Models for Choosing the Best Population

University Of Southern California, Los Angeles CA

Investigators

Abstract

This award will contribute to the advancement of national prosperity and economic welfare by investigating statistical rules for determining which of a given set of approaches to solving a problem is best. These rules will support the ability to make more reliable decisions in reduced time. In a statistical context, the project will study methods to find good rules for determining which of n populations has the largest mean. A decision is made at each stage as to which population to next sample from, with the decision made according to a rule which eventually calls for stopping and declaring which population has the largest mean. The project will impact many diverse application domains, including adaptive clinical trials, improved stochastic optimization procedures, and the impact of various online advertising campaigns. The award will support graduate students, and results will be disseminated through a variety of outlets, including textbooks. The project will study models both when the population distributions are Bernoulli and when they are normal, assuming in both cases that the unknown means can be regarded as being the values of independent random variables with known distributions. Different objectives are considered, such as choosing the population with the largest mean in a relatively small expected number of observations subject to the condition that the probability that a correct choice is made is at least some prescribed value; and of finding, with a high probability of being correct, the best population when the number of observations is fixed. The project also considers the problem when the set of means is known, but it is unknown which mean corresponds to which population. Several variations on this theme are addressed, including a model where the number of populations is unlimited and the objective is to find one whose mean is at least some prescribed value. Also studied is a model where there are a fixed set of items, each having an unknown value, and the objective is to find, via random comparisons, the item having the largest value. At every stage until stopping, an individual is shown a collection of items of the decision-maker's choice; the decision-maker learns which of these items the individual prefers. Assuming that an item is preferred in proportion to its value, the problem of interest is to determine a policy that has a high probability of choosing the item with the highest value after a relatively small mean number of comparisons. To obtain its goals, the research will combine and develop new techniques in stochastic dynamic programming, simulation, and stochastic model analysis. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.