Brown Analysis Seminar
Abstract: The theory of geometric discrepancy studies different variations of the following question: how well can one approximate a uniform distribution by a discrete one, and what are the limitations that necessarily arise in such approximations. Historically, the methods of harmonic analysis (Fourier transform, Fourier series, wavelets, Riesz products etc) have played a pivotal role in the subject. I will give an overview of the problems, methods, and results in the field and discuss some latest developments and connections with problems in probability and approximation.
Brown University Center for Statistical Sciences Seminar
Abstract:
We consider hierarchical functional data experiments that arise naturally in
our colon carcinogenesis experiments. The data are at three levels: individual
rats have multiple colonic crypts, and within each colonic crypt, multiple
measurements of biomarkers are made depending on the location of cells. In
such experiments, it is typical to assume that conditional on the individual,
the functions at the crypt level are independent. However, the biology
suggests that the functions probably are not independent, conditional on the
individual, and they are instead spatially correlated, and it is of
considerable interest to understand whether this is true and, if so, to
quantify the degree of dependence.
In our example, the marker p27 is analyzed (p27 is a predictor of programmed
cell death and cell proliferation). We will exhibit both fixed effects and
random effects approach. We exhibit frequentist and Bayesian analyses of these
problems, analyses that suggest surprisingly strong spatial correlations
among the functions. We also provide an alternative, completely nonparametric
approach.
***Faculty Search Candidate Talk***
Abstract: Inexact Newton methods play a fundamental role in the solution of large-scale unconstrained optimization problems and nonlinear equations. The key advantage of these approaches is that they can be made to emulate the properties of Newton's method while allowing flexibility in the computational cost per iteration. Due to the multi-objective nature of *constrained* optimization problems, however, that require an algorithm to find both a feasible and optimal point, it has not been known how to successfully apply an inexact Newton method within a globally convergent framework. In this talk, we present a new methodology for applying inexactness to the most fundamental iteration in constrained optimization: a line-search primal-dual Newton algorithm. We illustrate that the choice of merit function is crucial for ensuring global convergence, and discuss novel techniques for handling non-convexity, ill-conditioning, and the presence of inequality constraints in such an environment. Preliminary numerical results are presented for PDE-constrained optimization problems.
Brown University Center for Statistical Sciences Seminar
Abstract:
The predictiveness curve was recently proposed as a graphical tool to evaluate
risk prediction markers or models by portraying the population distribution of
risk conveyed by a model. In this talk, I will propose generalization of this
technique for evaluating biomarkers as surrogate endpoints.
In a randomized trial, substituting surrogate endpoints for the primary clinical
endpoint can save time and cost when comparing interventions. Biomarkers
identified might also help elucidate treatment mechanism. Recently a new
definition of surrogate endpoint, the `principal surrogate', was proposed
based on causal treatment effect. Despite its appealing statistical properties,
limited research has been conducted with regard to this concept, and existing
methods focus on models of a single marker. How to make a clinically
meaningful comparison between general risk models with respect to their
principal surrogate values remains an open research question.
I will present a novel summary measure derived from the predictiveness curve
for comparing the surrogate value of markers and for assessing the increment
in principal surrogacy gained by adding a marker to a baseline risk model. I
will propose a semiparametric pseudo-likelihood method to estimate the joint
principal surrogate value of multiple biomarkers. This method is more widely
applicable than nonparametric methods by incorporating continuous baseline
covariates to predict potential biomarker value, and more robust than
parametric methods by leaving the error distribution of markers unspecified. I
will illustrate the methodology using a simulated example set in the context of
HIV vaccine trials, where the use of immune responses as surrogate endpoints
for HIV infection is evaluated.
Candidate for Assistant Professor in the
Biostatistics Section of the Program in Public Health
***Faculty Search Candidate Talk***
Abstract: This talk presents a strategy for computational wave propagation that consists in decomposing the solution wavefield onto a largely incomplete set of eigenfunctions of the weighted Laplacian, with eigenvalues chosen randomly. The recovery method is the ell-1 minimization of compressed sensing. For the mathematician, we establish three possibly new estimates for the wave equation that guarantee accuracy of the numerical method in one spatial dimension. For the engineer, the compressive strategy offers a unique combination of parallelism and memory savings that should be of particular relevance to applications in reflection seismology. Joint work with Gabriel Peyre.
Center for Computational Molecular Biology Seminar
Faculty candidate | |
Abstract:
The various genetic variation discovery projects (The SNP Consortium, The
HapMap, The 1000 Genomes Projects etc.) aim to identify as much as possible of
the underlying genetic variation in different human populations. The question
we address in this talk is how many new (not yet seen) genetic variants are
yet to be found.
We regard this question as an instance of the species problem in ecology,
where the goal is to estimate the number of unseen species in a closed
population. Using a parametric empirical Bayes model, we propose a method to
estimate the number of new variants with a desired minimum frequency to be
discovered in future studies, based on observed sequence data for a small
number of individuals. The approach can also be used to predict the number of
individuals necessary to sequence in order to capture all (or a fraction of)
the variation with a specified minimum frequency.
We show results based on sequence data from four human populations, and
discuss applications of these methods in the context of disease association
studies with rare variants.
Lecture: Thursday, Feb. 12th 2009 4:30pm C.I.T. SWIG ~ Room 241
Chalk Talk: Friday, Feb. 13, 2009 Noon 182 George St~Rm 110