Martin A. Tanner

The Calculation of Posterior Distributions by Data Augmentation

Abstract The idea of data augmentation arises naturally in missing value problems, as exemplified by the standard ways of filling in missing cells in balanced two-way tables. Thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze. This device is used to great advantage by the EM algorithm (Dempster, Laird, and Rubin 1977) in solving maximum likelihood problems. In situations when the likelihood cannot be approximated closely by the normal likelihood, maximum likelihood estimates and the associated standard errors cannot be relied upon to make valid inferential statements. From the Bayesian point of view, one must now calculate the posterior distribution of parameters of interest. If data augmentation can be used in the calculation of the maximum likelihood estimate, then in the same cases one ought to be able to use it in the computation of the posterior distribution. It is the purpose of this article to explain how this can be done. The basic idea ...

Tools for statistical inference : methods for the exploration of posterior distributions and likelihood functions

A unified introduction to a variety of computational algorithms for likelihood and Bayesian inference. This third edition expands the discussion of many of the techniques presented, and includes additional examples as well as exercise sets at the end of each chapter.

Modeling Agreement among Raters

Abstract An approach to the modeling of agreement among raters is proposed. By examining a hierarchy of log-linear models, it is shown how one can analyze the agreement among the raters in a manner analogous to the analysis of association in a contingency table. Specific attention is given to the problems of the K-rater agreement and the agreement between several observers and a standard. Examples are used to illustrate how this approach provides a general framework for modeling agreement in a variety of problem situations.

Bayesian Inference in Mixtures-of-Experts and Hierarchical Mixtures-of-Experts Models with an Application to Speech Recognition

Abstract Machine classification of acoustic waveforms as speech events is often difficult due to context dependencies. Here a vowel recognition task with multiple speakers is studied via the use of a class of modular and hierarchical systems referred to as mixtures-of-experts and hierarchical mixtures-of-experts models. The statistical model underlying the systems is a mixture model in which both the mixture coefficients and the mixture components are generalized linear models. A full Bayesian approach is used as a basis of inference and prediction. Computations are performed using Markov chain Monte Carlo methods. A key benefit of this approach is the ability to obtain a sample from the posterior distribution of any functional of the parameters of the given model. In this way, more information is obtained than can be provided by a point estimate. Also avoided is the need to rely on a normal approximation to the posterior as the basis of inference. This is particularly important in cases where the posteri...

Acute Respiratory Tract Infection in Daycare Centers for Older Persons

OBJECTIVE: To evaluate the rate of specific pathogens and clinical syndromes associated with acute respiratory tract infections (ARTI) in frail older persons attending daycare.

Psychosexual adaptation to breast cancer surgery

Disturbances associated with a breast cancer diagnosis were defined when psychological assessments from 63 patients with a known breast cancer diagnosis were compared to those from 56 patients with an as yet undiagnosed malignancy. Subsequent assessments from the 56 patients with an undiagnosed breast cancer showed disturbances after they saw a physician compared with the assessments from 72 similar patients ultimately diagnosed as benign. Apprehension apparently arose from clues given before a biopsy was done even though the cancer was not yet diagnosed. Compared with the benign breast disease group, the disturbances in patients suspected or diagnosed with breast cancer were found chiefly in assessments of mood and adjustment, and less in assessments of more durable characteristics of personality, psychopathology, and sexual behavior. Psychological problems associated with breast cancer decreased over time, but residuals persisted for at least 16 months postoperatively. Few differences were found between 41 patients who elected breast‐conserving surgery and 78 who were treated with mastectomy. Problems were not eliminated by operations which saved the breast.

Binomial-Beta Hierarchical Models for Ecological Inference

The authors develop binomial-beta hierarchical models for ecological inference using insights from the literature on hierarchical models based on Markov chain Monte Carlo algorithms and Kings ecological inference model. The new approach reveals some features of the data that Kings approach does not, can be easily generalized to more complicated problems such as general R × C tables, allows the data analyst to adjust for covariates, and provides a formal evaluation of the significance of the covariates. It may also be better suited to cases in which the observed aggregate cells are estimated from very few observations or have some forms of measurement error. This article also provides an examples of a hierarchical model in which the statistical idea of “borrowing strength” is used not merely to increase the efficiency of the estimates but to enable the data analyst to obtain estimates.

Data-Based Nonparametric Estimation of the Hazard Function with Applications to Model Diagnostics and Exploratory Analysis

Two general classes of nonparametric kernel estimators of the hazard function are introduced, which include both a 1-parameter estimator and a more complex 3-parameter estimator. In addition, employing the idea of cross-validation, the authors present a data-based algorithm for smoothing parameter selection. The article compares the data-based 1and 3-parameter estimators in a simulation experiment to the maximum likelihood estimator assuming the correct failure distribution and censoring mechanism. The 3-parameter estimator is found to perform well over a wide range of settings. On the average, the estimator recovers the shape of the underlying failure hazard and is competitive with the parametric estimator over a subset of the positive half line. Two examples illustrate possible uses of the nonparametric estimators.

A comparison of tocopherol and tocotrienol for the chemoprevention of chemically induced rat mammary tumors

Two forms of vitamin E, tocopherol and tocotrienol, were tested for chemopreventive activity in two chemically induced rat mammary-tumor models. When mammary tumors were induced by 7,12-dimethylbenz(a)anthracene (DMBA, 50 mg/kg), only the tocotrienol group had a statistically significant increase in tumor latency. There was no effect of either compound on tumor multiplicity. When tumors were induced by N-nitrosomethylurea (NMU, 30 mg/kg), neither analogue of vitamin E modified latency, whereas tocotrienol increased tumor multiplicity. In summary, neither vitamin analog had a major impact on mammary-tumor development after tumor induction with either DMBA or NMU.

Ordinary Economic Voting Behavior in the Extraordinary Election of Adolf Hitler

The enormous Nazi voting literature rarely builds on modern statistical or economic research. By adding these approaches, we find that the most widely accepted existing theories of this era cannot distinguish the Weimar elections from almost any others in any country. Via a retrospective voting account, we show that voters most hurt by the depression, and most likely to oppose the government, fall into separate groups with divergent interests. This explains why some turned to the Nazis and others turned away. The consequences of Hitler’s election were extraordinary, but the voting behavior that led to it was not.