An iterative Monte Carlo method for nonconjugate Bayesian analysis

The Gibbs sampler has been proposed as a general method for Bayesian calculation in Gelfand and Smith (1990). However, the predominance of experience to date resides in applications assuming conjugacy where implementation is reasonably straightforward. This paper describes a tailored approximate rejection method approach for implementation of the Gibbs sampler when nonconjugate structure is present. Several challenging applications are presented for illustration.     

Low-Income Children's Participation in a Public Health Insurance Program in Georgia

To expand health care coverage to uninsured, low-income children, the Congress created the State Children's Health Insurance Program (SCHIP) in 1997. Given ample evidence that state Medicaid programs have failed to enroll many eligible children, experts questioned whether SCHIP could successfully enroll low-income children. Using Georgia state SCHIP data, we analyzed enrollment patterns and identified factors contributing to program enrollment. This study found that the children's enrollment is explained by perceived costs and benefits of joining the program as well as the underlying family structure, demographic factors, and health status. We discuss implications of these findings on the participation of low-income families in public sector programs.     

Inference in model-based cluster analysis

A new approach to cluster analysis has been introduced based on parsimonious geometric modelling of the within-group covariance matrices in a mixture of multivariate normal distributions, using hierarchical agglomeration and iterative relocation. It works well and is widely used via the MCLUST software available in S-PLUS and StatLib. However, it has several limitations: there is no assessment of the uncertainty about the classification, the partition can be suboptimal, parameter estimates are biased, the shape matrix has to be specified by the user, prior group probabilities are assumed to be equal, the method for choosing the number of groups is based on a crude approximation, and no formal way of choosing between the various possible models is included. Here, we propose a new approach which overcomes all these difficulties. It consists of exact Bayesian inference via Gibbs sampling, and the calculation of Bayes factors (for choosing the model and the number of groups) from the output using the Laplace–Metropolis estimator. It works well in several real and simulated examples.     

Detecting active effects in unreplicated designs

Unreplicated factorial designs pose a difficult problem in analysis because there are no degrees of freedom left to estimate the error. Daniel [Technometrics 1 (1959), pp. 311-341] proposed an ingenious graphical method that does not require σ to be estimated. Here we try to put Daniel's method into a formal framework and lift the subjectiveness that carries. A simulation study has been conducted that shows that the proposed method behaves better than Lenth's [Technometrics 31 (1989), pp. 469-473] popular method.     

Kurtosis and spread

An increase in kurtosis is achieved through the location- and scale-free movement of probability mass from the “shoulders” of a distribution into its centre and tails. We introduce a coherent structure of ordering and measures, requiring no symmetry assumption, that represent different formalizations of this movement. For this purpose spread functions and spread-spread plots are defined. The orderings impose growth patterns on the spread-spread plot of the distributions involved, and the weakest involve both a specific scale-matching technique and placement of “shoulders”. The role of existing kurtosis orderings and measures in this general context is identified and examples discussed throughout.     

The Time Squeeze: Parental Statuses and Feelings About Time With Children

Policy makers, parents, and the public are concerned with perceived declines in parents’ time with children. Data from two national surveys (N = 1,159 and N = 821) used in this study show that nearly half of parents report feeling too little time with children. Work hours are strongly related to these feelings, even controlling for time spent with children, and explain why fathers more than mothers feel time strain. For fathers, those whose youngest child is an adolescent feel more strain than similarly situated mothers. Controlling for work hours, single parents are not more likely than married parents to feel that they spend insufficient time with children.     

Renyi's entropy for residual lifetime distribution

In the present paper, we introduce and study Renyi's information measure (entropy) for residual lifetime distributions. It is shown that the proposed measure uniquely determines the distribution. We present characterizations for some lifetime models. Further, we define two new classes of life distributions based on this measure. Various properties of these classes are also given.