Brown University Division of Biology and Medicine.
Center for Statistical Sciences,
Fall 2005 Seminar Series
Abstract: Density estimation and comparison are the fundamental problems in statistical inference. When parametric distribution assumptions are further made, the problems become estimation and comparison of the parameters of interest. In the situation that the parameters of interest are indexed by a set of covariates, regression is the most powerful tool for estimation and inference. In many situations, the densities are multimodal and parametric assumptions are difficult to make. In these cases, nonparametric density estimation methods are preferred. In this paper, we propose a functional linear model for the situation where a group of densities are indexed by a set of covariates. The basic unit of the data analysis is a density. Through a logistic density transformation, the relationship between the densities and covariates are modeled by a varying coefficient model. This is an extension of regression to a nonparametric setting in which no parametric distribution assumption is needed. Similar to the regression setting, we can borrow information across units in the estimation, make inference on the covariate effects, and make prediction on a new unit. We term the proposed model ``density regression model'' (DENREG). The method is illustrated by a numerical example and a nerve fiber density data.
Brown University,
Joint Materials/ Solid Mechanics Seminar Series
Johns Hopkins University, Baltimore, MD 21218 | |
Abstract: Electrodeposition is increasingly used for the fabrication of nanostructured materials and in confined geometries, however, many aspects of electrodeposition at short length scales are poorly understood. We have used in situ transmission electron microscopy to study the kinetics of island growth during electrodeposition of copper. We compare the results to existing models for nucleation and diffusion limited growth and highlight limitations associated with these models. Nucleation and growth also plays an important role in electrodeposition into patterned features. We show how soft lithography can be exploited to create a range of novel structures.
Special Colloquium
Abstract: Importance sampling is a widely used variance reduction technique for fast simulation of probabilities and expected values associated with rare-events. The key idea of importance sampling is to find an alternative distribution from which the samples are generated, and then the outcomes of simulation are multiplied by likelihood ratios to form unbiaed estimates. Despite the huge amount of work on this topic, there was no systematic approach toward the design and analysis of efficient importance sampling algorithms. In fact, there were only some rudimentary heuristics, based on which the traditional (state-independent) importance sampling schemes could be designed for some simple models. However, they were shown to perform poorly even in the simplest settings. For mildly complicated stochastic systems, there was no heuristics to guide the design of importance sampling.
The talk will focus on importance sampling schemes from a game-theoretic point of view. A fundamental observation is that in the core of importance sampling lies a differential game, and the asymptotic optimal performace of importance sampling can be characterized by the solution to the Isaacs equation (a nonlinear PDE) associated with the game. We demonstrate that classical subsolutions of the Isaacs equation, when properly constructed, can lead to simple and efficient importance sampling schemes. This game-theoretic framework toward importance sampling is comprehensive and can be applied to very broad settings, including sums of iid random variables, sums of functionals of Markov chains, small noise diffusion processes, stochastic networks, random variables with heavy tailed distributions, and so on.
Brown University
Center for Statistical Sciences Seminar
Department of Biostatistics and CHS Coordinating Center
Candidate for Assistant Professor (Tenure Track) | |
1st Fl Conference Room 106 |
Abstract:
An important application of genomic studies is to discover genomic
biomarkers, among tens of thousands of genes assayed, for disease
classification. There is a need for statistical methods that can
efficiently use such high-throughput data, select biomarkers with
discriminant power and construct classification rules. The ROC
(receiving operator characteristic) technique has been widely used
in disease classification with low dimensional biomarkers because
(1.) it does not assume a parametric form of the class
probability;
(2.) it accommodates case-control designs; and
(3.) it allows treating false positives and false negatives
differently.
However, due to computational difficulties, the ROC based
classification has not been used with genomic data. Moreover, the
standard ROC technique does not incorporate built-in biomarker
selection.
We propose a novel method for biomarker selection and classification using the ROC technique for genomic data. The proposed method uses a sigmoid approximation to the area under the ROC curve as the objective function for classification and the threshold gradient descent regularization method for estimation and biomarker selection. Tuning parameter selection based on the V-fold cross validation and predictive performance evaluation are also investigated. The proposed approach is demonstrated with the Colon cancer study and a HIV vaccine study. The proposed approach yields parsimonious models with excellent classification performance.
<--- 2005 Index