Identification of the variance components in the general two-variance linear model

Bayesian analyses frequently employ two-stage hierarchical models involving two-variance parameters: one controlling measurement error and the other controlling the degree of smoothing implied by the model's higher level. These analyses can be hampered by poorly identified variances which may lead to difficulty in computing and in choosing reference priors for these parameters. In this paper, we introduce the class of two-variance hierarchical linear models and characterize the aspects of these models that lead to well-identified or poorly identified variances. These ideas are illustrated with a spatial analysis of a periodontal data set and examined in some generality for specific two-variance models including the conditionally autoregressive (CAR) and one-way random effect models. We also connect this theory with other constrained regression methods and suggest a diagnostic that can be used to search for missing spatially varying fixed effects in the CAR model.     

多层砖混房屋抗震设防问题探讨

随着我国住宅建设的飞速发展,造型各异的砖混房屋建筑应运而生,其抗震性能越来越受到人们的重视。本文从震害的主要图素入手,探讨抗震设防的措施。     

Block designs for random treatment effects

A Bayesian design criterion for selection experiments in plant breeding is derived using a utility function that minimizes the risk of an incorrect selection. A prior distribution on the heritability parameter is used to complete the definition of the design optimality criterion. An example is given with evaluations of the criterion for different prior distributions on the heritability. Though coming from a genetic motivation this criterion should prove useful for any other types of experiments with random treatment effects.     

Linear latent structure analysis: Mixture distribution models with linear constraints

A new method for analyzing high-dimensional categorical data, Linear Latent Structure (LLS) analysis, is presented. LLS models belong to the family of latent structure models, which are mixture distribution models constrained to satisfy the local independence assumption. LLS analysis explicitly considers a family of mixed distributions as a linear space, and LLS models are obtained by imposing linear constraints on the mixing distribution.LLS models are identifiable under modest conditions and are consistently estimable. A remarkable feature of LLS analysis is the existence of a high-performance numerical algorithm, which reduces parameter estimation to a sequence of linear algebra problems. Simulation experiments with a prototype of the algorithm demonstrated a good quality of restoration of model parameters.     

Bayesian classification of Neolithic tools

The classification of Neolithic tools by using cluster analysis enables archaeologists to understand the function of the tools and the technological and cultural conditions of the societies that made them. In this paper, Bayesian classification is adopted to analyse data which raise the question whether the observed variability, e.g. the shape and dimensions of the tools, is related to their use. The data present technical difficulties for the practitioner, such as the presence of mixed mode data, missing data and errors in variables. These complications are overcome by employing a finite mixture model and Markov chain Monte Carlo methods. The analysis uses prior information which expresses the archaeologist's belief that there are two tool groups that are similar to contemporary adzes and axes. The resulting mixing densities provide evidence that the morphological dimensional variability among tools is related to the existence of these two tool groups.     

Interpreting forensic DNA mixtures: allowing for uncertainty in population substructure and dependence

We consider the assessment of deoxyribonucleic acid (DNA) profiles from biological samples containing a mixture of DNA from more than one person. The problem has been investigated in the context of likelihood ratios by Weir and co-workers under the assumption of independent alleles in DNA profiles. However, uncertainty about independence may arise from various factors such as population substructure and relatedness. This issue has received considerable attention in recent years. Ignoring this uncertainty may seriously overstate the strength of the evidence and therefore disadvantage innocent suspects. Taking this uncertainty into account, we develop a general formula for calculating the match probabilities of DNA profiles. Thus, we extend the result derived by Weir and co-workers to the dependence situation, which is often more to the benefit of the defendant in comparison with the simple product rule result based on an independence assumption. The effect of dependence of alleles on likelihood ratio estimates can be seen in the analysis of two real data sets.     

Applying discrete choice models to predict Academy Award winners

Summary.  Every year since 1928, the Academy of Motion Picture Arts and Sciences has recognized outstanding achievement in film with their prestigious Academy Award, or Oscar. Before the winners in various categories are announced, there is intense media and public interest in predicting who will come away from the awards ceremony with an Oscar statuette. There are no end of theories about which nominees are most likely to win, yet despite this there continue to be major surprises when the winners are announced. The paper frames the question of predicting the four major awards—picture, director, actor in a leading role and actress in a leading role—as a discrete choice problem. It is then possible to predict the winners in these four categories with a reasonable degree of success. The analysis also reveals which past results might be considered truly surprising—nominees with low estimated probability of winning who have overcome nominees who were strongly favoured to win.     

逻辑函数结构及组合险象

本文使用混合逻辑代数这个新理论和新方法,定义了逻辑函数的结构,导出了基本逻辑函数,复合逻辑函数及一般逻辑函数的结构表达式,得到了逻辑函数必须遵从的一些特别重要的结构结论。并设计出了无逻辑冒险,无功能冒险的无险象组合电路,布尔逻辑函数理论分析及实验结果与新理论符合得特别好。无疑这种新理论和新方法使计算机电路及离散系统设计增加了新手段。     

On singular elliptical models

The probability density function (pdf) ofsingular elliptical distributions is represented as an integralseries of singular normal distributions. Explicit formulas for the pdf and the cdf of the generalized Chi-square distribution are derived under singular elliptical assumptions extending the result of Díaz-García [(2002). Singular elliptical distribution: density and applications. Commun. Stat.—Theory Methods 31:665–681]. Applications are given of the proposed result for singular mixedmodels.