[Read before The Royal Statistical Society at a meeting organized by the Research

e wrong, which is even worse. Please let us know of any successes or failures. Beware - Gibbs sampling can be dangerous!. BUGS c flcopyright MRC Biostatistics Unit 1995. ALL RIGHTS RESERVED. The support of the Economic and Social Research Council (UK) is gratefully acknowledged. The work was funded in part by ESRC (UK) Award Number H519 25 5023. 1 2 Contents 1 Introduction 5 1.1 What is BUGS? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 For what kind of problems is BUGS best suited? . . . . . . . . . . . . . . . . . . . . . 5 1.3 Markov Chain Monte Carlo (MCMC) techniques . . . . . . . . . . . . . . . . . . . . 5 1.4 A simple example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.5 Hardware platforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.6 Software . . .

An approach for developing Bayesian outlier and goodness of fit statistics is presented for the linear model and extended to a hierarchical random effects model for repeated measures data. Diagnostics for univariate outliers, missing covariates, multivariate outliers and global goodness of fit are developed. Distribution theory for the posterior of the residuals is worked out. A local approach is used to show how omitted covariates and fixed and random effects affect residual summaries. Standard plots are interpreted in light of these understandings. Key Words: Bayesian Data Analysis, Goodness-of-Fit, Hierarchical Models, Longitudinal Data, Outlier, Philosophy of Statistics, Shrinkage. 1 Introduction. This paper develops a Bayesian approach to residual analysis and extends the approach to the random effects model (REM) used to model repeated Robert E. Weiss is Assistant Professor, Department of Biostatistics, Box 177220; UCLA School of Public Health; Los Angeles CA 90095-1772 U.S....

this article, Bayesian discrete-time stochastic models are developed for inference from cross-sectional data consisting of the age at first diagnosis, the current presence of disease, and one or more surrogates of disease severity. Semiparametric models are used for the age-specific hazards of onset and diagnosis, and a normal underlying variable approach is proposed for modeling of changes with latency time in disease severity. The model accommodates multiple surrogates of disease severity having different measurement scales and heterogeneity among individuals in disease progression. A Markov chain Monte Carlo algorithm is described for posterior computation, and the methods are applied to data from a study of uterine leiomyoma

SUMMARY. Cervical mucus hydration increases during the fertile interval prior to ovulation. Since sperm can only penetrate mucus having a high water content, cervical secretions provide a reliable marker of the fertile days of the menstrual cycle. This article develops a Bayesian approach for modeling of daily observations of cervical mucus, and applies the approach to assess heterogeneity among women and cycles from a given woman with respect to the increase in mucus hydration during the fertile interval. The proposed model relates the mucus observations to an underlying normal mucus hydration score, which varies relative to a peak hydration day. Uncertainty in the timing of the peak is accounted for, and a novel weighted mixture model is used to characterize heterogeneity in distinct features of the underlying mean function. Prior information on the mucus hydration trajectory is incorporated, and a Markov chain Monte Carlo approach is developed. Based on data from a study of daily fecundability, there appears to be substantial heterogeneity among women in detected preovulatory increases in mucus hydration but only minimal differences among cycles from a given woman.

this paper and in a few others

and produce answers that are wrong, which is even worse. Please let us know of any successes or failures. Beware - Gibbs sampling can be dangerous!. BUGS c flcopyright MRC Biostatistics Unit 1995. ALL RIGHTS RESERVED. The support of the Economic and Social Research Council (UK) is gratefully acknowledged. The work was funded in part by ESRC (UK) Award Number H519 25 5023. 1 2 Contents 1 Introduction 5 1.1 What is BUGS? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 For what kind of problems is BUGS best suited? . . . . . . . . . . . . . . . . . . . . . 5 1.3 Markov Chain Monte Carlo (MCMC) techniques . . . . . . . . . . . . . . . . . . . . 5 1.4 A simple example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.5 Hardware platforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

This paper considers small-area estimation with proportion data, and discusses the choice of upper-level model for the variation over areas. Inference about the random e#ects for the areas may depend strongly on the choice of this model, but this choice is not a straightforward matter. We show that posterior distributions of the deviances for the competing models provide a valuable tool for this purpose, and for the model averaging needed when several models fit equally well. We illustrate the approach with a well-known data set, and contrast it with the deviance information criterion approach

Outlier observations can have an adverse effect on statistical inference. Identification and elimination of such observations are one option, however, dealing with outliers in this manner has many drawbacks. An alternative approach is to utilize statistical methods that are robust to outliers. Robustness is a desirable property of statistical estimators because it ensures that the estimator reflects the pattern in the majority of the data, without being too sensitive to a handful of outliers. In this dissertation robust methodology for constructing empirical Bayes confidence intervals is presented. Three different robust models are proposed: a variance inflation model, a location-shift model and a heavy-tailed model. These three general types of models are described within a hierarchical Bayes framework and are applied in two separate contexts. In the first, we apply the robust methodologies to the normal means problem, and in the second we apply them to the modelling of longitudinal data by random-effects models. The Gibbs sampler is used for analysis of these complex models. Four alternative types of confidence intervals are proposed and evaluated. The proposed

❙ X: Επίπεδο εστριόλης (estriol) των εγκύων γυναικών ❚ Υ i ~ Normal(μ i, σ 2) ❚ μ i =η i =α+βΧ i 6 … ΑΠΛΟΙ ΕΛΕΓΧΟΙ ΥΠΟΘΕΣΕΩΝ 6.1. Εισαγωγή: Εκ-των-Υστερων Λόγος