摘要:

One method for evaluating the sensitivity of a Bayesian analysis is to embed the prior into a class of priors. Then bounds on prior and posterior quantities of interest must be computed. This approach to inference, often called robust Bayesian inference, has received much attention lately. Implementing robust Bayesian methods entails difficult computations, especially if the parameter space is high dimensional. In this article we develop a Monte Carlo approach to computing these bounds and also explore some interesting theoretical properties of certain classes of priors. The methods can be useful in other situations in which bounds on expectations are required.

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10475234

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

Constrained parameter problems arise in a wide variety of applications, including bioassay, actuarial graduation, ordinal categorical data, response surfaces, reliability development testing, and variance component models. Truncated data problems arise naturally in survival and failure time studies, ordinal data models, and categorical data studies aimed at uncovering underlying continuous distributions. In many applications both parameter constraints and data truncation are present. The statistical literature on such problems is very extensive, reflecting both the problems’ widespread occurrence in applications and the methodological challenges that they pose. However, it is striking that so little of this applied and theoretical literature involves a parametric Bayesian perspective. From a technical viewpoint, this perhaps is not difficult to understand. The fundamental tool for Bayesian calculations in typical realistic models is (multidimensional) numerical integration, which often is problematic in unconstrained contexts and can be well-nigh impossible for the kinds of constrained problems we consider. In this article we show that Bayesian calculationscanbe implemented routinely for constrained parameter and truncated data problems by means of the Gibbs sampler. Specific models discussed include constrained multinormal parameters, constrained linear model parameters, ordered parameters in experimental family models, data and order restricted parameters from exponential distributions, straight line regression with censoring and bivariate grouped data models. Analysis of data sets illustrating the first two of these settings is provided.

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10475235

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

Bayesian techniques are widely used in these days for simultaneous estimation of several parameters in compound decision problems. Often, however, the main objective is to produce an ensemble of parameter estimates whose histogram is in some sense close to the histogram of population parameters. This is for example the situation in subgroup analysis, where the problem is not only to estimate the different components of a parameter vector, but also to identify the parameters that are above, and the others that are below a certain specified cutoff point. We have proposed in this paper Bayes estimates in a very general context that meet this need. These estimates are obtained by matching the first two moments of the histogram of the estimates, and the posterior expectations of the first two moments of the histogram of the parameters, and minimizing, subject to these conditions, the posterior expectation of the Euclidean distance between the estimates and the parameters. Several applications of the main result are provided in the normal and other models. Also, the results are applied to an actual data set.

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10475236

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

Suppose we think that most observations in a sample have been generated from a distribution with densityf(x) but we fear that a few outliers from a distribution with densityg(x) may have contaminated our sample. In many situations, we might assume thatf(x) is a density depending on a parameter θ and thatg(x) is of the same form asfbut with parameterθ + δorθδ. A number of Bayesian models for this problem whenfis normal have been discussed by Freeman. He points out that with a vague improper prior for contaminating parameters, most posterior weight is put on the model allowing for the largest number of outliers. He therefore confines attention to proper priors when trying to answer the question of “how many outliers?” However, in many situations we do not have very certain information on the contaminating parameters and would like to make inferences about outliers when using improper priors for the parameters of the model. In this article, we apply the ideas of Spiegelhalter and Smith to this problem. In particular, we use their idea of assigning the value of the constant in the improper prior for the parameter of the contaminating distribution by the device of an imaginary training sample. This enables us to calculate the Bayes factor comparing a model with no outliers to a model with one outlier. We also can extend the ideas to more than one outlier. We illustrate the method in the case of univariate normal distributions, simple linear regression, and exponential samples.

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10475237

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

A partial rank correlation coefficientT(n)XY|Z, based on comparing pairs for which the values of the conditioning variable follow each other in a numerical ordering, is studied. Simulation results show that it is possible to obtain reasonably good confidence intervals by estimatingσ2/(1 −τ2XY|Z). The advantage of using the coefficientT(n)XY|Zis that it is always clear what this coefficient measures, in contrast to, for example, Pearson's, Spearman's, or Kendall's partial correlation coefficients, which can give values far from 0 even in cases of conditional independence. The main disadvantage is that the asymptotic efficiency relative to the sample partial correlation coefficient (in the case of trivariate normal variables) is never higher than .33. Coefficients likeT(n)XY|Zhave been studied by Goodman and by Quade.

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10475238

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

Ranked-set samples have been shown to lead to improved methods of estimation in parametric settings under specific distributional forms when actual measurement of the sample observations is difficult but ranking them is relatively easy. The earliest work with ranked-set data concentrated on estimating a population mean or variance. More recently, a ranked-set sample estimator of a cumulative distribution function was developed and used to obtain a simultaneous confidence interval for the function. In this article, we take the next logical step and use this ranked-set empirical distribution function to construct distribution-free competitors to the standard Mann–Whitney–Wilcoxon estimation and testing procedures. The appropriate null distribution tables for the associated test are presented for the case of perfect ranking. Asymptotic relative efficiency comparisons between the simple random sample Mann–Whitney–Wilcoxon procedures and their ranked-set analogues are discussed, and the results of a small-sample Monte Carlo simulation study of the same are presented.

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10475239

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

In the 11 years since AIDS became a defined disease, programs for the development and evaluation of new drugs for this disease have grown rapidly. Although the fundamental principles that drive the design, conduct, and analysis of clinical trials are as applicable to AIDS as to other diseases, there is no question that we have been confronted with unusually difficult challenges in studying therapeutic approaches for this disease. These include the multiple treatment needs of individual patients, identification of appropriate endpoints, rapidly changing “natural history,” and the need for interaction with an informed and vocal patient community that continues to express dissatisfaction with the pace of research. In this context, statisticians have taken a leadership role in identifying and addressing important methodological issues in the evaluation of AIDS drugs.

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10475240

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10475241

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10475242

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1992.10475243

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor