On the Sample Information About Parameter and Prediction

The Bayesian measure of sample information about the parameter, known as Lindley's measure, is widely used in various problems such as developing prior distributions, models for the likelihood functions and optimal designs. The predictive information is defined similarly and used for model selection and optimal designs, though to a lesser extent. The parameter and predictive information measures are proper utility functions and have been also used in combination. Yet the relationship between the two measures and the effects of conditional dependence between the observable quantities on the Bayesian information measures remain unexplored. We address both issues. The relationship between the two information measures is explored through the information provided by the sample about the parameter and prediction jointly. The role of dependence is explored along with the interplay between the information measures, prior and sampling design. For the conditionally independent sequence of observable quantities, decompositions of the joint information characterize Lindley's measure as the sample information about the parameter and prediction jointly and the predictive information as part of it. For the conditionally dependent case, the joint information about parameter and prediction exceeds Lindley's measure by an amount due to the dependence. More specific results are shown for the normal linear models and a broad subfamily of the exponential family. Conditionally independent samples provide relatively little information for prediction, and the gap between the parameter and predictive information measures grows rapidly with the sample size.Comment: Published in at http://dx.doi.org/10.1214/10-STS329 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

BAYESIAN DESIGN OF ACCELERATED LIFE TESTS 1

In this article we present the Bayesian decision theoretic setup for design of accelerated life tests. We review some of the key contributions to the Bayesian design of accelerated life tests. In so doing, we discuss approximate Bayesian designs based on linear Bayesian methods and Monte Carlo based methods. We consider computational issues regarding the evaluation of expectation and optimization steps in the solution of the decision problem and discuss some recent Monte Carlo approaches that can reduce the computational effort in the design problem

Statistical Medical Fraud Assessment: Exposition to an Emerging Field

Health care expenditures constitute a significant portion of governmental budgets. The percentage of fraud, waste and abuse within that spending has increased over years. This paper introduces the emerging area of statistical medical fraud assessment, which becomes crucial to handle the increasing size and complexity of the medical programmes. An overview of fraud types and detection is followed by the description of medical claims data. The utilisation of sampling, overpayment estimation and data mining methods in medical fraud assessment are presented. Recent unsupervised methods are illustrated with real world data. Finally, the paper introduces potential future research areas such as integrated decision making approaches and Bayesian methods and concludes with an overall discussion. The main goal of this exposition is to increase awareness about this important area among a broader audience of statisticians

Mathematical reliability: an expository perspective

In this volume consideration was given to more advanced theoretical approaches and novel applications of reliability to ensure that topics having a futuristic impact were specifically included. Topics like finance, forensics, information, and orthopedics, as well as the more traditional reliability topics were purposefully undertaken to make this collection different from the existing books in reliability. The entries have been categorized into seven parts, each emphasizing a theme that seems poised for the future development of reliability as an academic discipline with relevance. The seven parts are networks and systems; recurrent events; information and design; failure rate function and burn-in; software reliability and random environments; reliability in composites and orthopedics, and reliability in finance and forensics. Embedded within the above are some of the other currently active topics such as causality, cascading, exchangeability, expert testimony, hierarchical modeling, optimization and survival analysis. These topics, when linked with utility theory, constitute the science base of risk analysis