Bayesian analysis of elapsed times in continuous‐time Markov chains

The authors consider Bayesian analysis for continuous‐time Markov chain models based on a conditional reference prior. For such models, inference of the elapsed time between chain observations depends heavily on the rate of decay of the prior as the elapsed time increases. Moreover, improper priors on the elapsed time may lead to improper posterior distributions. In addition, an infinitesimal rate matrix also characterizes this class of models. Experts often have good prior knowledge about the parameters of this matrix. The authors show that the use of a proper prior for the rate matrix parameters together with the conditional reference prior for the elapsed time yields a proper posterior distribution. The authors also demonstrate that, when compared to analyses based on priors previously proposed in the literature, a Bayesian analysis on the elapsed time based on the conditional reference prior possesses better frequentist properties. The type of prior thus represents a better default prior choice for estimation software.     

The evaluation of DNA evidence in pedigrees requiring population inference

Summary. The evaluation of nuclear DNA evidence for identification purposes is performed here taking account of the uncertainty about population parameters. Graphical models are used to detail the hypotheses being debated in a trial with the aim of obtaining a directed acyclic graph. Graphs also clarify the set of evidence that contributes to population inferences and they also describe the conditional independence structure of DNA evidence. Numerical illustrations are provided by re-examining three case-studies taken from the literature. Our calculations of the weight of evidence differ from those given by the authors of case-studies in that they reveal more conservative values.     

康德先验逻辑的基本问题

康德的先验逻辑对传统哲学特别是形而上学所运用的范畴在分类的基础上作了新的理解,指出了范畴作为思维的逻辑功能,是对感性直观的固有关系。这就决定了先验逻辑的基本问题是范畴与直观的固有关系问题。它构成先验逻辑不同于形式逻辑和思辨逻辑的根本点。     

Causal Reasoning from Longitudinal Data*

Abstract. This paper reviews some of the key statistical ideas that are encountered when trying to find empirical support to causal interpretations and conclusions, by applying statistical methods on experimental or observational longitudinal data. In such data, typically a collection of individuals are followed over time, then each one has registered a sequence of covariate measurements along with values of control variables that in the analysis are to be interpreted as causes, and finally the individual outcomes or responses are reported. Particular attention is given to the potentially important problem of confounding. We provide conditions under which, at least in principle, unconfounded estimation of the causal effects can be accomplished. Our approach for dealing with causal problems is entirely probabilistic, and we apply Bayesian ideas and techniques to deal with the corresponding statistical inference. In particular, we use the general framework of marked point processes for setting up the probability models, and consider posterior predictive distributions as providing the natural summary measures for assessing the causal effects. We also draw connections to relevant recent work in this area, notably to Judea Pearl's formulations based on graphical models and his calculus of so‐called do‐probabilities. Two examples illustrating different aspects of causal reasoning are discussed in detail.     

Conditional Likelihood Estimators for Hidden Markov Models and Stochastic Volatility Models

ABSTRACT.  This paper develops a new contrast process for parametric inference of general hidden Markov models, when the hidden chain has a non-compact state space. This contrast is based on the conditional likelihood approach, often used for ARCH-type models. We prove the strong consistency of the conditional likelihood estimators under appropriate conditions. The method is applied to the Kalman filter (for which this contrast and the exact likelihood lead to asymptotically equivalent estimators) and to the discretely observed stochastic volatility models.     

中国人口性别结构的区域差异及演变动态分析

人口性别构成是影响人类婚姻、人口再生产的基本因素，也影响国家经济、政治、文化、教育等方面的发展，也是编制经济、文化、教育、科技、卫生、人民生活、劳动、城乡建设等发展规划的重要依据。同时对于中国当前正在进行的和谐社会建设也具有重要意义。利用中国五次人口普查资料及2005年1％人口抽样资料分析了中国总人口性别比演变动态及地理分布特征。表明：（1）中国在历史上是一个性别比偏高的国家，新中国总人口性别比呈下降趋势；（2）1953到2005年，年龄性别比曲线越来越平稳，性别比最高峰值呈现有低龄组向中龄组及高龄组转移的趋势；（3）各省区之间及城乡之间的性别结构差异由大变小；（4）山区性别比高于平原。重工业城市高于其他城市。大城市高于小城市。     

A modified false discovery rate multiple-comparisons procedure for discrete data, applied to human immunodeficiency virus genetics

Summary.  To help to design vaccines for acquired immune deficiency syndrome that protect broadly against many genetic variants of the human immunodeficiency virus, the mutation rates at 118 positions in HIV amino-acid sequences of subtype C versus those of subtype B were compared. The false discovery rate (FDR) multiple-comparisons procedure can be used to determine statistical significance. When the test statistics have discrete distributions, the FDR procedure can be made more powerful by a simple modification. The paper develops a modified FDR procedure for discrete data and applies it to the human immunodeficiency virus data. The new procedure detects 15 positions with significantly different mutation rates compared with 11 that are detected by the original FDR method. Simulations delineate conditions under which the modified FDR procedure confers large gains in power over the original technique. In general FDR adjustment methods can be improved for discrete data by incorporating the modification proposed.     

A circular-cone test for testing homogeneity against a simple tree order

Several methods exist for the problem of testing the equality of several treatments against the one-sided alternative that the treatments are better than the control. These methods include Dunnett's test, Bartholomew's likelihood-ratio test, the Abelson-Tukey-Schaafsma-Smid optimal-contrast test, and the multiple-contrast test of Mukerjee, Robertson, and Wright. A new test is proposed based on an approximation of the likelihood-ratio test of Bartholomew. This test involves using a circular cone in place of the alternative-hypothesis cone. The circular-cone test has excellent power characteristics similar to those of Bartholomew's test. Moreover, it has the advantages of being simpler to compute and may be used with unequal sample sizes.     

Bayesian analysis of outlier problems using divergence measures

A Bayesian approach is presented for detecting influential observations using general divergence measures on the posterior distributions. A sampling-based approach using a Gibbs or Metropolis-within-Gibbs method is used to compute the posterior divergence measures. Four specific measures are proposed, which convey the effects of a single observation or covariate on the posterior. The technique is applied to a generalized linear model with binary response data, an overdispersed model and a nonlinear model. An asymptotic approximation using Laplace method to obtain the posterior divergence is also briefly discussed.     

关于R—积分的区问可列可加性

本文将数学分析中R—积分(即黎曼积分)的区间可加性加以推广,给出了R—积分区间可列可加性.