Lefschetz Center for Dynamical Systems Seminar
Brown University Center for Statistical Sciences Seminar
Abstract: In regression models for longitudinal data, repeated observations on the same individual mean that the independence assumption in linear regression and in generalized linear models is violated. A variety of methods are now used to model longitudinal data that take this lack of independence into account. In the interest of interpretability, it is desirable to obtain diagnostic methods that are analogous to those used in models for independent observations. Because of the lack of independence, however, it is not always obvious how to extend diagnostic methods to longitudinal data. This talk will survey a variety of model checking diagnostics that have been successfully implemented. These include nonparametric regression for checking the systematic form of covariate-response relationships, analogues to local influence and deletion influence, and added variable plots. All of these have been extended to provide diagnostics to mean and covariance structure. The emphasis will be on concepts common to a variety of longitudinal models, including linear mixed models, marginal models, and generalized linear mixed models.
Brown Applied Mathematics Pattern Theory and Vision Seminar
Abstract: The observed distribution of visual images is far from uniform. On the contrary, images have complex and important structure that can be used for image processing, recognition and analysis. There have been many proposed approaches to the principled statistical modeling of images, but there remains limits on the complexity of the models or the complexity of the images. We present a non-parametric multi-scale statistical model for images that can be used for recognition, image de-noising, and in a ``generative mode'' to synthesize high quality textures.
Brown Analysis Seminar
PDE Seminar
Department of Mathematics Colloquium
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