A critical issue for users of Markov Chain Monte Carlo (MCMC) methods in applications is how to determine when it is safe to stop sampling and use the samples to estimate characteristics of the distribution of interest. Research into methods of computing theoretical convergence bounds holds promise for the future but currently has yielded relatively little that is of practical use in applied work. Consequently, most MCMC users address the convergence problem by applying diagnostic tools to the output produced by running their samplers. After giving a brief overview of the area, we provide an expository review of thirteen convergence diagnostics, describing the theoretical basis and practical implementation of each. We then compare their performance in two simple models and conclude that all the methods can fail to detect the sorts of convergence failure they were designed to identify. We thus recommend a combination of strategies aimed at evaluating and accelerating MCMC sampler conver...

Problems: Though there are approximately 400,000 Master's or Doctoral degrees awarded nationally each year, many of the students involved are poorly prepared for a lifelong career in which electronic publishing and access to networked information systems will be commonplace. At the same time, graduate education and the whole scholarly research enterprise suffer because, after considerable investment is made in the generation and preservation of theses and dissertations, access to them is severely constrained, greatly limiting possibilities of knowledge transfer and re-use, and missing an opportunity to unlock valuable university resources. Activities: This project will train the future professorate, and the next generation of scholars, to be "information literate", so that they can publish electronically and can make effective use of digital libraries. In particular, we will embark upon a national effort so that theses and dissertations can be prepared and submitted in electronic form, allowing them to be easily cataloged, indexed, archived, searched, accessed, browsed, and re-used. We also will pave the way for electronic theses and dissertations (ETDs) to be enriched through the use of hypertext methods, and the inclusion of multimedia components. We will scale up our current pilot effort to

Purpose: Advance state of the art Special math needed: Maximum likelihood estimation Special math needed for results: None Results useful to: Reliability analyses and statisticians Abstract- Complicated structure of BCrooning experiments coupled with censored data resulting from life-testing of durable products makes the characterization and optimization of process variables very difficult. Existing methods are inadequate for J" analyzing such data from highly fractionated experiments because important effects are identified wrongly. By studying contrasts from censored data, we can. identify an appropriate initial model for the "imputation-modeling-maximization " algorithm to compare many models simultaneously and select the best model for process· optimization. We demonstrate the procedure by reanalyzing data sets from Specht's heat exchanger experiments and show its superiority over some existing methods by comparing their predicted lifetimes

Special math needed to use results: None Results useful to: Reliability analysts and statisticians Summary and Conclusions-Censored data coupled with complexity of the design structure in screening experiments creat.es problems in the maximum likelihood (ML) estimation procedures. Since sample sizes in screening experiments are usually small, statistical inferences based on large sample distributions of the ML estimators can be inappropriate. In this article, Wei and Tanner's Bayesian estimation procedure is applied to analyze a data set taken from Specht's heat exchanger experiments. Marginal posterior distributions and the highest probability density intervals of model parameters and mean responses are obtained and compared to several approximated confidence intervals derived from asymptotic theory of the ML estimators. Bayesian intervals of the difference of mean responses are examined to check whether the best combination of process variables produces the most reliable products under consideration of experimental errors