Bayesian Analysis of a Generalized Poisson Distribution

A generalized form of the Poisson Distribution with two parameters will be estimated by the Bayesian technique. When one of the parameters is known, several important parametric functions will be estimated and a numerical comparison with estimates obtained by the methods of maximum likelihood and unbiased minimum variance will be drawn. The simplicity of the posterior distribution of the unknown parameter enables us to construct exact probability intervals, and to devise a statistic to test the homogeneity of several populations. When the two parameters are unknown, dependent priors are being considered. Although the posterior distributions are sensitive to the choice of the prior, the posterior estimates are very stable and we use the Pearson system of curves to construct approximate posterior confidence limits for the parameters.     

A Single Form for t-Distributions and Symmetric Beta Distributions

A single parametric form is given for the symmetric distributions in the Pearson system with finite variance. In effect, these are Student's t-distributions with ν > 2 and all centered symmetric beta distributions. A different parametrization allows the inclusion of the t-distributions with ν ≤2 at the expense of symmetric beta distributions with a low shape parameter.     

Nonparametric Predictive Multiple Comparisons of Lifetime Data

We consider lifetime experiments to compare units from different groups, where the units’ lifetimes may be right censored. Nonparametric predictive inference for comparison of multiple groups is presented, in particular lower and upper probabilities for the event that a specific group will provide the largest next lifetime. We include the practically relevant consideration that the overall lifetime experiment may be terminated at an early stage, leading to simultaneous right-censoring of all units still in the experiment.     

Approximations to the distribution of weighted combination of independent probabilities

Two simple approximations are proposed for the distribution of the weighted combina-tion of n independent probabilities. The approximations are compared with other avail-able approximations. It is shown that one of the proposed approximations is better than the other approximations.     

Sensitivity to imputation models and assumptions in receiver operating characteristic analysis with incomplete data

Modern statistical methods using incomplete data have been increasingly applied in a wide variety of substantive problems. Similarly, receiver operating characteristic (ROC) analysis, a method used in evaluating diagnostic tests or biomarkers in medical research, has also been increasingly popular problem in both its development and application. While missing-data methods have been applied in ROC analysis, the impact of model mis-specification and/or assumptions (e.g. missing at random) underlying the missing data has not been thoroughly studied. In this work, we study the performance of multiple imputation (MI) inference in ROC analysis. Particularly, we investigate parametric and non-parametric techniques for MI inference under common missingness mechanisms. Depending on the coherency of the imputation model with the underlying data generation mechanism, our results show that MI generally leads to well-calibrated inferences under ignorable missingness mechanisms.     

Improving an estimator of Hsieh and Turnbull for the binormal ROC curve

The estimator of Hsieh and Turnbull (1996) for the binormal receiver operating characteristic (ROC) curve is extended from grouped to ungrouped data. The new estimator is shown to be consistent and asymptotically normally distributed, and simulation results show that it outperforms Hsieh and Turnbull's original estimator.     

Trajectory of quality of mother-child interactions: Prospective links with child socioemotional functioning

Research shows that the quality of mother-child interactions is a robust antecedent of child socioemotional functioning. Yet, relatively little is known about the evolution of this relational quality over time, and even less about how changes in relational quality may bear on child adjustment. This study aimed to describe the trajectory of quality of mother-child interactions between ages 2 and 7 and to investigate associations between individual differences in this trajectory and child socioemotional functioning at age 8. In a sample of 233 mother-child dyads primarily comprised of White French-Canadian mothers, the quality of interactions was assessed during 10-min play sequences when children were aged 2, 4, and 7 years. Child internalizing, externalizing, and prosocial behaviors were reported by a subsample of 171 teachers at age 8. The results showed that on average, quality of mother-child interactions decreased over time. In terms of individual differences, children who experienced a slower decrease in the quality of interactions with their mother from 2 to 7 years showed less internalizing behavior at age 8, over and above initial quality at 2 years. Children involved in higher quality interactions with their mother at 2 years showed more prosocial and less externalizing behavior at age 8, independent of the subsequent decrease in the quality of those interactions. The findings suggest that initial levels and subsequent changes in the quality of mother-child interactions are two distinct indicators of their relationship with potentially different implications for child adjustment.     

民国初年关于行政诉讼体制的争论

民国初年,围绕正在构建的行政诉讼体制应采取何种模式,一批学者、政客曾展开激烈争论。争论主要涉及三个层面内容,即法理上行政审判权的性质与归属、体制上行政审判机关与行政机关之间是“一元制”还是“二元制”、传统都察院的去留。争论不但影响了民国初年的行政立法,还使当时行政体制的构建与完善过程进一步复杂化。究其原因,争论既是学理争论和辩异的结果,又是各种政治势力角逐的必然。