BAYESIAN SUBSET SELECTION AND MODEL AVERAGING USING A CENTRED AND DISPERSED PRIOR FOR THE ERROR VARIANCE

This article proposes a new data‐based prior distribution for the error variance in a Gaussian linear regression model, when the model is used for Bayesian variable selection and model averaging. For a given subset of variables in the model, this prior has a mode that is an unbiased estimator of the error variance but is suitably dispersed to make it uninformative relative to the marginal likelihood. The advantage of this empirical Bayes prior for the error variance is that it is centred and dispersed sensibly and avoids the arbitrary specification of hyperparameters. The performance of the new prior is compared to that of a prior proposed previously in the literature using several simulated examples and two loss functions. For each example our paper also reports results for the model that orthogonalizes the predictor variables before performing subset selection. A real example is also investigated. The empirical results suggest that for both the simulated and real data, the performance of the estimators based on the prior proposed in our article compares favourably with that of a prior used previously in the literature.     

Bayesian analysis of elapsed times in continuous‐time Markov chains

The authors consider Bayesian analysis for continuous‐time Markov chain models based on a conditional reference prior. For such models, inference of the elapsed time between chain observations depends heavily on the rate of decay of the prior as the elapsed time increases. Moreover, improper priors on the elapsed time may lead to improper posterior distributions. In addition, an infinitesimal rate matrix also characterizes this class of models. Experts often have good prior knowledge about the parameters of this matrix. The authors show that the use of a proper prior for the rate matrix parameters together with the conditional reference prior for the elapsed time yields a proper posterior distribution. The authors also demonstrate that, when compared to analyses based on priors previously proposed in the literature, a Bayesian analysis on the elapsed time based on the conditional reference prior possesses better frequentist properties. The type of prior thus represents a better default prior choice for estimation software.     

先前经验、学习风格与创业能力的实证研究

如何提升创业者的创业能力是目前创业实践中亟待解决的问题。在将经验和能力区分开的基础上,从创业学习的视角出发,深入挖掘创业者先前经验与创业能力之间的作用关系机制,探讨创业者经验向创业能力转化的内在机理,采用探索性因子分析、验证性因子分析、层级回归分析等方法,对173家中国新创企业的调查问卷进行分析。研究结果表明,学习风格在创业者先前经验与创业能力的关系中发挥调节作用,不同类型的先前经验对不同类型的创业能力产生影响,创业者的学习风格也并非像以往研究所认为的那样存在优劣之分,而是存在一个匹配关系,当创业者的信息获取/转化方式与他的先前经验类型相匹配时,这一类型的经验才能更好的转化为创业能力。     

转型经济体制下创业团队的先前经验、无力感与适应能力

在资源依赖理论的基础上,从创业团队的先前经验出发,通过分析4家高科技创业企业的案例资料,考察了创业团队无力感与适应能力之间的关联性,并分析了创业团队的认知趋同性对该作用过程的影响机制,从而为新创企业提高在动态环境中的生存能力提供建议.研究表明,创业团队先前经验可以降低团队成员的无力感,从而提升团队的适应能力,且当创业团队认知趋同性越高时,无力感与适应能力的负向作用越强.     

On predictive distributions and Bayesian networks

In this paper we are interested in discrete prediction problems for a decision-theoretic setting, where the task is to compute the predictive distribution for a finite set of possible alternatives. This question is first addressed in a general Bayesian framework, where we consider a set of probability distributions defined by some parametric model class. Given a prior distribution on the model parameters and a set of sample data, one possible approach for determining a predictive distribution is to fix the parameters to the instantiation with the maximum a posteriori probability. A more accurate predictive distribution can be obtained by computing the evidence (marginal likelihood), i.e., the integral over all the individual parameter instantiations. As an alternative to these two approaches, we demonstrate how to use Rissanen's new definition of stochastic complexity for determining predictive distributions, and show how the evidence predictive distribution with Jeffrey's prior approaches the new stochastic complexity predictive distribution in the limit with increasing amount of sample data. To compare the alternative approaches in practice, each of the predictive distributions discussed is instantiated in the Bayesian network model family case. In particular, to determine Jeffrey's prior for this model family, we show how to compute the (expected) Fisher information matrix for a fixed but arbitrary Bayesian network structure. In the empirical part of the paper the predictive distributions are compared by using the simple tree-structured Naive Bayes model, which is used in the experiments for computational reasons. The experimentation with several public domain classification datasets suggest that the evidence approach produces the most accurate predictions in the log-score sense. The evidence-based methods are also quite robust in the sense that they predict surprisingly well even when only a small fraction of the full training set is used.     

