Please join us before the talk for tea and cookies in the math lounge (RH 305) 15 minutes before any colloquium.
Abstract: The simplest designed experiment is the two sample location problem. In 1945, Wilcoxon developed a test based on ranks for this problem. Later, Hodges and Lehmann inverted the Wilcoxon test to obtain an estimator and showed that it is highly efficient to the maximum likelihood estimator at the normal. Then, in the seventies, Jurec¹ková and Jaeckel obtained a rank-based estimator for the linear regression model. In the first part of the talk, we discuss the two sample location problem via an adaptive nonparametric procedure applied to microarray data. Then, in the remaining time, we discuss a Jaeckel estimator for modeling randomized block designs.
Abstract: In 2006 there were almost forty million people around the world living with HIV/AIDS (UNAIDS). In May 2003, the U.S. President announced a global program, known as the President’s Emergency Plan for AIDS Relief (PEPFAR), to address this epidemic. We seek to estimate patient mortality in PEPFAR in an effort to monitor and evaluate this program. This effort, however, is thwarted by loss to follow-up that occurs at very high rates. As a consequence, standard survival data and analysis on observed non-dropout data is generally biased, and provide no ob jective evidence to correct the potential bias. We develop and apply double-sampling designs and methodology to estimate mortality in PEPFAR. In this talk, we show that the estimate of yearly mortality based on our methods is substantially better than the estimate based on standard methods; and we examine profiles of lost to follow-up individuals whom researchers should target for double-sampling.
Abstract: A volume-outcome study is typically used to evaluate whether patients treated by high-volume health care providers (e.g. surgeons or hospitals) have better post-treatment outcomes than those treated by low-volume providers. Previous methodological literature does not provide definitive guidance on appropriate methods for a volume-outcome analysis. To provide a unified framework I explore a recurrent marked point process and examine the use of existing longitudinal analysis methods in the context of disaggregate volume-outcome data. Results from a simulation study indicate that generalized estimating equations and linear mixed models may provide a biased estimate of the volume-outcome association. However, an independence estimating equation provides an unbiased estimate with nominal confidence interval coverage. In this talk I will review the analysis of typical longitudinal data. I will then describe the recurrent marked point process setting and discuss implications for a volume-outcome analysis.
Abstract: A very famous theorem of Smale, dating back to the late fifties, states that it is possible to turned a sphere inside out through a continuous family of immersions. We will explain his result and especially his proof which follows a cut and paste strategy. After this we will turn to Goodwillie's extension of that strategy to the study of embeddings and illustrate this in the case of high-dimensional knots. (Part of this is joint work with Greg Arone, Victor Turchin, and Ismar Volic.)
Lecture 1: Algorithms: a common language for nature, man and computer
Lecture 2: Time, space and the cosmology of computational problems
Abstract: Take a number and write it as the sum of smaller numbers; this is called a partition. This sounds like such a simple idea and yet partitions are so natural that they appear in many deep theories of mathematics and physics. We will explore some of the methods for studying these results -- combinatorics, power series, even complex analysis. This talk will be accessible to anyone interested in math; the only prerequisite is a love of numbers!