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| 2006-07 seminars 2005-06 seminars Seminars 2007-2008 past Upcoming WEDNESDAY
April 30,
2008 - SOBEL LECTURE
[Event
Flyer] Dirichlet
orderings, differential expression, and gene sets WEDNESDAY May 14, South Hall 5607F, 3:15 PM, Refreshments served at 3:00 PM Dorota M. Dabrowska, University of California, Los Angeles Bivariate proportional hazard regression models In this talk I will discuss application of marked point processes in real time towards defining bivariate proportional hazard models and estimation of their parameters in the presence of monotone and non-monotone censoring. The approach applies to both single and multi-type models. WEDNESDAY May 21, South Hall 5607F, 3:15 PM, Refreshments served at 3:00 PM Chi-hong Tseng, University of California, Los Angeles Non-parametric Estimation of a Survival Function with Two-stage Design Studies The two-stage design is popular in epidemiology studies and clinical trials due to its cost effectiveness. Typically, the first stage sample contains cheaper and possibly biased information, while the second stage validation sample consists of a subset of subjects with accurate and complete information. In this paper, we study estimation of a survival function with right-censored survival data from a two-stage design. A non-parametric estimator is derived by combining data from both stages. We also study its large sample properties and derive pointwise and simultaneous confidence intervals for the survival function. The proposed estimator effectively reduces the variance and finite-sample bias of the Kaplan~VMeier estimator solely based on the second stage validation sample. Finally, we apply our method to a real data set from a medical device postmarketing surveillance study.
Mathew Penrose, University of Bath, UK A
survey of Random Geometric Graphs WEDNESDAY October 3, South Hall 5607F, 3:15 PM, Refreshments served at 3:00 PM Stephane Villeneuve (Toulouse, France, visiting PSTAT) Title: Optimal dividend policy and growth option We analyse the interaction between dividend policy and investment decision in a growth opportunity of a liquidity constrained firm. This leads us to study a mixed singular control/optimal stopping problem for a diffusion that we solve quasi-explicitly establishing connection with an optimal stopping problem. We characterize situations where it is optimal to postpone dividend distribution in order to invest at a subsequent date in the growth opportunity. We show that uncertainty and liquidity shocks have ambiguous effect on the investment decision. WEDNESDAY October 10, South Hall 5607F, 3:15 PM, Refreshments served at 3:00 PM Helgi Tomasson (University of Iceland, visiting PSTAT) Some Computational Aspects for Inference on Diffusion Processes The theory of diffusion processes is fundamental for modern mathematical-finance. Real data are assumed to be observations of a continuous-time process at discrete time-points. The statistical toolbox for financial data is briefly reviewed. A computer program, written in R, for approximation of the likelihood function for some simple processes is shown. The approximation is based on a Taylor-expansion of the Kolmogorov-forward equation in the spirit of Ait-Sahalia(1999, 2002). Properties of maximum-likelihood estimators are illustrated by simulation. Some aspects of applying the approximation to Bayesian inference and statistical-surveillance (change-point-detection) are discussed WEDNESDAY October 17, South Hall 5607F, 3:15 PM, Refreshments served at 3:00 PM Hyekyung Min (postdoc, PSTAT) Title: A Stochastic Control Model of Optimal Dividend and Capital Financing The stochastic control model, introduced by Peura and Keppo (2006), is considered for valuing a firm whose capital evolves according to Brownian motion with a drift. The firm controls the flow of capitals not only by paying out the dividends but also by raising the capital in the presence of fixed cost (K) and delay (D). A solution to this control problem is obtained by solving a system of quasi-variational inequalities. It is shown that a unique solution exists for all values of K >= 0 and D > 0. The asymptotic behavior of the optimal dividend and capital issue barriers, and the ruin probability and the expected lifetime of the firm following the optimal policy will be discussed. Wednesday,
Oct 24th, Source Separation algorithms applied to cerebral signals Physiological
activity in the brain can be evaluated by means of non-invasive
electrophysiological techniques like electroencephalogram, EEG,
and magnetoencephalogram, MEG: such instruments are able to obtain
cerebral processing measures with the optimal time resolution.
