Optimal Budget-Constrained Sample Allocation for Selection Decisions with Multiple Uncertain Attributes

A decision-maker, when faced with a limited and fixed budget to collect data in support of a multiple attribute selection decision, must decide how many samples to observe from each alternative and attribute. This allocation decision is of particular importance when the information gained leads to uncertain estimates of the attribute values as with sample data collected from observations such as measurements, experimental evaluations, or simulation runs. For example, when the U.S. Department of Homeland Security must decide upon a radiation detection system to acquire, a number of performance attributes are of interest and must be measured in order to characterize each of the considered systems. We identified and evaluated several approaches to incorporate the uncertainty in the attribute value estimates into a normative model for a multiple attribute selection decision. Assuming an additive multiple attribute value model, we demonstrated the idea of propagating the attribute value uncertainty and describing the decision values for each alternative as probability distributions. These distributions were used to select an alternative. With the goal of maximizing the probability of correct selection we developed and evaluated, under several different sets of assumptions, procedures to allocate the fixed experimental budget across the multiple attributes and alternatives. Through a series of simulation studies, we compared the performance of these allocation procedures to the simple, but common, allocation procedure that distributed the sample budget equally across the alternatives and attributes. We found the allocation procedures that were developed based on the inclusion of decision-maker knowledge, such as knowledge of the decision model, outperformed those that neglected such information. Beginning with general knowledge of the attribute values provided by Bayesian prior distributions, and updating this knowledge with each observed sample, the sequential allocation procedure performed particularly well. These observations demonstrate that managing projects focused on a selection decision so that the decision modeling and the experimental planning are done jointly, rather than in isolation, can improve the overall selection results.

SEMIPARAMETRIC METHODS IN THE ESTIMATION OF TAIL PROBABILITIES AND EXTREME QUANTILES

In quantitative risk analysis, the problem of estimating small threshold exceedance probabilities and extreme quantiles arise ubiquitously in bio-surveillance, economics, natural disaster insurance actuary, quality control schemes, etc. A useful way to make an assessment of extreme events is to estimate the probabilities of exceeding large threshold values and extreme quantiles judged by interested authorities. Such information regarding extremes serves as essential guidance to interested authorities in decision making processes. However, in such a context, data are usually skewed in nature, and the rarity of exceedance of large threshold implies large fluctuations in the distribution's upper tail, precisely where the accuracy is desired mostly. Extreme Value Theory (EVT) is a branch of statistics that characterizes the behavior of upper or lower tails of probability distributions. However, existing methods in EVT for the estimation of small threshold exceedance probabilities and extreme quantiles often lead to poor predictive performance in cases where the underlying sample is not large enough or does not contain values in the distribution's tail. In this dissertation, we shall be concerned with an out of sample semiparametric (SP) method for the estimation of small threshold probabilities and extreme quantiles. The proposed SP method for interval estimation calls for the fusion or integration of a given data sample with external computer generated independent samples. Since more data are used, real as well as artificial, under certain conditions the method produces relatively short yet reliable confidence intervals for small exceedance probabilities and extreme quantiles.