Bayesian analysis of multivariate survival data using Monte Carlo methods

This paper deals with the analysis of multivariate survival data from a Bayesian perspective using Markov-chain Monte Carlo methods. The Metropolis along with the Gibbs algorithm is used to calculate some of the marginal posterior distributions. A multivariate survival model is proposed, since survival times within the same group are correlated as a consequence of a frailty random block effect. The conditional proportional-hazards model of Clayton and Cuzick is used with a martingale structured prior process (Arjas and Gasbarra) for the discretized baseline hazard. Besides the calculation of the marginal posterior distributions of the parameters of interest, this paper presents some Bayesian EDA diagnostic techniques to detect model adequacy. The methodology is exemplified with kidney infection data where the times to infections within the same patients are expected to be correlated.     

Restricted most powerful Bayesian tests for linear models

Uniformly most powerful Bayesian tests (UMPBTs) are a new class of Bayesian tests in which null hypotheses are rejected if their Bayes factor exceeds a specified threshold. The alternative hypotheses in UMPBTs are defined to maximize the probability that the null hypothesis is rejected. Here, we generalize the notion of UMPBTs by restricting the class of alternative hypotheses over which this maximization is performed, resulting in restricted most powerful Bayesian tests (RMPBTs). We then derive RMPBTs for linear models by restricting alternative hypotheses to g priors. For linear models, the rejection regions of RMPBTs coincide with those of usual frequentist F‐tests, provided that the evidence thresholds for the RMPBTs are appropriately matched to the size of the classical tests. This correspondence supplies default Bayes factors for many common tests of linear hypotheses. We illustrate the use of RMPBTs for ANOVA tests and t‐tests and compare their performance in numerical studies.     

Bayesian comparative study on binary time series

In this paper, we consider the Bayesian analysis of binary time series with different priors, namely normal, Students' t, and Jeffreys prior, and compare the results with the frequentist methods through some simulation experiments and one real data on daily rainfall in inches at Mount Washington, NH. Among Bayesian methods, our results show that the Jeffreys prior perform better in most of the situations for both the simulation and the rainfall data. Furthermore, among weakly informative priors considered, Student's t prior with 7 degrees of freedom fits the data most adequately.     

Natural (Non‐)Informative Priors for Skew‐symmetric Distributions

In this paper, we present an innovative method for constructing proper priors for the skewness (shape) parameter in the skew‐symmetric family of distributions. The proposed method is based on assigning a prior distribution on the perturbation effect of the shape parameter, which is quantified in terms of the total variation distance. We discuss strategies to translate prior beliefs about the asymmetry of the data into an informative prior distribution of this class. We show via a Monte Carlo simulation study that our non‐informative priors induce posterior distributions with good frequentist properties, similar to those of the Jeffreys prior. Our informative priors yield better results than their competitors from the literature. We also propose a scale‐invariant and location‐invariant prior structure for models with unknown location and scale parameters and provide sufficient conditions for the propriety of the corresponding posterior distribution. Illustrative examples are presented using simulated and real data.     

Sexual fantasies about one's partner versus someone else: Gender differences in incidence and frequency

Gender differences in the proportion of sexual fantasies involving someone other than a current partner (extradyadic fantasies) were explored using an anonymous questionnaire administered to 349 university students and employees (ages 18 to 70) who reported that they were currently in heterosexual relationships. Eighty‐seven percent of the sample (98% of men and 80% of women) reported having extradyadic fantasies in the past 2 months. A hierarchical regression analysis revealed that, compared to women, a larger percentage of men's sexual fantasies were extradyadic even after controlling for the effects of relationship length, number of prior sex partners, any prior incidents of actual extradyadic sexual behavior or “cheating” on the current partner, and socioeconomic status. In addition, it was found that the proportion of extradyadic fantasies increased as a function of relationship length for both genders, while prior incidents of extradyadic sexual behavior and a larger number of prior partners were associated with a higher proportion of extradyadic fantasies for women only.     

