Brown University Center for Statistical Sciences Seminar
Abstract: In many health sciences applications the study units can be regarded as a random sample from a population of interest. Often, on each unit one only observes coarsened data, i.e. and incomplete part of the intended (full) data to be ideally recorded, and a coarsening variable indicating what part of the full data were actually observed. Often, the relevant scientific problem is the estimation of a parameter of the full data law. Generally, the observed data alone do not identify the full-data law. However, the full data law is identified under the assumption that the data are coarsened at random, that is, under the assumption that the conditional distribution of the coarsening variable given the full data is a function only of the observed data. While sufficient for identification of the full data law, coarsening at random alone is generally insufficient for inference because of the curse of dimensionality. Two strategies to dimension reduction are generally available. The first places models on the law of the full data, the second places models on the coarsening mechanism. Both strategies can lead to serious biases if the assumed models are incorrect.
In this talk I describe doubly-robust estimators that remain consistent and asymptotically normal under misspecification of either (but not both) the model for the coarsening mechanism or the model for the distribution of the full data. I will illustrate how doubly-robust estimation can be applied to the analysis of repeated measures with missing data and right-censored (univariate or multivariate failure time data). I will argue that the existence of doubly robust estimators is a consequence of the particular likelihood factorization that arises under coarsening at random. If time allows I will point out to other, non-missing data, models often used in Biostatistics which have the required likelihood factorization so that doubly-robust inference is plausible.
Brown Applied Mathematics Pattern Theory and Vision Seminar
Abstract: We present some experiments on natural images, showing that the distribution of sizes of homogeneous and connected regions is well approximated by a power law. Through these experimental results, we show that the bounded variation norm of natural images is not finite. We then present an occlusion model for the formation of images, and address some questions related to the distribution of the sizes of visible objects. Eventually, we show how our approach can be used to synthesize realistic textures.
Wednesday, May 3, 2000, Continued......
Brown Analysis Seminar
LATE SPECIAL ANNOUNCEMENT
Scientific Computing Seminar
Abstract: It was in 1969, Oganesyan and Rukhovetz compared under a uniform triangulation the linear finite element approximation (FEA) with the linear interpolation for Poisson equation, and found that they are so called superclose. In 1990, in order to relax the uniform restriction on the mesh, we turned to the general rectangulation, and found an integral identity which implies immediately the same superclose result without regular restriction and hence holds for, e.g. Shishkin mesh. Once obtained superclose, a global superconvergence comes out by an interpolation processing. Such an integral identity and interpolation processing can be easily generalized to various deformed rectangulations (including Babuska's local refinement and mortar mesh), various PDEs (including biharmonic, Stokes and Maxwell systems, even nonlinear conservation laws) and various FEMs (including mixed and non-conforming elements). The result makes some non-convergent FEMs to become convergent, and makes slowly convergent FEMs to become fast convergent. Further we show in this paper how the integral identity and interpolation processing can also be generalized to the discontinuous Galerkin method (DGM) for the first order hyperbolic equation and make the slowly DGM to become fast.
Special Analysis/PDE Seminar
Department of Mathematics Colloquium
<--- 2000 Index