No abstract

Case-deleted analysis is a popular method for evaluating the influence of a subset of cases on inference. The use of Monte Carlo estimation strategies in complicated Bayesian settings leads naturally to the use of importance sampling techniques to assess the divergence between full-data and case-deleted posteriors and to provide estimates under the case-deleted posteriors. However, the dependability of the importance sampling estimators depends critically on the variability of the case-deleted weights. We provide theoretical results concerning the assessment of the dependability of case-deleted importance sampling estimators in several Bayesian models. In particular, these results allow us to establish whether or not the estimators satisfy a central limit theorem. Because the conditions we derive are of a simple analytical nature, the assessment of the dependability of the estimators can be verified routinely before estimation is performed. We illustrate the use of the results in several examples.

extreme observations, long tails, mixture models, reaction times, sequential dependencies, time series modeling, wavelet-based trend,

No abstract

Risk of impaired cognitive function and behavior can be predicted from snoring history, sleep efficiency, sleep latency, and race but not tonsil size. The combination of snoring history and polysomnographic variables predicted impaired cognitive scores better than did either alone. The snoring history predicted more test scores than the number of episodes of apnea and hypopnea per 1 hour of sleep.