DMS 9625672 Huzurbazar This research involves the application of flowgraph and saddlepoint methods to problems in statistics with particular emphasis on prediction in stochastic networks. Stochastic network models are of current interest in statistics and can be applied to study a variety of natural phenomena. Consider the progression of diseases such as kidney failure, cancer, or AIDS. Of interest is the prediction of a survival time for a patient. Survival times can be thought of as first passage times from one state to another in a stochastic network so that prediction of a survival time for a patient involves analysis of a complex stochastic network. This research is concerned with such prediction. Methodology is developed for computation of Bayesian predictive distributions for stochastic networks in situations involving a multitude of covariates and heavily censored data. These methods are used in conjunction with generalized linear models and proportional hazards models, so that predictive distributions as well as predictive hazards and predictive survival functions for first passage times between any two states of a disease, or more generally, stochastic networks, are computed. %%% This is a study of flowgraphs which extends beyond the natural emphasis area of survival analysis into several diverse areas of engineering systems. Flowgraphs were originally developed in the engineering sciences to design and analyze complex systems. For example, these systems could be descriptions of a manufacturing process, the reliability of an artificial organ, or the predicted time to completion of a building project. The analysis of flowgraphs traditionally has been hampered by computational difficulties. Current engineering methods involve time-consuming computer simulations. The computational aspects of this research are based on saddlepoint approximations. Saddlepoint approximations are high performance computationally intensive techniques that provid e fast and accurate approximations to these problems. The results developed here are applicable in the areas of reliability, and industrial, electrical, and systems engineering, in addition to survival analysis. ***
