Arthur P. Dempster

Upper and Lower Probabilities Induced by a Multivalued Mapping

A multivalued mapping from a space X to a space S carries a probability measure defined over subsets of X into a system of upper and lower probabilities over subsets of S. Some basic properties of such systems are explored in Sects. 1 and 2. Other approaches to upper and lower probabilities are possible and some of these are related to the present approach in Sect. 3. A distinctive feature of the present approach is a rule for conditioning, or more generally, a rule for combining sources of information, as discussed in Sects. 4 and 5. Finally, the context in statistical inference from which the present theory arose is sketched briefly in Sect. 6.

A Generalization of Bayesian Inference

Procedures of statistical inference are described which generalize Bayesian inference in specific ways. Probability is used in such a way that in general only bounds may be placed on the probabilities of given events, and probability systems of this kind are suggested both for sample information and for prior information. These systems are then combined using a specified rule. Illustrations are given for inferences about trinomial probabilities, and for inferences about a monotone sequence of binomial pi. Finally, some comments are made on the general class of models which produce upper and lower probabilities, and on the specific models which underlie the suggested inference procedures.

Estimation in Covariance Components Models

Abstract Estimation techniques for linear covariance components models are developed and illustrated with special emphasis on explaining computational processes. The estimation of fixed and random effects when the variances and covariances are known is presented in Bayesian terms, Point estimates of the unknown variances and covariances are computed using the EM algorithm for maximum likelihood estimation from incomplete data. The techniques are illustrated with data on law schools, field mice, and professional football teams.

A Simulation Study of Alternatives to Ordinary Least Squares

Abstract Estimated regression coefficients and errors in these estimates are computed for 160 artificial data sets drawn from 160 normal linear models structured according to factorial designs. Ordinary multiple regression (OREG) is compared with 56 alternatives which pull some or all estimated regression coefficients some or all the way to zero. Substantial improvements over OREG are exhibited when collinearity effects are present, noncentrality in the original model is small, and selected true regression coefficients are small. Ridge regression emerges as an important tool, while a Bayesian extension of variable selection proves valuable when the true regression coefficients vary widely in importance.

The direct use of likelihood for significance testing

An approach to significance testing by the direct interpretation of likelihood is defined, developed and distinguished from the traditional forms of tail-area testing and Bayesian testing. The emphasis is on conceptual issues. Some theoretical aspects of the new approach are sketched in the two cases of simple vs. simple hypotheses and simple vs. composite hypotheses.

New Methods for Reasoning Towards Posterior Distributions Based on Sample Data

This paper redefines the concept of sampling from a population with a given parametric form, and thus leads up to some proposed alternatives to the existing Bayesian and fiducial arguments for deriving posterior distributions. Section 2 spells out the basic assumptions of the suggested class of sampling models, and Sect. 3 suggests a mode of inference appropriate to the sampling models adopted. A novel property of these inferences is that they generally assign upper and lower probabilities to events concerning unknowns rather than precise probabilities as given by Bayesian or fiducial arguments. Sections 4 and 5 present details of the new arguments for binomial sampling with a continuous parameter p and for general multinomial sampling with a finite number of contemplated hypotheses. Among the concluding remarks, it is pointed out that the methods of Sect. 5 include as limiting cases situations with discrete or continuous observables and continuously ranging parameters.

Combining Historical and Randomized Controls for Assessing Trends in Proportions

Abstract A statistical method for incorporating historical control data in the analysis of proportions is proposed and illustrated. The method has as its extremes logistic regressions completely pooling and completely ignoring historical controls. The degree of pooling used is determined by the variability from experiment to experiment in the control incidences. The fit of historical control groups to an assumed normal logistic model is assessed using probability plotting techniques. Monte Carlo studies evaluate the adequacy of the asymptotic approximation used. Sensitivity analyses show that results are insensitive to alternative priors. The method is applied to several sets of tumor data from animal experiments.

A Bayesian approach to the multiplicity problem for significance testing with binomial data.

Statistical analyses of simple tumor rates from an animal experiment with one control and one treated group typically consist of hypothesis testing of many 2 X 2 tables, one for each tumor type or site. The multiplicity of significance tests may cause excessive overall false-positive rates. This paper presents a Bayesian approach to the problem of multiple significance testing. We develop a normal logistic model that accommodates the incidences of all tumor types or sites observed in the current experiment simultaneously as well as their historical control incidences. Exchangeable normal priors are assumed for certain linear terms in the model. Posterior means, standard deviations, and Bayesian P-values are computed for an average treatment effect as well as for the effects on individual tumor types or sites. Model assumptions are checked using probability plots and the sensitivity of the parameter estimates to alternative priors is studied. The method is illustrated using tumor data from a chronic animal experiment.

An overview of multivariate data analysis

A cross section of basic yet rapidly developing topics in multivariate data analysis is surveyed, emphasizing concepts required in facing problems of practical data analysis while de-emphasizing technical and mathematical detail. Aspects of data structure, logical structure, epistemic structure, and hypothesis structure are examined. Exponential families as models, problems of interpretation, parameters, causality, computation, and data cleaning and missing values are discussed.

Sensitivity Analysis of Seasonal Adjustments: Empirical Case Studies

Abstract Three detailed case studies illustrating the seasonal analysis of economic time series are presented using component models for seasonal and nonseasonal behavior. Analyses are performed within a semi-Bayesian framework where inferences for target quantities of interest, such as seasonally adjusted values, are obtained as posterior distributions conditional on observed data and fitted parameter values. Such an approach is similar to previous model-based methods of seasonal analysis, but new models and algorithms are used and, more important, a sensitivity analysis is performed to determine the extent to which conclusions vary across a range of plausible fitted models. It is found that sensitivity to variation across plausible models is not unusual in practice. The logical conclusion of the investigation is that a fully Bayesian analysis is required that averages conditional posteriors over a posterior distribution for the model parameters. Such an analysis is necessarily sensitive to the choice of...