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 selectio...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.展开更多
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 ar...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.展开更多
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...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.展开更多
Surface wave methods have received much attention due to their efficient, flexible and convenient characteristics. However, there are still critical issues regarding a key step in surface wave inversion. In most exist...Surface wave methods have received much attention due to their efficient, flexible and convenient characteristics. However, there are still critical issues regarding a key step in surface wave inversion. In most existing methods, the number of layers is assumed to be known prior to the process of inversion. However, improper assignment of this parameter leads to erroneous inversion results. A Bayesian nonparametric method for Rayleigh wave inversion is proposed herein to address this problem. In this method, each model class represents a particular number of layers with unknown S-wave velocity and thickness of each layer. As a result, determination of the number of layers is equivalent to selection of the most applicable model class. Regarding each model class, the optimization search of S-wave velocity and thickness of each layer is implemented by using a genetic algorithm. Then, each model class is assessed in view of its efficiency under the Bayesian framework and the most efficient class is selected. Simulated and actual examples verify that the proposed Bayesian nonparametric approach is reliable and efficient for Rayleigh wave inversion, especially for its capability to determine the number of layers.展开更多
The power-expected-posterior prior is used in this paper for comparing nested linear models.The asymptotic behaviour of the method is investigated for different values of the power parameter of the prior.Focus is give...The power-expected-posterior prior is used in this paper for comparing nested linear models.The asymptotic behaviour of the method is investigated for different values of the power parameter of the prior.Focus 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.展开更多
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...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.展开更多
文摘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.
文摘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.
基金The National Natural Science Foundation of China(No.30900356,81071135)
文摘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.
基金Science and Technology Development Fund of the Macao SAR under research grant SKL-IOTSC-2018-2020the Research Committee of University of Macao under Research Grant MYRG2016-00029-FST。
文摘Surface wave methods have received much attention due to their efficient, flexible and convenient characteristics. However, there are still critical issues regarding a key step in surface wave inversion. In most existing methods, the number of layers is assumed to be known prior to the process of inversion. However, improper assignment of this parameter leads to erroneous inversion results. A Bayesian nonparametric method for Rayleigh wave inversion is proposed herein to address this problem. In this method, each model class represents a particular number of layers with unknown S-wave velocity and thickness of each layer. As a result, determination of the number of layers is equivalent to selection of the most applicable model class. Regarding each model class, the optimization search of S-wave velocity and thickness of each layer is implemented by using a genetic algorithm. Then, each model class is assessed in view of its efficiency under the Bayesian framework and the most efficient class is selected. Simulated and actual examples verify that the proposed Bayesian nonparametric approach is reliable and efficient for Rayleigh wave inversion, especially for its capability to determine the number of layers.
文摘The power-expected-posterior prior is used in this paper for comparing nested linear models.The asymptotic behaviour of the method is investigated for different values of the power parameter of the prior.Focus 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.
基金Supported by National Natural Science Foundation of China under grant(No.11371062,11671338)Beijing Center for Mathematics and Information Interdisciplinary Science and UIBE NetworkingCollaboration Center for China’s Multinational Business(No.201504YY006A)
文摘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.
