This proposal considers problems in the area of optimal choice of observation times for a random process. Bayesian inference and decision theory provide a general and successful theoretical framework. Within this framework, the goal of the proposed research is to seek advances in important application areas. In particular, goals are: To lay the groundwork for Bayesian dynamic adjustment of sampling frequency in monitoring a random process for control and other purposes; to study models for detecting the presence of conditions that do not manifest naturally; and to study design problems in which the goal of taking observations is learning about process parameters. Acquiring information about random phenomena over time is often costly and hard. Efficiency can be substantially enhanced by careful choice of observation times. The proposed research examines specific applications in the hope of a) providing solutions to pressing practical problems; b) indicating general strategies. Examples of applications include timing of screening exams for the early detection of cancer; designing tests for improving software reliability; efficient monitoring in meteorology, seismology and environmental sciences; efficient implementation of process control and quality control in manufacturing; regulation of airplane maintenance and others.
