This project involves interdisciplinary research in which algorithmic approaches are developed to design and analyze adaptive experiments. An adaptive (sequential) design is one whose characteristics change in accordance with information arising from the ongoing experiment, as opposed to classical statistical designs where such characteristics are set in advance and remain fixed throughout. Adaptive designs have a wide range of application in clinical trials, destructive testing, behavioral ecology, computer performance prediction, adaptive control, etc., where they 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 analytic solutions are rarely available, and thus, historically, such designs have been predominantly approached via asymptotic methods and ad hoc approximations. Computationally, adaptive designs require significant time and space that has often made exact calculations infeasible.
This project will expand the size and scope of solvable problems by developing new computational approaches for creating and evaluating designs 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 in modeling their statistical and cost objectives. For many of these problems, exact optimality will be unattainable, and thus techniques for producing near-optimal designs will also be pursued. Several of these techniques are based on optimizing smaller or simpler problems and extrapolating their solution structure to larger or more complex problems. This compliments analytical, asymptotic work and provides new insights into the structure of solutions. In other cases, a shift from serial algorithms to parallel ones will be used to address the additional complexity.