The crucial problem is then to gain access to the inner neural
code starting from the extra-cranial recordings: cerebral signals
related to significant activity are mixed and embedded in unstructured
noise and in other physiological artefacts, non relevant to the
desired observation. To deal with this problem, a statistical-based
approach has been recently introduced, based on exploiting statistical
properties of sources composed in the observed signals without
any assumption about the biophysical model underlying the recorded
signals. In particular, the “Independent Component Analysis” (ICA)
model assumes that sources are statistically mutually independent;
to extract them from the mixture a measure of non-gaussianity
is maximized (i.e. kurtosis). Wednesday,
October 31, South Hall 5607F, 3:15 PM, Refreshments served at
3:00 PM BOOTSTRAP DIAGNOSTICS Over the past two decades bootstrap methods have become increasingly widely used in statistical applications. Apparently "easy" solutions for a wide range of statistical problems, together with wide availability of cheap/fast computing has seduced many researchers into using resampling (bootstrap) methods for just about anything. But the validity and accuracy of bootstrap methods do require some assumptions. This talk will describe methods for checking some of the assumptions for specific contexts, and for some cases will describe appropriate modifications of bootstrap methods to make them more reliable. [This is joint work with Angelo Canty, Anthony Davison and Valerie Ventura.] CANCELLED Tests for Exponentiality Based on Characterizations There is considerable literature on the problem of testing for exponentiality. The reasons are many-fold and chief among these are: the watershed role played by the exponential distribution in reliability and survival analysis, its nice mathematical properties, as well as the availability of several characterizations. In the talk, some test statistics based on characterizations will be reviewed. Characterization based on spacings and constancy of the mean residual life will be considered in detail. After discussing the construction of test statistics for the hypothesis of exponentiality, the relevant asymptotic theory will be discussed. To assess the performance of the proposed procedures, the approximate Bahadur slope as well as Monte Carlo power studies against several common alternatives to exponentiality will be provided. Power comparisons with other classical and recent tests for exponentiality, show that in most cases the test procedures proposed compare very well with their competitors.
Wednesday,
Nov 14, South Hall 5607F, 3:15 PM, Refreshments served at 3:00
PM Discrete Approximations to Reflected Brownian Motion
In this talk, we will present three discrete or semi-discrete
approximation schemes for reflected Brownian motion on bounded
Euclidean domains. For a class of bounded domains $D$ in $R^n$
that includes all bounded Lipschitz domains and the von Koch snowflake
domain, we show that the laws of both discrete and continuous
time simple random walks on $D\cap 2^{-k} Z^n$ moving at rate
$2^{-2k}$ with stationary initial distribution converge weakly
in the space $D([0, 1], R^n)$, equipped with the Skorokhod topology,
to the law of the stationary reflected Brownian motion on $D$.
We further show that the following ``myopic conditioning'' algorithm
generates, in the limit, a reflected Brownian motion on any bounded
domain $D$. For every integer $k\geq 1$, let $\{X^k_{j2^{-k}},
j=0, 1, 2, \dots \}$ be a discrete time Markov chain with one-step
transition probabilities being the same as those for the Brownian
motion in $D$ conditioned not to exit $D$ before time $2^{-k}$.