Analysis of Competing Risks by Using Bayesian Smoothing

We consider the competing risks set-up. In many practical situations, the conditional probability of the cause of failure given the failure time is of direct interest. We propose to model the competing risks by the overall hazard rate and the conditional probabilities rather than the cause-specific hazards. We adopt a Bayesian smoothing approach for both quantities of interest. Illustrations are given at the end.     

引入信息成本的信息结构与股权融资成本

本文放松了Easley和O’Hara信息成本为0的假设,在他们的信息结构模型的理论框架下,构建了一个引入信息成本因素的信息结构模型。从信息结构的四个方面：信息成本、信息风险、信息披露的质量和先验信息质量研究了信息结构与股权融资成本之间的关系,得出了四个推论,从而拓展了信息结构模型。在进一步的实证研究中,选取市场微观结构理论中的逆向选择成本、知情交易概率-PIN分别作为信息成本和信息风险的衡量指标,研究发现：信息成本与股权融资成本之间呈倒‘U’型曲线关系;信息风险越高的股票股权融资成本越高;信息披露质量越高的公司,股权融资成本越低;先验信息质量越高,股权融资成本越低;从而对推论进行了有效验证。本文与Easley和O’Hara最大不同在于引入了信息成本因素,并且用实证方法对推论进行了验证,具有一定的开创性。     

The empirical Bayes estimators of the parameter of the Poisson distribution with a conjugate gamma prior under Stein's loss function

For the hierarchical Poisson and gamma model, we calculate the Bayes posterior estimator of the parameter of the Poisson distribution under Stein's loss function which penalizes gross overestimation and gross underestimation equally and the corresponding Posterior Expected Stein's Loss (PESL). We also obtain the Bayes posterior estimator of the parameter under the squared error loss and the corresponding PESL. Moreover, we obtain the empirical Bayes estimators of the parameter of the Poisson distribution with a conjugate gamma prior by two methods. In numerical simulations, we have illustrated: The two inequalities of the Bayes posterior estimators and the PESLs; the moment estimators and the Maximum Likelihood Estimators (MLEs) are consistent estimators of the hyperparameters; the goodness-of-fit of the model to the simulated data. The numerical results indicate that the MLEs are better than the moment estimators when estimating the hyperparameters. Finally, we exploit the attendance data on 314 high school juniors from two urban high schools to illustrate our theoretical studies.     

Nonparametric Bayesian inference for multivariate density functions using Feller priors

Multivariate density estimation plays an important role in investigating the mechanism of high-dimensional data. This article describes a nonparametric Bayesian approach to the estimation of multivariate densities. A general procedure is proposed for constructing Feller priors for multivariate densities and their theoretical properties as nonparametric priors are established. A blocked Gibbs sampling algorithm is devised to sample from the posterior of the multivariate density. A simulation study is conducted to evaluate the performance of the procedure.     

A Method to Handle Zero Counts in the Multinomial Model

In the context of an objective Bayesian approach to the multinomial model, Dirichlet(a, …, a) priors with a < 1 have previously been shown to be inadequate in the presence of zero counts, suggesting that the uniform prior (a = 1) is the preferred candidate. In the presence of many zero counts, however, this prior may not be satisfactory either. A model selection approach is proposed, allowing for the possibility of zero parameters corresponding to zero count categories. This approach results in a posterior mixture of Dirichlet distributions and marginal mixtures of beta distributions, which seem to avoid the problems that potentially result from the various proposed Dirichlet priors, in particular in the context of extreme data with zero counts.