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Minimum Description Length and Empirical Bayes Methods of Identifying SNPs Associated with Disease
, 2010
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Inference after checking multiple Bayesian models for data conflict. Working Paper
"... Two major approaches have developed within Bayesian statistics to address uncertainty in the prior distribution and in the overall model more generally. First, methods of model checking, including those assessing priordata conflict, determine whether the prior and the rest of the model are adequat ..."
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Two major approaches have developed within Bayesian statistics to address uncertainty in the prior distribution and in the overall model more generally. First, methods of model checking, including those assessing priordata conflict, determine whether the prior and the rest of the model are adequate for purposes of inference and estimation or other decisionmaking. The main drawback of this approach is that it provides little guidance for inference in the event that the model is found to be inadequate, that is, 1 in conflict with the data. Second, the robust Bayes approach determines the sensitivity of inferences and decisions to the prior distribution and other model assumptions. This approach includes rules for making decisions on the basis of a set of posterior distributions corresponding to the set of reasonable model assumptions. Drawbacks of the second approach include the inability to criticize the set of models and the lack of guidance for specifying such a set. Those two approaches to model uncertainty are combined in order to overcome the limitations of each approach. The first approach checks each model within a large class of models to assess which models are in conflict with the data and which models are adequate for purposes of data analysis. The resulting set of adequate models is then used for inference according to decision rules developed for the robust Bayes approach and for imprecise probability more generally. This proposed framework is illustrated by the application of a class of hierarchical models to a simple data set.
Coherent frequentism
, 2009
"... By representing the range of fair betting odds according to a pair of confidence set estimators, dual probability measures on parameter space called frequentist posteriors secure the coherence of subjective inference without any prior distribution. The closure of the set of expected losses correspon ..."
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By representing the range of fair betting odds according to a pair of confidence set estimators, dual probability measures on parameter space called frequentist posteriors secure the coherence of subjective inference without any prior distribution. The closure of the set of expected losses corresponding to the dual frequentist posteriors constrains decisions without arbitrarily forcing optimization under all circumstances. This decision theory reduces to those that maximize expected utility when the pair of frequentist posteriors is induced by an exact or approximate confidence set estimator or when an automatic reduction rule is applied to the pair. In such cases, the resulting frequentist posterior is coherent in the sense that, as a probability distribution of the parameter of interest, it satisfies the axioms of the decisiontheoretic and logictheoretic systems typically cited in support of the Bayesian posterior. Unlike the pvalue, the confidence level of an interval hypothesis derived from such a measure is suitable as an estimator of the indicator of hypothesis truth since it converges in samplespace probability to 1 if the hypothesis is true or to 0 otherwise under general conditions.
Copyright c○2009 by the authors. Validation of Differential Gene Expression Algorithms: Application Comparing Fold Change Estimation to Hypothesis Testing
"... Sustained research on the problem of determining which genes are differentially expressed on the basis of microarray data has yielded a plethora of statistical algorithms, each justified by theory, simulation, or ad hoc validation and yet differing in practical results from equally justified algorit ..."
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Sustained research on the problem of determining which genes are differentially expressed on the basis of microarray data has yielded a plethora of statistical algorithms, each justified by theory, simulation, or ad hoc validation and yet differing in practical results from equally justified algorithms. The widespread confusion on which method to use in practice has been exacerbated by the finding that simply ranking genes by their fold changes sometimes outperforms popular statistical tests. Algorithms may be compared by quantifying each method’s error in predicting expression ratios, whether such ratios are defined across microarray channels or between two independent groups. For the data sets considered, estimating prediction error by cross validation demonstrates that empirical Bayes methods based on the lognormality assumption tend to outperform both a nonparametric method and algorithms based on selecting genes by their fold changes. The general comparison methodology is applicable to both singlechannel and dualchannel microarrays. As a theoretically sound method of estimating prediction error from observed expression levels, cross validation provides an empirical approach to assessing
METHODOLOGY ARTICLE Open Access
"... algorithms: Application comparing foldchange estimation to hypothesis testing ..."
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algorithms: Application comparing foldchange estimation to hypothesis testing
Estimating the null distribution for conditional inference and
, 2009
"... genomescale screening ..."
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unknown title
, 2014
"... Model fusion and multiple testing in the likelihood paradigm: Shrinkage and evidence supporting a point null hypothesis ..."
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Model fusion and multiple testing in the likelihood paradigm: Shrinkage and evidence supporting a point null hypothesis
unknown title
, 2014
"... Selfconsistent confidence sets and tests of composite hypotheses applicable to restricted parameters ..."
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Selfconsistent confidence sets and tests of composite hypotheses applicable to restricted parameters
Bayes Methods of Identifying SNPs Associated with Disease
, 2010
"... Copyright c○2010 by the authors. Minimum Description Length and Empirical ..."
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Copyright c○2010 by the authors. Minimum Description Length and Empirical