Brown University Center for Statistical Sciences Seminar
Abstract: Computing posterior modes (e.g., maximum likelihood estimates) for models involving latent variables or missing data often involves complicated optimization procedures. By splitting this task into two simpler parts, however, EM-type algorithms often offer a simple solution. Although this approach has proven useful, in some settings even these simpler tasks are challenging. In particular, computations involving latent variables are typically difficult to simplify. Thus, in models such as hierarchical models with complicated latent variable structures, computationally intensive methods may be required for the expectation step of EM. We describe how nesting two or more EM algorithms can take advantage of closed form conditional expectations and lead to algorithms which converge faster, are straightforward to implement, and enjoy stable convergence properties. Methodology to monitor convergence of nested EM algorithms is developed using importance and bridge sampling. The strategy is applied to hierarchical probit and t regression models (e.g., models for binary and robust longitudinal analysis respectively) to compute maximum likelihood estimates with substantial computational gain relative to the standard Monte-Carlo EM algorithm. We also show how nesting can be used to improve algorithms for analysis of spectral data obtained with the Chandra X-ray Observatory (launched by the space shuttle Columbia July, 1999). The various resulting algorithms incorporate aspects of Monte-Carlo EM, PX-EM, efficient data augmentation, and nesting in order to combine computational efficiency with easy implementation.
*Refreshments following seminar at 167 Angell St., 2nd Floor Conference Room
Brown Analysis Seminar
PDE Seminar
Joint Division of Engineering and Center for Fluid Mechanics Seminar
Abstract: Subject of the talk is the evolution of swirl with a well-defined characteristic of solid-body rotation introduced at an initial station into a turbulent flow in a pipe. The study has been conducted experimentally by a non-intrusive measurement technique. The generation of swirl with such a well-defined characteristic is by a device of special design based on the principle of a rotating honeycomb which permits realization of the flow with swirl of the desired characteristic over a wide parameter range. The measurements are done with a 3-D Laser-Doppler velocimeter in conjunction with the technique of refractive-index matching of the working fluid of the facility. The results obtained which cover both the mean and fluctuating quantities, draw attention to some novel evolution features of the flow and turbulence due to swirl.
<--- 1999 Index