We prove that the laws of $X^k$ converge to that of the reflected
Brownian motion on $D$. These approximation schemes give not only
new ways of constructing reflected Brownian motion but also implementable
algorithms to simulate reflected Brownian motions. Wednesday, Nov. 28, South Hall 5607F, 3:15 PM, Refreshments served at 3:00 PM Dr. Phillip M. Feldman (Systems Performance, Northrop Grumman Space Technology) A Random Sample of Applied Statistics Problems from Northrop Grumman Abstract: The talk will begin with a brief overview of the Space Technology sector of Northrop Grumman and some background about the life cycle of space systems. This will be followed by discussion of two or three open statistical problems that arose in connection with engineering projects. Monday,
Dec 10, South Hall 5607F, 3:15 PM, Refreshments served at 3:00
PM Hedging and pricing with execution delay. We
consider impulse control problems in finite horizon for diffusions
with decision lag and execution delay. The new feature is that
our general framework deals with the important case when several
consecutive orders may be decided before the effective execution
of the first one. Monday,
January 7th, 2:30pm, Refreshments served at 2:15pm Nonparametric Assessment of Properties of Space-Time Covariance Functions and its Application in Paleoclimate Reconstruction Abstract: Friday,
January 11th, 3:15-4:15PM, South Hall 5607F,refreshments served
at 3:00PM Models for Models: Statistical Methods for Climate Model Output and Other Massive Datasets I
will present two novel statistical methods applicable to analyzing
climate model output. The first, likelihood approximation using
covariance tapering, is useful in analyzing the large spatial
datasets that climate models often produce, for which The second method addresses the question of how we can attribute sources of variability in climate model output. In particular, I will consider regional climate models (RCMs). RCMs address smaller spatial regions than do global climate models (GCMs), but their higher resolution better captures the impact of local features such as lakes and mountains. GCM output is often used to provide boundary conditions for RCMs, and it is an open scientific question how much variability in the RCM output is attributable to the RCM itself, and how much is due simply to large-scale forcing from the GCM. I will consider data from the Prudence Project, in which RCMS were crossed with GCM forcings in a designed experiment. Using this dataset as a motivating example, I will present a framework for Bayesian functional ANOVA modeling using Gaussian process prior distributions. In this framework, inference can be carried out either in a summary fashion, by examining the joint posterior distribution of the covariance parameters in the corresponding Gaussian processes, or locally, by studying functional and fully Bayesian versions of the usual ANOVA decompositions. These decompositions can be used to create useful graphical displays summarizing the contributions of each factor across space. MONDAY
Jan 14, 3:15-4:15PM, South Hall 5607F,refreshments served at
3:00PM Pricing and Hedging of Convertible Bonds with Credit Risk In our works [3]-[6], we attempt to shed more light on mathematical modeling of convertible bonds, thus continuing the previous research presented, for instance, in Andersen and Bu®um [1], Ayache et al. [2], Davis and Lischka [7], Kallsen and KÄuhn [8], and Kwok and Lau [9]. In [3], we consider the problem of the decomposition of a convertible bond into a bond component and an option component. This decomposition is indeed well established in the case of an `exchange option', when the conversion can only occur at maturity, and there are no put or call clauses. However, it was not previously studied in the general case of a defaultable convertible bond with call and/or put covenants. In [4], we specify the valuation results for a defaultable game option (in particular, a convertible bond) to the context of default risk model based on the hazard process. The approach is based on the reduction of the information flow from the full ¯ltration to the reference ¯ltration. Our main existence result for hedging strategies in a hazard process set-up can be informally stated as follows: under the assumption that a related doubly re°ected BSDE admits a solution under some risk-neutral measure, the state-process multiplied by the default indicator process is the minimal super-hedging price up to a sigma martingale cost process. The associated hedging strategies are subsequently analyzed by means of a martingale decomposition of a solution to the related doubly reflected BSDE. It is worth stressing that these decompositions are by no means arti¯cial. On the contrary, they arise naturally in the context of a Markovian framework, which is studied in some detail in the follow-up paper [5]. Under a rather general speci¯cation of the in¯nitesimal generator of a driving Markov factor process, we develop in [5] the variational inequality approach to pricing and hedging of a defaultable game option. In [6], we consider a Markovian diffusion set-up with default. In this model, we show that a doubly reflected BSDE related to the convertible security has a solution, and we provide the related super-hedging strategy. Moreover, we characterize the price of a convertible security in terms of a viscosity solution of the associated variational inequality and we prove the convergence of a suitable approximation scheme. References Wednesday,
