Monday, October 5, 2009 at 3:00 PM in SAS 4201
Dr. Avanti Athreya, SAMSI
Metastability in a nearly-Hamiltonian system
Metastability can be understood through the theory of large
deviations for dynamical systems subject to random
perturbations. In particular, we present some results on
averaging and metastability in a Hamiltonian system with
both deterministic and random perturbations.Monday, October 19, 2009 at 3:00 PM in SAS 4201
Julien Cornebise, Duke university and SAMSI
Adaptation and Sequential Monte Carlo algorithms: new theory and algorithms
In the last 15 years, Sequential Monte Carlo
algorithms, also known as particle filters or sequential importance sampling, have reached
widespread use in the most intricate problems, ranging from
non-linear non-gaussian stochastic filtering to Bayesian sequential
estimation, with applications to finance, signal processing,
robotics, and population genetics, to name a few.
They basically in at approximating a sequence of intricate distributions by
updating a weighted sample through Markovian probability kernels, hence sampling
from "easy" distributions, and reweighting by adequate Radon-Nikodym derivatives.
In this talk, we will show how state-of-the-art Sequential Monte algorithms,
encompassed in the auxiliary particle filter framework from Pitt and
Shephard (1999, JASA), can be taken to new heights and deal with
models of soaring complexity, including multi-modal or highly
non-linear target kernels and distributions.
We will first present new theoretical results that serve as a basis to our
algorithms -- rather than empirical ad hoc methods, as has been
common practice so far. We link common quality criteria (namely the
coefficient of variation and entropy of the importance weights) to
commonly used divergences between probability measures, such as chi-square and
Kullback-Leibler divergence, both asymptotically and for finite sample size.
We will then show how adaptation of the proposal kernel and of the adjustment
multiplier weights stem from these criteria, sharing common ground with pilot
sampling, mixture of experts, EM algorithm and its SAEM and MCEM
variants.
After simulation examples that allow for both rigorous and intuitive
visual interpretation, we will conclude on the perspective of
extensions to the latest Sequential Monte Carlo methods, such as the
SMC samplers of Del Moral, Doucet and Jasra, (2006, JRSSB).Monday, November 9, 2009 at 3:00 PM in SAS 4201
Linyuan Li, University of New Hampshire
On Non-Parametric Wavelet Regression with Long Memory Errors
We consider the wavelet-based estimators of the mean regression functions with long memory errors (e.g., fractional Gaussian processes or infinite moving average processes) and investigate their asymptotic rates of convergence of estimators based on thresholding of empirical wavelet coefficients. We show that these estimators achieve nearly optimal minimax convergence rates with a logarithmic term over a large range of Besov function classes. Therefore, in the presence of long memory correlated errors, our estimators still achieve nearly optimal convergence rates.
Thursday, November 19, 2009 at 2:30 PM in SAS 4201
Matthew Nicol, University of Houston Mathematics Department
Statistical properties of dynamical systems
We discuss recent progress in understanding certain key statistical properties of nonuniformly hyperbolic dynamical systems, in particular large deviations, extreme value theory and approximation by Brownian motion.Monday, November 23, 2009 at 3:00 PM in SAS 4201
Kevin Lin, University of Arizona
Nonequilibrium Steady States of Certain Dynamical Transport Models
In statistical physics, "nonequilibrium steady states" refer to the
processes that take place in systems maintained out of thermal
equilibrium, for example heat flow across a rod whose ends are held at
different temperatures. This talk concerns nonequilibrium steady
states in a class of models introduced by J.-P. Eckmann and L.-S.
Young as paradigms for transport processes. In these models,
energetic particles are injected and absorbed by heat reservoirs into
the system at the boundary; these particles interact with local
degrees of freedom and carry energy around the system. I will review
a strategy for predicting macroscopic profiles (e.g., mean energy at
each site) in these models using the assumption of local thermal
equilibrium (LTE). I will discuss numerical evidence for the
effectiveness of this prediction strategy and the validity of the LTE
assumption, as well as the results of a numerical study of spatial
correlations in these models.
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Seminar Organizer: Min Kang