Constrained Statistical Decisions in Evolving Environments

This paper suggests a modeling framework for constrained decision making in a constantly evolving environment. The goal is to enable a user or system to anticipate impending points of interest and prepare accordingly. The methodology presented leads to a decision process that is based on a single score, which has simple and desirable statistical properties. This approach allows one to easily compute point and confidence interval estimates for future scores. The crucial advantage gained by employing this approach is the simplification of the decision process from a complex set of decision rules (as might be generated by a decision tree) down to a single number. Storage constraints imposed by the need to model phenomena in real time are also addressed. Scan statistics are used in this context to deal with the random number of observations encountered in some situations. The impact of randomly occurring observations on the amount of memory necessary is contrasted with that of regularly occurring observations by means of an example. We illustrate this process using a real-world weather data set. The ultimate goal in this case is to identify future points in time when the weather is predicted to be unsafe for the operation of outdoor machinery.