Jan. 16, South Hall 5607F, 3:15 PM, Refreshments served at 3:00
PM On the Path to Extinction Short abstract: Populations can certainly die out for divers reasons, the most basic probably being through stably unsufficient reproductive power (whatever the ground for that may be). Even in this case there is an abundance of paths to extinction. Still, if the starting population is large, a simple and beautiful pattern emerges, where random and determistic effects are of roughly the same order of magnitude. We describe this path and the time to extinction of large subcritical branching populations, and discuss whether mathematically 'large' could be biologically 'small' (=threatened) Friday,
January 18th, South Hall 5607F, 2:00PM, refreshments served
at 1:45PM. Copula Based Independent Component Analysis We propose a parametric version of Independent Component Analysis (ICA) via Copulas - families of multivariate distributions that join univariate margins to multivariate distributions. Our procedure exploits the role for copula models in information theory and in measures of association, specifically: the use of copulae densities as parametric mutual information, and as measures of association on the rank statistics. Friday,
January 18th, South Hall 5607F, 3:15PM, refreshments served
at 3:00PM Tradeable Measures of Risk
The main idea of this talk is to introduce Tradeable Measures
of Risk as an objective and model independent way of Tuesday,
January 22nd, South Hall 5607F, 10:00AM, refreshments served
at 9:45am. Optimal Stopping and Optimal Switching for Hidden Markov Models We study optimal stopping and optimal switching problems for hidden Markov chains with Poissonian information structures. In our model, the controller maximizes expected rewards that depend on an unobserved Markovian environment with information collected through a (compound) Poisson observation process. Examples of such systems arise in investment timing, reliability theory, sequential tracking, and economic policy making. We solve the problem by performing Bayesian updates of the posterior likelihoods of the unobservable and studying the resulting optimization problem for a piecewise-deterministic process. We then prove the dynamic programming principle and explicitly characterize an optimal strategy. We also provide an efficient numerical scheme and illustrate our results with several computational examples. This is based on joint work with Semih Sezer and Erhan Bayraktar (U of M).
Wednesday,
January 23rd, South Hall 5607F, 3:15 PM, Refreshments served
at 3:00 PM Discovery of Latent Patterns with Hierarchical Bayesian Mixed-Membership Models and the Issue of Model Choice Model
choice is a major methodological issue in the explosive growth
of data-mining models involving latent structure for clustering
and classification, especially because models often have different
parameterizations and very different specifications and constraints.
Here, we work from a general formulation of hierarchical Bayesian
mixed-membership models and present several model specifications
and variations, both parametric and nonparametric, in the context
of learning the number of latent groups and associated patterns
for clustering units. We elucidate strategies for comparing
models and specifications by producing novel analyses of the
following two data sets: (1) a corpus of scientific publications
from the Proceedings of the National Academy of Sciences; (2)
data on functionally disabled American seniors from the National
Long Term Care Survey. Friday,
January 25rd, South Hall 5607F, 2:15 PM, Refreshments served
at 2:00 PM Designing Penalty Functions for Grouped and Hierarchical Selection Extracting
useful information from high-dimensional data is an important
focus of today's statistical research and practice. Wednesday,
February 13th, South Hall 5607F, 3:15 PM, Refreshments served
at 3:00 PM Mapping Ancient Forests: Bayesian Inference for Forest Composition Using the Fossil Pollen Proxy Record Ecologists are interested in understanding changes in tree species abundances and spatial distributions over thousands of years since the last glacial maximum. To estimate forest composition and investigate how much information is available from fossil pollen eposited in lake sediments, we build a Bayesian spatio-temporal hierarchical model that predicts forest composition in southern New England, USA, based on fossilized pollen. The critical relationships between abundances of taxa in the pollen record and abundances in actual vegetation are estimated using modern data and data from colonial records, for which both pollen and direct vegetation data are available. For these time periods, the model relates pollen and vegetation data to a latent multivariate spatial process representing forest composition, which allows estimation of several key parameters. For time periods in the past, we use only pollen data and the estimated model parameters to make predictions and assess uncertainty about the latent spatio-temporal process over the last 2000 years. A new graphical assessment of feature significance helps to infer which spatial patterns are reliably estimated. The modeling involves a complex hierarchical model that integrates disparate data sources. I will discuss a variety of issues arising in such models and the practical strategies we used to address them. I will also emphasize the importance of understanding which aspects of the data inform which aspects of the model. WEDNESDAY