CONFIDENCE INTERVALS UTILIZING PRIOR INFORMATION IN THE BEHRENS–FISHER PROBLEM

Consider two independent random samples of size f + 1 , one from an N (μ₁, σ²₁) distribution and the other from an N (μ₂, σ²₂) distribution, where σ²₁/σ²₂∈ (0, ∞) . The Welch ‘approximate degrees of freedom’ (‘approximate t‐solution’) confidence interval for μ₁?μ₂ is commonly used when it cannot be guaranteed that σ²₁/σ²₂= 1 . Kabaila (2005, Comm. Statist. Theory and Methods 34 , 291–302) multiplied the half‐width of this interval by a positive constant so that the resulting interval, denoted by J₀, has minimum coverage probability 1 ?α. Now suppose that we have uncertain prior information that σ²₁/σ²₂= 1. We consider a broad class of confidence intervals for μ₁?μ₂ with minimum coverage probability 1 ?α. This class includes the interval J₀, which we use as the standard against which other members of will be judged. A confidence interval utilizes the prior information substantially better than J₀ if (expected length of J)/(expected length of J₀) is (a) substantially less than 1 (less than 0.96, say) for σ²₁/σ²₂= 1 , and (b) not too much larger than 1 for all other values of σ²₁/σ²₂ . For a given f, does there exist a confidence interval that satisfies these conditions? We focus on the question of whether condition (a) can be satisfied. For each given f, we compute a lower bound to the minimum over of (expected length of J)/(expected length of J₀) when σ²₁/σ²₂= 1 . For 1 ?α= 0.95 , this lower bound is not substantially less than 1. Thus, there does not exist any confidence interval belonging to that utilizes the prior information substantially better than J₀.     

基于创业团队先前经验的新技术企业市场进入战略选择研究

基于社会认知和战略选择等理论知识,探讨创业团队先前经验构成特征与进入战略创新性的逻辑关系,并探索技术独享性和环境宽松性对团队决策的影响。基于随机抽样的问卷调研方法,利用150份新技术企业样本进行实证分析。研究结果表明,新技术企业初始战略来源于创业团队基于先前经验而达成的集体认知决策,技术导向型团队倾向于通过产品或服务的创新进入市场,而市场导向型的团队则会竭力从交易结构的创新入手,兼顾技术和市场导向的团队,虽然拥有多元化的认知模式,却没能迸发出应有的创造力。技术独享性在创业团队经验构成与进入战略创新性之间发挥正向调节作用,但没有改变团队成员固有认知模式;环境宽松性改变了创业团队在选择市场进入战略时的关注点,当环境较为宽松时,技术导向型和市场导向型的创业团队都呈现出对产品或服务创新的忽视,而加大了在交易结构上谋求创新的力度。     

佛教哲学与中国儒学的内在关系问题

儒家学说的底层解释模式是天人合德的宇宙哲学,具体表现为气感论学说以及这一学说所具有的自然主义形而上学特点。佛教的理论基础是缘起理论,业感缘起学说是其突出的特色。气感论与业感说的关系反映了儒家文化与佛教文化的差异,但因为“感”这一学说而使儒佛二种文化又具有某种沟通的内在基础。研究这两种学说的意义在于,可以进一步加深我们对中国传统文化的整体发展与演变的理解和把握。     

A classroom approach to the construction of Bayesian credible intervals of a Poisson mean

Abstract

The Poisson distribution is here used to illustrate Bayesian inference concepts with the ultimate goal to construct credible intervals for a mean. The evaluation of the resulting intervals is in terms of “mismatched” priors and posteriors. The discussion is in the form of an imaginary dialog between a teacher and a student, who have met earlier, discussing and evaluating the Wald and score confidence intervals, as well as confidence intervals based on transformation and bootstrap techniques. From the perspective of the student the learning process is akin to a real research situation. The student is supposed to have studied mathematical statistics for at least two semesters.     

Analytic Bayesian Solution of the Two-Stage Poisson-Type Problem in Probabilistic Risk Analysis

The basic purpose of probabilistic risk analysis is to make inferences about the probabilities of various postulated events, with an account of all relevant information such as prior knowledge and operating experience with the specific system under study, as well as experience with other similar systems. Estimation of the failure rate of a Poisson-type system leads to an especially simple Bayesian solution in closed form if the prior probability implied by the invariance properties of the problem is properly taken into account. This basic simplicity persists if a more realistic prior, representing order of magnitude knowledge of the rate parameter, is employed instead. Moreover, the more realistic prior allows direct incorporation of experience gained from other similar systems, without need to postulate a statistical model for an underlying ensemble. The analytic formalism is applied to actual nuclear reactor data.