Bayesian Estimation and Prediction for the Beta-Binomial Model

The beta-binomial distribution, which is generated by a simple mixture model, has been widely applied in the social, physical, and health sciences. Problems of estimation, inference, and prediction have been addressed in the past, but not in a Bayesian framework. This article develops Bayesian procedures for the beta-binomial model and, using a suitable reparameterization, establishes a conjugate-type property for a beta family of priors. The transformed parameters have interesting interpretations, especially in marketing applications, and are likely to be more stable. More specifically, one of these parameters is the market share and the other is a measure of the heterogeneity of the customer population. Analytical results are developed for the posterior and prediction quantities, although the numerical evaluation is not trivial. Since the posterior moments are more easily calculated, we also propose the use of posterior approximation using the Pearson system. A particular case (when there are two trials), which occurs in taste testing, brand choice, media exposure, and some epidemiological applications, is analyzed in detail. Simulated and real data are used to demonstrate the feasibility of the calculations. The simulation results effectively demonstrate the superiority of Bayesian estimators, particularly in small samples, even with uniform (“non-informed”) priors. Naturally, “informed” priors can give even better results. The real data on television viewing behavior are used to illustrate the prediction results. In our analysis, several problems with the maximum likelihood estimators are encountered. The superior properties and performance of the Bayesian estimators and the excellent approximation results are strong indications that our results will be potentially of high value in small sample applications of the beta-binomial and in cases in which significant prior information exists.     

Regression analysis of longitudinal data with outcome‐dependent sampling and informative censoring

We consider a regression analysis of longitudinal data in the presence of outcome‐dependent observation times and informative censoring. Existing approaches commonly require a correct specification of the joint distribution of longitudinal measurements, the observation time process, and informative censoring time under the joint modeling framework and can be computationally cumbersome due to the complex form of the likelihood function. In view of these issues, we propose a semiparametric joint regression model and construct a composite likelihood function based on a conditional order statistics argument. As a major feature of our proposed methods, the aforementioned joint distribution is not required to be specified, and the random effect in the proposed joint model is treated as a nuisance parameter. Consequently, the derived composite likelihood bypasses the need to integrate over the random effect and offers the advantage of easy computation. We show that the resulting estimators are consistent and asymptotically normal. We use simulation studies to evaluate the finite‐sample performance of the proposed method and apply it to a study of weight loss data that motivated our investigation.     

Joint analysis of longitudinal data and competing terminal events in the presence of dependent observation times with application to chronic kidney disease

In many prospective clinical and biomedical studies, longitudinal biomarkers are repeatedly measured as health indicators to evaluate disease progression when patients are followed up over a period of time. Patient visiting times can be referred to as informative observation times if they are assumed to carry information in addition to that of the longitudinal biomarker measures alone. Irregular visiting times may reflect compliance with physician instruction, disease progression and symptom severity. When the follow-up time may be stopped by competing terminal events, it is possible that patient observation times may correlate with the competing terminal events themselves, thus making the observation times difficult to assess. To explicitly account for the impact of competing terminal events and dependent observation times on the longitudinal data analysis in the context of such complex data, we propose a joint model using latent random effects to describe the association among them. A likelihood-based approach is derived for statistical inference. Extensive simulation studies reveal that the proposed approach performs well for practical situations, and an analysis of patients with chronic kidney disease in a cohort study is presented to illustrate the proposed method.     

Bayesian integrative analysis for multi-fidelity computer experiments

This paper proposes a Bayesian integrative analysis method for linking multi-fidelity computer experiments. Instead of assuming covariance structures of multivariate Gaussian process models, we handle the outputs from different levels of accuracy as independent processes and link them via a penalization method that controls the distance between their overall trends. Based on the priors induced by the penalty, we build Bayesian prediction models for the output at the highest accuracy. Simulated and real examples show that the proposed method is better than existing methods in terms of prediction accuracy for many cases.     

再论过去分词形容词的语用制约

制约是一种对语言使用产生某种限制或规约的语言运作机制。“语用制约”是指HN（名词中心词）与其前置修饰语之间在使用过程中形成的互动和限制。纵聚合语义信息制约要求APP（过去分词式形容词）必须能刻画出HN所指的超越典型的区分性特征和非常状态。最简结构制约要求APP＋HN实现语符数最小化，同时达到所承载的语义信息量最大化。从属性上看，纵聚合语义信息制约为语义性制约；而最简结构制约则为结构性制约。     

Reference priors for constrained rate models of count data

We derive reference priors for constrained rate models of count data using the sequential algorithm of Berger and Bernardo (1992b). The event counts for various groups of subjects are modeled as discrete random variables (Poisson, binomial, or negative binomial) with group specific rates. We consider situations in which the groups can be completely ordered according to one covariate. The priors enforce monotonicity (or monotonicity and convexity) of the rates with respect to the ordering. We use the priors to model a data set on mortality rates for men in different age groups assuming that the mortality rates increase with respect to age. We also consider the situation in which the parameter space is augmented to include rates corresponding to unobserved age groups, and the case of a random upper bound on the mortality rates. In addition, we provide an evaluation of the out-of-sample predictive performance of the proposed methods.     

Bayes estimation and prediction of the two-parameter gamma distribution

In this article, the Bayes estimates of two-parameter gamma distribution are considered. It is well known that the Bayes estimators of the two-parameter gamma distribution do not have compact form. In this paper, it is assumed that the scale parameter has a gamma prior and the shape parameter has any log-concave prior, and they are independently distributed. Under the above priors, we use Gibbs sampling technique to generate samples from the posterior density function. Based on the generated samples, we can compute the Bayes estimates of the unknown parameters and can also construct HPD credible intervals. We also compute the approximate Bayes estimates using Lindley's approximation under the assumption of gamma priors of the shape parameter. Monte Carlo simulations are performed to compare the performances of the Bayes estimators with the classical estimators. One data analysis is performed for illustrative purposes. We further discuss the Bayesian prediction of future observation based on the observed sample and it is seen that the Gibbs sampling technique can be used quite effectively for estimating the posterior predictive density and also for constructing predictive intervals of the order statistics from the future sample.     

Bayesian Estimators for Small Area Models when Auxiliary Information is Measured with Error

Small area estimators in linear models are typically expressed as a convex combination of direct estimators and synthetic estimators from a suitable model. When auxiliary information used in the model is measured with error, a new estimator, accounting for the measurement error in the covariates, has been proposed in the literature. Recently, for area‐level model, Ybarra & Lohr (Biometrika, 95, 2008, 919) suggested a suitable modification to the estimates of small area means based on Fay & Herriot (J. Am. Stat. Assoc., 74, 1979, 269) model where some of the covariates are measured with error. They used a frequentist approach based on the method of moments. Adopting a Bayesian approach, we propose to rewrite the measurement error model as a hierarchical model; we use improper non‐informative priors on the model parameters and show, under a mild condition, that the joint posterior distribution is proper and the marginal posterior distributions of the model parameters have finite variances. We conduct a simulation study exploring different scenarios. The Bayesian predictors we propose show smaller empirical mean squared errors than the frequentist predictors of Ybarra & Lohr (Biometrika, 95, 2008, 919), and they seem also to be more stable in terms of variability and bias. We apply the proposed methodology to two real examples.     

黑龙江省农村信息化发展情况研究

农村信息服务体系不健全,农民信息意识差,重平台建设轻服务内容成为当今农村信息化发展的主要制约因素。因此,要充分发挥政府的领导力,大力整合各种信息资源,完善农村信息服务体系,配合市场化运营模式,以实现农村信息化的持续健康发展。