... In this article we present the general outlook and discuss general families of elaborations for use in practice; the exponential connection elaboration plays a key role. We then describe model elaborations for use in diagnosing: departures from normality, goodness of fit in generalized linear models, and variable selection in regression and outlier detection. We illustrate our approach with two applications.

this article we attempt to remedy this, as well as to answer the call of Dempster (1985) for a more formal criterion for judging influence and to develop such a measure justified in the decision-theoretic framework of learning about parameters of interest

This paper describes an approach to Bayesian sensitivity analysis that uses an influence statistic and an outlier statistic to assess the sensitivity of a model to perturbations. The basic outlier statistic is a Bayes factor, while the influence statistic depends strongly on the purpose of the analysis. The task of influence analysis is aided by having an interpretable influence statistic. Two alternative divergences, an L1 distance and a Ø 2 divergence are proposed and shown to be interpretable. The Bayes factor and the proposed influence measures are shown to be summaries of the posterior of a perturbation function. Keywords: Bayes Factor; Censoring; Conditional Predictive Ordinate; Diagnostics, Influence Analysis. 1 Introduction This paper describes an approach to Bayesian sensitivity analysis that uses an influence statistic and an outlier statistic to assess the sensitivity of a model to perturbations. Let the likelihood and prior from an initial model M 0 combine to give the ...

Advances in computation mean it is now possible to fit a wide range of complex models, but selecting a model on which to base reported inferences is a difficult problem. Following an early suggestion of Box and Tiao, it seems reasonable to seek `inference robustness' in reported models, so that alternative assumptions that are reasonably well supported would not lead to substantially different conclusions. We propose a four-stage modelling strategy in which we: iteratively assess and elaborate an initial model, measure the support for each of the resulting family of models, assess the influence of adopting alternative models on the conclusions of primary interest, and identify whether an approximate model can be reported. These stages are semi-formal, in that they are embedded in a decision-theoretic framework but require substantive input for any specific application. The ideas are illustrated on a dataset comprising the success rates of 46 in-vitro fertilisation clinics over three years. The analysis supports a model that assumes 43 of the 46 clinics have odds on success that are evolving at a constant proportional rate (i.e. linear on a logit scale), while three clinics are outliers in the sense of showing non-linear trends. For the 43 `linear' clinics, the intercepts and gradients can be assumed to follow a bivariate normal distribution except for one outlying intercept: the odds on success are significantly increasing for four clinics and significantly decreasing for three. This model displays considerable inference robustness and, although its conclusions could be approximated by other less-supported models, these would not be any more parsimonious. Technical issues include fitting mixture models of alternative hierarchical longitudinal models, t...

this paper, we propose two variable and transformation selection procedures on the predictor variables in the linear model. The first procedure is a simultaneous variable and transformation selection procedure. For data sets with many predictors, a stepwise variable selection procedure is also presented. The procedures are based on Bayesian model selection criteria introduced by Ibrahim and Laud (1994) and Laud and Ibrahim (1995). Several examples are given to illustrate the methodology.

Introduction Influence diagnostics have been widely discussed in the linear regression setting (see Belsley, Kuh & Welsch, 1980; Cook & Weisberg, 1982). In time series analysis, such diagnostics have received limited attention, although extensive research has appeared on the characterisation and classification of outliers. References on influence assessment in time series include Chernick, Downing & Pike (1982), Lattin (1983), Martin & Yohai (1986), Li & Hui (1987), Pe~na (1987, 1990, 1991), Abraham & Chuang (1989), Bruce & Martin (1989), Ledolter (1989), LeFrancois (1991) and Van Hui & Lee (1992). In the state-space setting, a primary inferential goal is to recover unobserved states using fixed-interval smoothing (de Jong, 1988; Kohn & Ansley, 1989); we introduce a diagnostic which assesses the influence of a case or set of cases on the smoothers. Our diagnostic is defined as the Kullback-Leibler directed divergence (Kullback, 1968, p. 5) between two versions of the conditional

We argue for the adoption of a predictive approach to model specification. Specifically, we derive the difference between means and the ratio of determinants of covariance matrices when a subset of explanatory variables is included or excluded from a regression. For several special cases these measures are shown to be related to widely used tools for studying model specification. Results for a set of simulated data and for two economic applications are presented as examples. Thanks to Professor Siddhartha Chib for comments. An earlier version of this paper was presented at the Midwest Econometrics Group meeting at Notre Dame in September 1991. 1 1

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