Our research is oriented toward implementation of Bayesian inference. There has been increasing interest recently in the Bayesian approach to statistics, in part because advances in computational ability have made it feasible in many settings, and in part because Bayesian analysis of data can make use of information from additional sources. Our work will build on our previous research in Bayesian statistics, part of which has been funded by NSF. Our main concerns are: (1) review and assessment of methods for choosing prior probability distributions by formal rules, and further development of methods for assessing sensitivity to the choices; (2) investigation of approximate and exact computational methods for Bayesian hypotheses testing; (3) modification and enhancement of numerical integration techniques and Monte Carlo simulation of posterior distributions; also, improvement of statistical computing environments including use of animation and three dimensional rendering for visualization of uncertainty in higher dimensions; (4) further work on the foundations of subjective probability; and (5) several other topics related to our previous work on elicitation of priors and asymptotic approximations. When analyzing data, it is important to combine all sources of information effectively. Bayesian statistical methods are tailored to this purpose. Our research focuses on finding practical ways to implement Bayesian methods and on investigating the theoretical basis for these methods. We are concerned with the development of computational and graphical techniques that make Bayesian inference feasible in complicated problems. These include: simulation, animation and the construction of statistical computing environments. We will also investigate theoretical issues that support Bayesian techniques. These issues include the foundations of subjective probability and the development of mathematical approximations.