Feb. 20, South Hall 5607F, 3:15 PM, Refreshments served at 3:00
PM Functional-based Multi-level Modeling of Multiple Longitudinal Outcomes: with applications to environmental epidemiology Flexible multi-level models are proposed to allow for cluster specific smooth estimation of growth curves, in a mixed-effects modeling format that includes subject-specific random effects on the growth parameters. Attention is then focused on models that examine between-cluster comparisons of the effects of an ecologic covariate of interest (e.g., air pollution) on nonlinear functionals of growth curves (e.g. maximum rate of growth). A Gibbs sampling approach is used to get posterior mean estimates of nonlinear functionals along with their uncertainty estimates. A second-stage ecologic random effects model is used to examine the association between a covariate of interest (e.g., air pollution) and the nonlinear functionals. A unified estimation procedure is presented along with its computational and theoretical details. This work is further extended to allow for modeling of multiple outcomes via a latent variable approach in order to connect several outcomes from a subject. The models are motivated by, and illustrated with, lung function, asthma and air pollution data from the Southern California Children's Health Study. WEDNESDAY
Feb. 27, South Hall 5607F, 3:15 PM, Refreshments served at 3:00
PM
Amy Braverman(Jet Propulsion Laboratory, California Institute of Technology) Massive Data Set Analysis for NASA's Atmospheric Infrared Sounder NASA's Atmospheric Infrared Sounder (AIRS) has been collecting large quantities of remote sensing data about the vertical structure of Earth's atmosphere since AIRS was launched aboard the Aqua spacecraft in mid-2002. These data pose a classic problem in the analysis of massive data sets: how do we understand the relationships among fine-scale phenomena within their global context? We answer that question here by partitioning the data on a coarse spatio-temporal grid, and estimating the multivariate distribution of the data within each grid cell. Then, we look for patterns in the evolution of those distributions as functions of space and time, and ultimately tie them back to physical phenomena generating the data sets. Quantifying this evolution is challenging because the data are high dimensional, and the distributions are complex. We attack the problem using the Wasserstein distance between distributions as a measure of similarity among grid cells' data, and therefore as a measure of similarity between the underlying physical processes. We close with some thoughts on how this strategy might be applied in other problems where massive data sets arise.
WEDNESDAY Markch 5, South Hall 5607F, 3:15 PM, Refreshments served at 3:00 PM Christopher Barr Voronoi-type estimators for spatial intensity A wide range of methods use Voronoi diagrams to estimate conditional intensity of an inhomogeneous Poisson point process. The inverse cell area (herein referred to as the Voronoi estimator) has been used as a simple, fully non-parametric estimator in neuroscience and astrophysics. Voronoi diagrams have also been used to build flexible prior distributions, and develop optimal quadrature approximations for psuedo-likelihood based approaches. The present work systematically investigates fundamental properties of the Voronoi estimator for inhomogeneous intensity. Known to be unbiased in the homogeneous case, we prove the Voronoi estimator is also approximately ratio unbiased in the inhomogeneous case, and that its bias goes to zero exponentially as conditional intensity increases. Simulation studies show the sampling distribution is well approximated by the inverse gamma model, but generally has high variance. Two additional Voronoi-type estimators (one based on the centroidal Voronoi diagram, the other using k-means clustering) are presented and offer more stable results. WEDNESDAY April 9, South Hall 5607F, 3:15 PM, Refreshments served at 3:00 PM Dr. Richard Sowers, Department of Mathematics at University of Illinois at Urbana-Champaigny A
propagation-of-chaos type result in stochastic averaging WEDNESDAY April 16, South Hall 5607F, 3:15 PM, Refreshments served at 3:00 PM Dr. Suojin Wang, Department of Statistics at the Texas A&M University A
New Semiparametric Procedure for Matched Case-Control Studies with
Missing Covariate Data THURSDAY April 17, South Hall 5607F, 3:30 PM-4:45PM Steve Snapinn, Vice President, Global Biostatistics and Epidemiology, Amgen Some
Statistical Problems in the Pharmaceutical Industry WEDNESDAY April 23, South Hall 5607F, 3:15 PM, Refreshments served at 3:00 PM Annie Qu, Department of Statistics at the Oregon State University Efficient aggregate unbiased estimating functions approach for correlated data with missing at random We develop a consistent and highly efficient marginal model for
missing at random data using an estimating function approach. Our |
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