Proposal: DMS 95-04379 PI: Bradley Efron Institution: Stanford University Title: Statistical Theory and Methodology' ABSTRACT: The main research areas investigated under this award include: (1) Exact methods for large, sparse contingency tables based on Markov Chain Monte Carlo techniques; (2) Improvements on the accuracy of classical normal and Edgeworth expansions, based on Stein's method; (3) The use of specially designed exponential families for density estimation and empirical Bayes situations; (4) The application of bootstrap-based techniques for confidence intervals, likelihood analysis, and bias-correction; and (5) Length and volume calculations based on Hotelling's tube formula for routine use in simultaneous testing situations. The long-term goal of this research is the development of promising theoretical ideas into methodologies of direct value to applied statisticians and their scientific clients. This form of technology transfer aims to take advantage of current developments in the range and power of new statistical methodology. The ideas here fall into the general category of "computer-intensive methods", which are methods that take advantage of modern computer power to free statistical analysis from the bounds of classical mathematical tractability. The research does not banish mathematics, but uses mathematics to produce statistical tools that can work automatically on a wide variety of problems. The computer-intensive part comes in at the level of the statistical consumer, where computation is substituted for the usual normal theory approximations and routine but difficult mathematical computations.
