Computationally Aggressive Approaches to Adaptive Design

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AbstractThis project involves interdisciplinary research in which algorithmicapproaches are developed to design and analyze adaptive experiments. Anadaptive (sequential) design is one whose characteristics change inaccordance with information arising from the ongoing experiment, as opposed to classical statistical designs where such characteristics areset in advance and remain fixed throughout. Adaptive designs have a widerange of application in clinical trials, destructive testing, behavioralecology, computer performance prediction, adaptive control, etc., wherethey have the potential to reduce the expenditure of experimental ``resources'' such as time, money, or quality of life. Unfortunately,adaptive designs are difficult to analyze and optimize. Exact analyticsolutions are rarely available, and thus, historically, such designs havebeen predominantly approached via asymptotic methods and ad hocapproximations. Computationally, adaptive designs require significanttime and space that has often made exact calculations infeasible.This project will expand the size and scope of solvable problems bydeveloping new computational approaches for creating and evaluatingdesigns and utilizing state of the art computational facilities.Attention is directed to problems that are important in applications,with a major emphasis on supplying researchers greater flexibility inmodeling their statistical and cost objectives. For many of theseproblems, exact optimality will be unattainable, and thus techniques forproducing near-optimal designs will also be pursued. Several of thesetechniques are based on optimizing smaller or simpler problems andextrapolating their solution structure to larger or more complexproblems. This compliments analytical, asymptotic work and provides newinsights into the structure of solutions. In other cases, a shift fromserial algorithms to parallel ones will be used to address theadditional complexity.