffreys’s and uniform priors. We consider full Bayesian significance test (FBST) and Bayes factor (BF) for testing precise hypothesis on the fraction of nondisjunction in Meiosis I. The ultimate goal of this paper is to compare these two test procedures through simulation studies using both prior specifications. An application to Down Syndrome data is also presented.
Test manuscript No. (will be inserted by the editor) Combining Bayesian procedures for testing
, 2009
"... Abstract Jeffreys and PereiraStern Bayesian procedures for testing provide measures of evidence in favour the null hypothesis which can lead to different decisions. We introduce two procedures for testing based on pooling the posterior evidences in favour of the null hypothesis provided by these pr ..."
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Abstract Jeffreys and PereiraStern Bayesian procedures for testing provide measures of evidence in favour the null hypothesis which can lead to different decisions. We introduce two procedures for testing based on pooling the posterior evidences in favour of the null hypothesis provided by these procedures. We prove that the proposed procedure which has been built using the linear pool of probability is a Bayes test and does not lead to JeffreysLindley paradox. We apply the results for testing precise hypothesis about parameters of some asymmetric family of distributions including the skewnormal one.
FBST: Compositionality
"... Abstract. In this paper, the relationship between the credibility of a complex hypothesis, H, and those of its constituent elementary hypotheses, H j, j = 1...k, is analyzed, in the independent setup, under the Full Bayesian Significance Testing (FBST) mathematical apparatus. ..."
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Abstract. In this paper, the relationship between the credibility of a complex hypothesis, H, and those of its constituent elementary hypotheses, H j, j = 1...k, is analyzed, in the independent setup, under the Full Bayesian Significance Testing (FBST) mathematical apparatus.
Full Bayesian Signi cance Test for Coe cients of Variation
"... Jul012000 rev. Oct102000 New application of the Full Bayesian Signi cance Test (FBST) for precise hypotheses are presented. The FBST is an alternative to signi cance tests or, equivalently, topvalues. In the FBST we compute the evidence of the precise hypothesis. This evidence is the probabilit ..."
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Jul012000 rev. Oct102000 New application of the Full Bayesian Signi cance Test (FBST) for precise hypotheses are presented. The FBST is an alternative to signi cance tests or, equivalently, topvalues. In the FBST we compute the evidence of the precise hypothesis. This evidence is the probability of a credible set \tangent " to the submanifold (of the parameter space) that de nes the null hypothesis. We use the FBST to compare coe cients of variation, in applications arising in nance and industrial engineering.
A Weibull Wearout Test: Full Bayesian Approach Telba
, 2000
"... The Full Bayesian Signi cance Test (FBST) for precise hypotheses is presented, with some applications relevant to reliability theory. The FBST is an alternative to signi cance tests or, equivalently, to pvalues. In the FBST we compute the evidence of the precise hypothesis. This evidence is the pro ..."
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The Full Bayesian Signi cance Test (FBST) for precise hypotheses is presented, with some applications relevant to reliability theory. The FBST is an alternative to signi cance tests or, equivalently, to pvalues. In the FBST we compute the evidence of the precise hypothesis. This evidence is the probability of the complement of a credible set \tangent " to the submanifold (of the parameter space) that de nes the null hypothesis. We use the FBST in an application requiring a quality control of used components, based on remaining life statistics.
MATHEMATICAL CLUSTERING INTEGRATED WITH SWOT ANALYSIS AS A TOOL FOR DESIGN OF SUSTAINABLE DEVELOPMENT STRATEGIES
"... The paper describes planning procedures used originally for drafting the Sustainable Development Strategic Framework (SDSF) of the Czech Republic in 2008–2009 and compares them with the use of a selforganizing map (SOM), combined with the Ward’s clustering method. Clustering followed by a series of ..."
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The paper describes planning procedures used originally for drafting the Sustainable Development Strategic Framework (SDSF) of the Czech Republic in 2008–2009 and compares them with the use of a selforganizing map (SOM), combined with the Ward’s clustering method. Clustering followed by a series of SWOT analyses is a new technique that allows for the development of largescope strategic documents covering many sectors and accommodating various economic, social, and environmental issues. Large initial sets of statements (problems, trends, forecasts, etc.) can be converted by multiple SWOT analyses into a consistent set of interventions. An optimal structure of the clustered statements has to be found experimentally. Use of SOM makes searching for the optimal structure (information model of the strategy) effi cient. Such information model can be broadly discussed by stakeholders and purposefully modifi ed (generation of strategic alternatives) before the best alternative is transformed into a fi nal strategy text.
METHODOLOGY ARTICLE Open Access Testing allele homogeneity: the problem of nested hypotheses
"... Background: The evaluation of associations between genotypes and diseases in a casecontrol framework plays an important role in genetic epidemiology. This paper focuses on the evaluation of the homogeneity of both genotypic and allelic frequencies. The traditional test that is used to check allelic ..."
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Background: The evaluation of associations between genotypes and diseases in a casecontrol framework plays an important role in genetic epidemiology. This paper focuses on the evaluation of the homogeneity of both genotypic and allelic frequencies. The traditional test that is used to check allelic homogeneity is known to be valid only under HardyWeinberg equilibrium, a property that may not hold in practice. Results: We first describe the flaws of the traditional (chisquared) tests for both allelic and genotypic homogeneity. Besides the known problem of the allelic procedure, we show that whenever these tests are used, an incoherence may arise: sometimes the genotypic homogeneity hypothesis is not rejected, but the allelic hypothesis is. As we argue, this is logically impossible. Some methods that were recently proposed implicitly rely on the idea that this does not happen. In an attempt to correct this incoherence, we describe an alternative frequentist approach that is appropriate even when HardyWeinberg equilibrium does not hold. It is then shown that the problem remains and is intrinsic of frequentist procedures. Finally, we introduce the Full Bayesian Significance Test to test both hypotheses and prove that the incoherence cannot happen with these new tests. To illustrate this, all five tests are applied to real and simulated datasets. Using the celebrated power analysis, we show that the Bayesian method is comparable to the frequentist one and has the advantage of being coherent. Conclusions: Contrary to more traditional approaches, the Full Bayesian Significance Test for association studies provides a simple, coherent and powerful tool for detecting associations.