Bayesian Inference for Some Mixture Problems in Quality and Reliability

This is an expository paper dealing with Bayesian inference for three important mixture problems in the area of quality and reliability. The traditional approach for estimation in these situations is the method of maximum likelihood. The corresponding inference based on large-sample theory can, however, be misleading in situations where the likelihood cannot be well approximated by the normal distribution. The Bayesian approach, on the other hand, has been viewed as compu-tationally intractable due to the complex nature of mixture models. Recent advances in Bayesian computational methods have alleviated this problem considerably. We illustrate the use of data augmentation methods for doing Bayesian inference in these applications. While the framework is formally Bayesian in nature, it can also be viewed as a computational device for calculating the likelihood function and doing likelihood-based inference. An additional advantage of data augmentation methods is that no further complications arise when failure time data are grouped or censored.