... 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 paper develops a predictive model for National Football League (NFL) game scores using data from the period 1988--1993. The parameters of primary interest, measures of team strength, are expected to vary over time. Our model accounts for this source of variability by modeling football outcomes using a state-space model that assumes team strength parameters follow a first-order autoregressive process. Two sources of variation in team strengths are addressed in our model; week-to-week changes in team strength due to injuries and other random factors, and season-to-season changes resulting from changes in personnel and other longer-term factors. Our model also incorporates a home-field advantage while allowing for the possibility that the magnitude of the advantage may vary across teams. The aim of the analysis is to obtain plausible inferences concerning team strengths and other model parameters, and to predict future game outcomes. Iterative simulation is used to obtain samples fro...