Lefschetz Center for Dynamical Systems Seminar
Brown University-Division of Biology and Medicine, Center for Statistical Sciences Seminar
Abstract: For independent data, nonparametric likelihoods based on empirical family have proved useful competitors to empirical likelihoods. This talk will examine nonparametric likelihoods for serially correlated data using an empirical exponential family supported on blocks of data. Blocking has proved useful in resampling analysis of serially correlated data. Explicit construction of such a likelihood will be outlined for the case of the autoregressive coefficient of an AR(1) process. Simulated numerical illustrations will show the comparative coverages of nonparametric and normal-theory confidence intervals. Some asymptotic results will be mentioned.
*This is a joint work with Professor David Hinkley at UC, Santa Barbara.
Special Brown University, Division of Applied Mathematics Seminar
Abstract: At each site (i,j) in a 2-dimensional lattice, we attach an identically distributed, independent random variable. We regard, for example, the random variable at each site as the time required to pass through that site. Then the interest is in the last passage time to go from the site (1,1) to the site (M,N) along directed paths, as M,N tend to infinity. This last passage percolation problem has applications to random growth models, queuing theory and interacting particle systems. In recent years, the limiting distribution of the last passage time, after suitable centering and scaling, has been found for a few special cases of random variables. We also discuss the symmetrized versions of last passage percolation models.
Center for Fluid Mechanics Seminar
Abstract:
Particle Image Velocimetry (PIV) is used to study the slow
settling motions of spheres in suspensions ranging from dilute
to highly concentrated,$0.0001<.\phi<0.50$.
During sedimentation,
particle velocity fluctuations are found to be organized into
regions of characteristic size $\xi\sim 11\alpha\phi^{-1/3}$.
A simple model, based upon buoyant mass fluctuations $\Delta m$
given by random density fluctuations in a region of size $\xi$,
accurately predicts the magnitudes of the velocity fluctuations
$\Delta V$. We also find a new universal relation for particle
diffusion during sedimentation. It can be written in a Stokes-
Einstein form as $D\sim(\Delta mg\xi)/(6\pi\eta\xi)$, where
the effective temperature $\Delta mg\xi$ is the gravitational
potential energy of density fluctuations. In addition related
experiments examining inertial effects and transient states,
that are aimed at uncovering the origin of the new lengthscale
$\xi$, will also be given.
[1]P.N. Segre et al., Nature, 409, 594 (2001).
Special Mathematics Department Geometry Seminar
Brown University - Center for Statistical Sciences Seminar
Candidate for Assistant/Associate Professor, Community Health | |
Abstract: When testing a hypothesis, the sample size should be large enough to insure sufficient Power while not wasting resources or unnecessarily introducing ethical concerns. In comparison to sample size methods for hypothesis testing, very few methods have been developed for choosing an optimal sample size for confidence interval construction. Common methods seek to establish a sample size to obtain a specified width, defined as the event that the distance between the upper and lower limits of the confidence interval is no larger than a specified constant. Such calculations ignore validity, defined as the event that the interval contains the parameter of interest, and rejection, defined as the event that the interval excludes the null value. Current confidence interval sample size methods typically are based only on Width considerations. By neglecting the notions of Validity and Rejection, the methods often provide a sample size with a low likelihood of achieving other desired goals. By incorporating concern for Validity and Rejection, as well as Width, in choosing a sample size for finding confidence intervals, a higher likelihood of success can be achieved. This new sample size calculation can be written in terms of a probability which generalizes the concept of Power. An exact closed form is derived in the General Linear Multivariate Model with Gaussian errors. A motivating example and numerical results and plots are presented which emphasize the dramatic errors that can be made when sample size computations are not properly aligned with study outcomes.
Brown University Center for Statistical Sciences Seminar
University of Southern California Candidate for Assistant Professor, Department of Community Health | |
Abstract: Calibration studies are often performed on a subgroup contained within or external to large studies, for the purpose of correcting risk estimates for the effect of measurement errors. In this paper, we present a method to optimally allocate the number of subjects in the main cohort and calibration studies by minimizing the total cost while maintaining a fixed statistical power to detect a specified log relative risk. Measurement errors in the observed exposure are allowed to be subject to both random and systematic errors. We deal with the case when a gold standard is not available and repeated reference measures are obtained in calibration studies. It is shown that non-optimal choice of the number of replicates of reference measures per calibration study subject could result in a considerable waste of resources. Furthermore, the cost-efficient design is extended to a multivariate setting where covariates in the risk model are correlated. As the correlation between two covariates becomes stronger, the optimal sizes for both main cohort and calibration studies increase.
Scientific Computing Seminar
Special Brown University, Division of Applied Mathematics Seminar
Technion, Haifa, Israel | |
Abstract: I will begin by reviewing some recent concentration and large deviations results for the spectral measure of large random matrices. Then, I will explain how performance evaluation for multi-user communication leads to the study of the asymptotics of certain integrals over the unitary/ orthogonal groups, treated previously by Itzykson and Zuber in the physics literature. Using an appropriate stochastic analysis machinery and large deviations theory, I will describe how A. Guionnet and myself evaluated these (logarithmic)asymptotics.
PDE Seminar
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