Brown University Graduate School Dissertation Defense Information
Nonlinear Wave Seminar
Brown University Center for Statistical Sciences Seminar
Abstract: Sponsored by: The Bruce M. Bigelow Class of 1955 Lecture Series, The Charles K. Colver Lectureships and Publication Fund and the Department of Diagnostic Imaging at Brown University and Rhode Island Hospital/Lifespan.
A Lecture Series on Methodologic Challenges in Health Care and Policy Research.
Multivariable regression models are powerful tools for uncovering strength and shapes of relationships between predictors and response, for making tests of partial association, and for predicting outcomes of future subjects. Successful modeling must address problems such as missing values in the predictors, overfitting (solved by data reduction or shrinkage), relaxing linearity assumptions, fitting nonlinear interactions, and presenting results graphically so that non-statisticians can understand complex models.
There are a number of pre-modeling steps that can help the modeling process including (1) displaying distributions of predictors and response, (2) understanding inter-relationships among predictors, (3) displaying how missing values occur simultaneously among several predictors, and (4) uncovering what kinds of subjects tend to have missing values for some of the predictors. All of these are helpful in deciding whether and how to impute missing values. In addition, nonparametric regression is an excellent exploratory tool.
Once one is ready to model the response, techniques such as regression splines, pooled effect tests (main effects combined with interactions), automatic tests of linearity, shrinkage (penalized maximum likelihood estimation), and various graphical displays of how the predictors affect the response are very useful.
This talk will focus on live demonstrations of various pre-modeling and modeling strategies, using S-PLUS and add-on libraries Hmisc and Design (avaiable from Statlib). Two datasets will be used to demonstrate the methods. One of them contains information on passengers on the Titanic, where we will answer the question, "Were women and children first?"
Special Department of Mathematics Colloquium
Brown University Graduate School Dissertation Defense Information
Stochastic Systems Seminar
Brown Applied Mathematics Pattern Theory and Vision Seminar
Lefschetz Center for Dynamical Systems Seminar
Abstract: Wavelength Division Multiplexing (WDM) is an important technique used in modern optical fiber telecommunications. This technique consists in dividing the window of a fiber's optical transparency into several frequency channels, and transmitting the information through all the channels in parallel. We will present a mathematical model of soliton communications for WDM and a review of experimental results. The physical limitations, such as four-wave mixing due to inter-channel interaction, and polarization mode dispersion, will also be explained.
Special Stochastic Systems Seminar
PDE Seminar
Brown Analysis Seminar
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