S. James Press

Choosing between Logistic Regression and Discriminant Analysis

Abstract Classifying an observation into one of several populations is discriminant analysis, or classification. Relating qualitative variables to other variables through a logistic cdf functional form is logistic regression. Estimators generated for one of these problems are often used in the other. If the populations are normal with identical covariance matrices, discriminant analysis estimators are preferred to logistic regression estimators for the discriminant analysis problem. In most discriminant analysis applications, however, at least one variable is qualitative (ruling out multivariate normality). Under nonnormality, we prefer the logistic regression model with maximum likelihood estimators for solving both problems. In this article we summarize the related arguments, and report on our own supportive empirical studies.

Bayesian inference for pareto populations

Abstract Bayesian techniques for samples from classical, generalized and multivariate Pareto distributions are described. We place emphasis on choosing proper prior distributions that do not lead to anomalous posterior densities.

Compatible Conditional Distributions

Abstract Consider two families of candidate conditional densities (or probability mass functions), {f(x | y);y ∈ S y} and {f(y | x): x ∈ S x}. This article investigates necessary and sufficient conditions for the existence of a joint density (or joint probability mass function) f(x, y) with the given families as its associated conditional densities. This supplements previous work that has addressed the question of uniqueness of f(x, y) assuming its existence.

Bayesian Inference in Factor Analysis

We propose a new method for analyzing factor analysis models using a Bayesian approach. Normal theory is used for the sampling distribution, and we adopt a model with a full disturbance covariance matrix. Using vague and natural conjugate priors for the parameters, we find that the marginal posterior distribution of the factor scores is approximately a matrix T-distribution, in large samples. This explicit result permits simple interval estimation and hypothesis testing of the factor scores. Explicit point estimators of the factor score elements, in large samples, are obtained as means of the respective marginal posterior distributions. Factor loadings are estimated as joint modes (with the factor scores), or alternatively as means or modes of the distribution of the factor loadings conditional upon the estimated factor scores. Disturbance variances and covariances are estimated conditional upon the estimated factor scores and factor loadings.

The Subjectivity of Scientists and the Bayesian Approach: Press/The Subjectivity

Preface. Introduction. Selecting the Scientists. Some Well-Known Stories of Extreme Subjectivity. Stories of Famous Scientists. Subjectivity in Science in Modern Times: The Bayesian Approach. Appendix: References by Field of Application for Bayesian Statistical Science. Bibliography. Subject Index. Name Index.

Robustness of bayesian factor analysis estimates

This paper presents the result of a study of the robustness of posterior estimators of the factor loading matrix, the factor scores, and the disturbance covariance matrix (the main model parameters) in a Bayesian factor analysis with respect to variations in the values of the parameters of their prior distributions (the hyperparameter). We adopt the e - contamination model of Berger and Berliner(1986) to generate prior distributions whose hyper-paramters reflects small variations in the elements of the uncontaminated hyperparameters, and we use directional derivatives to examine the variation of the uncontaminated estimators with respect to changes in the values of the hyperparameters, in the directions of the main model parameters. Several matrix norms are used to measure the closeness of the resulting values. We illustrate the results with a numerical example.

Qualitative Controlled Feedback for Forming Group Judgments and Making Decisions

Abstract We present a new methodology for helping members of a group arrive at carefully reasoned value judgments or decisions. The new procedure, called qualitative controlled feedback, presents each group member with a common question; each member is asked independently for both an answer to the question and for reasons which he feels justify his answer. An intermediary collects all stated reasons and informs all group members of the composite of reasons (but not of the answers). The question is presented to the group members independently again, and the process is repeated until the individual judgments stabilize.

Bayesian and likelihood methods in statistics and econometrics : essays in honor of George A. Barnard

Introduction. A Survey of George Barnards Statistical Work. (D.V. Lindley). Foundations (Contributors: A.P. Dempster B.M. Hill J.S. Hodges D.A. Lane). Selected Applications (Contributors: S. Chib, S.R. Jammalamadaka, R.C. Tiwari L. Denby, R. Gnanadesikan, J.R. Kettenring, J.W. Suzansky S.E. Fienberg Y. Hiatovsky H. Tsurumi). Selected Inference Problems (Contributors: M.J. Bayarri, M.H. DeGroot L.D. Broemeling, M.S. Son, H.I. Hamdy C.-H. Chen, J.M. Dickey G.T. Duncan M. Ghosh, L.Y. Low, G. Meeden R.L. Winkler, A. Gaba). Predictive Methods and Applications (Contributors: S. Geisser R. Klein, S.J. Press P.J. Lenk A. Zellner, C. Hong, G.M. Gulati). Incompletely Specified Prior Distributions (Contributors: L.M. Berliner, P.K. Goel W. Bijak A. Madansky). Approximations and Computational Methods (Contributors: J.A. Achcar, A.F.M. Smith J.H. Larkin, J.B. Kadane R.E. Kass, L. Tierney, J.B. Kadane). Indexes.

Classification of oligonucleotide fingerprints: application for microbial community and gene expression analyses

MOTIVATIONnOligonucleotide fingerprinting of ribosomal RNA genes (OFRG) is a procedure that sorts rRNA gene (rDNA) clones into taxonomic groups through a series of hybridization experiments. The hybridization signals are classified into three discrete values 0, 1 and N, where 0 and 1, respectively, specify negative and positive hybridization events and N designates an uncertain assignment. This study examined various approaches for classifying the values including Bayesian classification with normally distributed signal data, Bayesian classification with the exponentially distributed data, and with gamma distributed data, along with tree-based classification. All classification data were clustered using the unweighted pair group method with arithmetic mean.nnnRESULTSnThe performance of each classification/clustering procedure was compared with results from known reference data. Comparisons indicated that the approach using the Bayesian classification with normal densities followed by tree clustering out-performed all others. The paper includes a discussion of how this Bayesian approach may be useful for the analysis of gene expression data.

A Modified Compound Poisson Process with Normal Compounding

The compound Poisson process in which the compounding variables are normally distributed is considered as a special case of a slightly more general process. The model is suggested for studying the behavior of security prices in the stock market. Distributional properties of the process are developed and it is shown that the distribution of the increments is skew-symmetric, peaked, “fat tailed,” and, generally, multimodal. A moment matching method based upon cumulants is suggested for estimating the parameters.