The Likelihood Method for Decision under Uncertainty

This paper introduces the likelihood method for decision under uncertainty. The method allows the quantitative determination of subjective beliefs or decision weights without invoking additional separability conditions, and generalizes the Savage–de Finetti betting method. It is applied to a number of popular models for decision under uncertainty. In each case, preference foundations result from the requirement that no inconsistencies are to be revealed by the version of the likelihood method appropriate for the model considered. A unified treatment of subjective decision weights results for most of the decision models popular today. Savage’s derivation of subjective expected utility can now be generalized and simplified. In addition to the intuitive and empirical contributions of the likelihood method, we provide a number of technical contributions: We generalize Savage’s nonatomiticy condition (“P6”) and his assumption of (sigma) algebras of events, while fully maintaining his flexibility regarding the outcome set. Derivations of Choquet expected utility and probabilistic sophistication are generalized and simplified similarly. The likelihood method also reveals a common intuition underlying many other conditions for uncertainty, such as definitions of ambiguity aversion and pessimism.     

Introduction to the Special Issue in Honor of Peter Wakker

Theory and Decision -     

Bayesian Inference in Dependent Right Censoring

In this article, we consider dependent right censoring when the lifetime and censoring variables have a Marshall–Olkin bivariate exponential distribution and obtain MLEs, MMEs and UMVUEs of the unknown parameters. The Bayes estimators as well as the Posterior Regret Gamma Minimax (PRGM) estimators of the parameters of interest under the SEL function are also obtained and a Monte Carlo simulation study is carried out to compare these estimators.     

Some moment properties and limit theorems of the reversed generalized logistic distribution with applications

In this paper we discuss an extended form of the logistic distribution and refer to it as the reversed generalized logistic distribution. We study some moment properties, and derive exact and explicit formulas for the mean, median, mode, variance, coefficients of skewness and kurtosis, and percentage points of this distribution. In addition, we study its limiting distributions as the shape parameter tends to zero or infinity. We also discuss some possible applications in bioassays through logistic regression approach.     

Dependent Right Censorship in the MOMW Distribution

In this paper, we consider paired survival data, in which pair members are subject to the same right censoring time, but they are dependent on each other. Assuming the Marshall–Olkin Multivariate Weibull distribution for the joint distribution of the lifetimes (X₁, X₂) and the censoring time X₃, we derive the joint density of the actual observed data and obtain maximum likelihood estimators, Bayes estimators and posterior regret Gamma minimax estimators of the unknown parameters under squared error loss and weighted squared error loss functions. We compare the performances of the maximum likelihood estimators and Bayes estimators numerically in terms of biases and estimated Mean Squared Error Loss.     

Statistical inference for discrete middle-censored data

In this paper we consider the discrete middle censoring where lifetime, lower bound and length of censoring interval are variables with geometric distribution. We obtain the likelihood function of observed data and derive the MLE of the unknown parameter using EM algorithm. Also we obtain the Bayes estimator of the unknown parameter under squared error loss (SEL) function and credible interval of unknown parameter using Monte Carlo methods.     

论国家权力与少数民族的自我发展

当现代社会把"平等"作为自己的目标追求及其存在的合法性基础时,就应看到"平等应当不仅是表面的,不仅在国家的领域中实行,它还应当是实际的,还应当在社会的、经济的领域中实行"[1]。这充分展示了实现各民族政治、经济和文化的平等发展权力在国家目标设置中的重要地位。忽视这一问题,不仅会导致国家经济发展目标设置的失误,而且会导致对国家权力的合法性基础的质疑。特别是社会转型期,这一问题已经成为少数民族和民族地区普遍关注的热点问题。     

The impact of education and occupation on domestic violence in Saudi Arabia

This study examined the role of education and occupation in connection with domestic violence in Saudi Arabia based on a survey administered to 917 women who had varying years of education and various types of occupations. Results show that education and occupation play a positive role in the life of Saudi women by reducing the level of domestic violence to which they are exposed. Education was found to lower the rate of domestic violence by around 7%. A significant difference in the level of domestic violence was found as well between employed and unemployed women. In Saudi Arabia, having an education and/or earning an income seems to give women more power and higher social status, which in turn appears to lower the level of domestic violence they experience compared with women who do not work, have few years of education or are not currently enrolled in education.     

Education for Coexistence and Arab-Jewish Encounters in Israel: Potential and Challenges

The killing of thirteen Arabs by Israeli police forces in October 2000 points to the mounting tension and hostility between Arabs and Jews in Israel. Encounter and coexistence programs constitute one of the few channels for the development of communication, trust, and genuine understanding of the complex Arab-Jewish reality in Israel. Thus, it is essential that these encounters be examined and professionally developed to respond to the needs of the two communities. This article examines certain shortcomings of these encounter programs and provides suggestions to improve their efficacy. The conclusions are based on an earlier empirical study conducted between 1992 and 1998, which investigated six encounter programs, and on a series of interviews with Arab-Jewish facilitators conducted in 2001.