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Effects of bayesian model selection on Frequentist Performances: An Alternative Approach

Applied Mathematics 2016年第10期7卷 1103-1115页

作者： Georges Nguefack-Tsague Walter Zucchini Biostatistics Unit Department of Public Health Faculty of Medicine and Biomedical Sciences University of Yaounde 1 Yaounde Cameroon Institute for Statistics and Econometrics University of Goettingen Goettingen Germany

It is quite common in statistical modeling to select a model and make inference as if the model had been known in advance;i.e. ignoring model selection uncertainty. The resulted estimator is called post-model selection estimator (PMSE) whose properties are hard to derive. Conditioning on data at hand (as it is usually the case), bayesian model selection is free of this phenomenon. This paper is concerned with the properties of bayesian estimator obtained after model selection when the frequentist (long run) performances of the resulted bayesian estimator are of interest. The proposed method, using bayesian decision theory, is based on the well known bayesian model averaging (BMA)’s machinery;and outperforms PMSE and BMA. It is shown that if the unconditional model selection probability is equal to model prior, then the proposed approach reduces BMA. The method is illustrated using Bernoulli trials.

关键词： model selection Uncertainty model Uncertainty bayesian model selection bayesian model Averaging bayesian Theory Frequentist Performance

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Learning Dynamic Causal Relationships Among Sugar Prices

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Acta Mathematicae Applicatae Sinica 2017年第3期33卷 809-818页

作者： Jing XU Xing-wei TONG Fang WANG Jian-ping CHEN School of Statistics University of International Business and EconomicsBeijing 100029China School of Statistics Beijing Normal UniversityBeijing 100875China COFCO Tunhe Co. LtdUrumqiXinjiang 830000China

In this paper, we are interested in exploring the dynamic causal relationships among two sets of three variables in different quarters. One set is futures sugar closing price in Zhengzhou futures exchange market （ZC）, spot sugar price in Zhengzhou （ZS） and futures sugar closing price in New York futures exchange market（NC） and the other includes futures sugar opening price in Zhengzhou （ZO）, ZS and NC. For each quarter, we first use bayesian model selection to obtain the optimal causal graph with the highest BD scores and then use bayesian model averaging approach to explore the causal relationship between every two variables. From the real data analysis, the two conclusions almost coincide, which shows that the two methods are practical.

关键词： bayesian Network dynamic causal relationships bayesian model selection bayesian model averaging

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Power-expected-posterior prior Bayes factor consistency for nested linear models with increasing dimensions

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Statistical Theory and Related Fields 2020年第2期4卷 162-171页

作者： D.Fouskakis J.K.Innocent L.Pericchi Department of Mathematics National Technical University of AthensAthensGreece Department of Mathematics University of Puerto RicoSan JuanUSA

The power-expected-posterior prior is used in this paper for comparing nested linear *** asymptotic behaviour of the method is investigated for different values of the power parameter of the *** is given on the consistency of the Bayes factor of comparing the full model M_(p) versus a generic submodel M_(l).In each case,we allow the true generating model to be either M_(p) or M_(l) and we keep the dimension of M_(l) fixed,while the dimension of M_(p) can be either fixed or(grow as)O(n),with n denoting the sample size.

关键词： bayesian model selection Bayes factor consistency expected-posterior prior Gaussian linear models increasing dimension power-expected-posterior prior

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Depression recognition using functional connectivity based on dynamic causal model

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Journal of Southeast University(English Edition) 2011年第4期27卷 367-369页

作者：罗国平刘刚赵竟姚志剑卢青东南大学学习科学研究中心南京210096 南京医科大学附属脑科医院南京210029

Dynamic casual modeling of functional magnetic resonance imaging（fMRI） signals is employed to explore critical emotional neurocircuitry under sad stimuli. The intrinsic model of emotional loops is built on the basis of Papez＇s circuit and related prior knowledge, and then three modulatory connection models are established. In these models, stimuli are placed at different points, which represents they affect the neural activities between brain regions, and these activities are modulated in different ways. Then, the optimal model is selected by bayesian model comparison. From group analysis, patients＇ intrinsic and modulatory connections from the anterior cingulate cortex （ACC） to the right inferior frontal gyrus （rlFG） are significantly higher than those of the control group. Then the functional connection parameters of the model are selected as classifier features. The classification accuracy rate from the support vector machine（SVM） classifier is 80.73%, which, to some extent, validates the effectiveness of the regional connectivity parameters for depression recognition and provides a new approach for the clinical diagnosis of depression.

关键词： depression recognition fMRI dynamic causal model bayesian model selection

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A Mixture-Based bayesian model Averaging Method

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Open Journal of Statistics 2016年第2期6卷 220-228页

bayesian model averaging (BMA) is a popular and powerful statistical method of taking account of uncertainty about model form or assumption. Usually the long run (frequentist) performances of the resulted estimator are hard to derive. This paper proposes a mixture of priors and sampling distributions as a basic of a Bayes estimator. The frequentist properties of the new Bayes estimator are automatically derived from bayesian decision theory. It is shown that if all competing models have the same parametric form, the new Bayes estimator reduces to BMA estimator. The method is applied to the daily exchange rate Euro to US Dollar.

关键词： Mixture bayesian model selection bayesian model Averaging bayesian Theory Frequentist Performance

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