Bayesian analysis of outlier problems using the Gibbs sampler

We consider the Bayesian analysis of outlier models. We show that the Gibbs sampler brings considerable conceptual and computational simplicity to the problem of calculating posterior marginals. Although other techniques for finding posterior marginals are available, the Gibbs sampling approach is notable for its ease of implementation. Allowing the probability of an outlier to be unknown introduces an extra parameter into the model but this turns out to involve only minor modification to the algorithm. We illustrate these ideas using a contaminated Gaussian distribution, at-distribution, a contaminated binomial model and logistic regression.     

Historical Overview of Tobacco Legislation and Regulation

In this paper we describe the legislative and regulatory history of tobacco control efforts and discuss ways in which the debate over tobacco control has been framed. From a regulatory perspective, primary concern is how to balance the individual's legal use of tobacco products with society's obligation to limit the use of a lethal product. Our review demonstrates the progress tobacco control advocates have made in enacting statewide legislation and local ordinances, especially during the past fifteen years, to restrict both smoking in public places and youth access to tobacco products. Nevertheless, this progress may be threatened by a powerful and determined tobacco industry. We discuss various strategies for determining how and where to allocate tobacco control resources.     

Infinitesimal sensitivity of posterior distributions

We measure the local sensitivity of a posterior expectation with respect to the prior by computing the norm of the Fréchet derivative of the posterior with respect to the prior over several different classes of measures. We compute the derivative of the posterior upper expectation when the prior varies in a restricted ?-contamination class. A bound on the global sensitivity of a class of priors is obtained. As an application, we show that of all sets with posterior probability 1 — α, the likelihood region minimizes the norm of the Fréchet derivative over the ?-contamination class and so is, in some sense, the most robust region with this posterior probability. But there exist counterexamples to this result for other classes of priors.     

Political beliefs and subjective indicators of quality of life

A recent article by Buttel et al. argued that the subjective satisfaction of individual respondents with their personal lives may be related to their political ideological beliefs. Employing survey data collected in Wisconsin in 1974 they demonstrated a significant linkage between total life satisfaction and political cynicism. This paper proceeds to reanalyze their results, employing 1972 election data collected by the Survey Research Center. The paper argues that one must differentiate a standard measure of political cynicism from the type of measure employed in the Buttel et al. work. For the standard measure of political cynicism no linkage was found with total life satisfaction, but for a personal measure that was similar to the one employed in the Buttel et al. article there was a relationship. The previous results suggest that the findings of the Buttel et al. article were brought about by the unique manner in which they defined political cynicism.