Joint Scientific Computing and Probability Seminar
University of California, Berkeley, California | |
Equations by Parallel Marginalization | |
Abstract: Markov chain Monte Carlo sampling methods often suffer from long correlation times. Long correlation times indicate that the Markov chain must be run for many time steps to generate an independent sample. In this talk a method is proposed to overcome this difficulty. The method utilizes information from rapidly equilibrating coarse Markov chains that sample marginal distributions of the full system. This is accomplished through exchanges between the full chain and the auxiliary coarse chains. Results of numerical tests on the bridge sampling and filtering/smoothing problems for a stochastic differential equation are presented.
Brown University Center for Statistical Sciences Seminar
University of North Carolina at Chapel Hill | |
(Refreshments beginning at 3:15pm) |
Abstract: In the first part of this talk, we develop a procedure for Bayesian variable selection in a regression mixture framework, motivated by the problem of discovering gene regulatory networks from genomic sequence and gene expression microarray data. A typical procedure often used is to cluster the expression data, followed by a search for gene regulatory motifs in promoter sequences of clustered genes. This stepwise approach ignores uncertainty in the sequence part of the model when modeling expression and vice-versa, leading to biases in parameter estimation, construction of non-significant clusters, and errors in motif discovery. We devise a novel unified Bayesian framework and a hybrid Monte Carlo procedure to simultaneously determine the latent groupings of genes and unknown sets of motifs involved in their regulation, from a large number of potential regulators. A statistical challenge that one immediately encounters is that the number of regression covariates (p) greatly exceeds the number of observations (n) in one or more clusters, leading to model non-identifiability in which parameters cannot be estimated. We develop a methodology for the specification of a class of prior distributions based on a generalization of the g-prior (Zellner 1986), having a ``ridge'' parameter that leads to posterior propriety of the regression coefficients even if p > n. Our methodology is demonstrated though simulation studies and an application to a yeast data set.
In the second part of the talk, we generalize the ``ridge'' g-prior model specification introduced in the first half, for more complex regression scenarios, focusing primarily on generalized linear models (GLMs). This generalized version of the prior, called the information matrix (IM) prior, is discovered to have several attractive properties, including being semiautomatic in nature and requiring very little hyper-parameter specification. It reduces to Jeffreys' prior as a limiting case, and to a Gaussian prior when the information matrix is independent of the regression coefficients. We illustrate operating characteristics of this prior through analytical and empirical investigations in the context of GLMs with high dimensional covariates.
Candidate for Assistant Professor in the Biostatistics Section of the Program in Public Health
Brown University --
Center for Computational Molecular Biology
Seminar Series Lecture
University of Maryland Biotechnology Institute | |
Refreshments will be served at 3:45 pm |
Abstract: How does genetic variation influence disease susceptibility? To partly address this question we have developed structure and sequence based models of the impact of SNPs on protein function in vivo. The models have been applied to a set of single nucleotide variants known to cause monogenic disease, and to a set found in the Human population, not known to be associated with disease. There are two surprising findings: First, most monogenic disease causing variants act by mildly destabilizing protein structure^{1}. The results imply that most proteins are only just sufficiently stable to operate effectively in vivo, and suggest a possible general strategy for developing therapeutics. Second, about a quarter of the population SNPs appear to seriously impair function at the molecular level^{2}. Examination of a set of these cases suggests a variety of mechanisms that make the larger scale system robust with respect to component defects. Network level robustness analysis has the potential to identify those SNPs that most likely contribute to susceptibility to complex diseases. To facilitate this, we we have integrated all the pertinent data into a `knowledgenet' interface (www.snps3d.org)^{3}, allowing rapid assessment of the known relationships between proteins relevant to a particular disease, as well as access to molecule level information and in the supporting literature.
Brown University Mathematics Department
Special Colloquium
Brown University, Division of Applied Mathematics
Transatlantic Seminar
Abstract:
Outer billiards is a basic dynamical system based on a planar convex
shape, B.H. Neumann introduced outer billiards in the 1950s and J. Moser
popularized it in the 1970's, noting connections between it and celestial
mechanics. All along, one of the central questions has been:
Does there exist an outer billiards system with an unbounded orbit. In this
talk I will show that outer billiards for the Penrose kite has an unbounded
orbit. The Penrose kite is the convex quadrilateral that arises in
connection with the famous Penrose tilings. My proof relates the problem to
self-similar tilings, polygon exchange maps, and arithmetic dynamics.
PDE Seminar
Abstract: I will talk about the stability problem of two-dimensional solitary waves arising in a hyperelastic plate with stiffness effect taken into account. I will show that this stiffness effect permits the existence and stability of solitary waves.
<--- 2007 Index