Brown University Center for Statistical Sciences Seminar
Abstract: Existing methods in non-stationary time series classification assume time series from different units within a population are generated by the same underlying stochastic process such that unit-specific second-order spectral properties are the same. This is usually not true in real applications and can lead to misclassification. In this paper, we propose a model for a family of time series by imposing a hierarchical structure on their log-spectra. This model assumes that while a family of time series share some similarity characterized by the population-average spectrum, each time series has its own characteristics modeled by the unit-specific deviation in terms of its log-spectrum. We then propose nonparametric methods to estimate the population-average log-spectrum and the between-unit variance function. We develop a quadratic rule for discriminating between different populations based on the estimated mean log-spectra and the variance functions. A simulation study is presented to empirically demonstrate the benefits of accounting for the between-time-series variability and the proposed procedure is used to discriminate pre-seizure EEG time series from non-seizure baseline data. This is joint work with Wensheng Guo and Brian Litt.
Probability Seminar
Abstract: We will consider the second initial boundary problem in narrow domains of width $\epsilon\ll 1$ for linear second order differential equations with nonlinear boundary conditions. Using probabilistic methods we show that the solution of such a problem converges as $\epsilon \downarrow 0$ to the solution of a standard reaction-diffusion equation in a domain of reduced dimension. This reduction allows to obtain some results concerning wave front propagation in narrow domains. In particular, we describe conditions leading to jumps of the wave front. In addition, an important and interesting problem, which is related to the previous one, is the Wiener process with instantaneous reflection in a narrow tube which, in contrast to before, is assumed to be non-smooth asymptotically.
Brown Applied Mathematics Pattern Theory and Vision Lunch Seminar
Abstract:
This is a new time and a new format for the pattern theory seminar, so we will begin with an organizational meeting. Bring ideas for things you'd like to see in our seminar series. With the remaining time, I will discuss a semi-parametric conditional inference perspective for modeling data that have fast (and interesting) dynamics confounded with slow, non-stationary (and not so interesting) dynamics. This is work in progress with Asohan Amarasingham and Stuart Geman.
http://www.dam.brown.edu/ptg/seminar.html
[pizza will be provided]