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Research Seminars: Probability and Statistics

Spring 2019

Time & Location: All talks are on Wednesdays in Gibson Hall 126 at 3:00 PM unless otherwise noted.
Organizer: Scott McKinley and Swati Patel

Archives

September 4
Title: TBA
Speaker | INSTITUTION
Abstract: TBA
 
September 11
Title: TBA
Speaker | INSTITUTION
Abstract: TBA
 
September 18
Title: TBA
Speaker | INSTITUTION
Abstract: TBA
 
September 25
Title: TBA
Speaker | INSTITUTION
Abstract: TBA
 
October 2
Title: Landscape configuration drives persistent spatial patterns of occupant distributions
Elizabeth Hamman | Tulane, Mathematics
Abstract:

Variation in the density of organisms among habitat patches is often attributed to variation in inherent patch properties. For example, higher quality patches might have higher densities because they attract more colonists or confer better post-colonization survival.

However, variation in occupant density can also be driven by landscape configuration if neighboring patches draw potential colonists away from the focal habitat (a phenomenon we call propagule redirection).

Here, we develop and analyze a stochastic model to quantify the role of landscape configuration and propagule redirection on occupant density patterns. We model a system with a dispersive larval stage and a sedentary adult stage. The model includes sensing and decision-making in the colonization stage and density-dependent mortality (a proxy for patch quality) in the post-colonization stage.

This investigation of how landscape variation can drive spatial patterns in the populations of occupants set the stage for our forthcoming work, where we study how the spatial distribution of the occupants can in turn affect the shape of the landscape itself.
 
October 16
Clifford Lectures
 
October 23
Title: Stochastic persistence and extinction
Alex Hening | Tufts University
Abstract: TBA
 
October 30
Title: TBA
Heather Zinn Brooks | UCLA
Abstract:

A key question in population biology is understanding the conditions under which the species of an ecosystem persist or go extinct. Theoretical and empirical studies have shown that persistence can be facilitated or negated by both biotic interactions and environmental fluctuations. We study the dynamics of n interacting species that live in a stochastic environment. Our models are described by n dimensional piecewise deterministic Markov processes. These are processes (X(t), r(t)) where the vector X denotes the density of the n species and r(t) is a finite state space process which keeps track of the environment. In any fixed environment the process follows the flow given by a system of ordinary differential equations. The randomness comes from the changes or switches in the environment, which happen at random times. We give sharp conditions under which the populations persist as well as conditions under which some populations go extinct exponentially fast. As an example we show how the random switching can `rescue' species from extinction. The talk is based on joint work with Dang H. Nguyen (University of Alabama).
 
November 6
Title: Recent Advances in Statistical Inference for Stochastic PDEs
Igor Cialenco | Department of Applied Mathematics; Illinois Institute of Technology
Abstract:

In the first part of the talk we will discuss the parameter estimation problems for discretely sampled SPDEs driven by an additive space-time white noise.  We will present some general results on derivation of consistent and asymptotically normal estimators based on computation of the p-variations of stochastic processes and their smooth perturbations, that consequently are conveniently applied to SPDEs. Both the drift and the volatility coefficients are estimated using two sampling schemes that use surprisingly little information: observing the solution at a fixed time and on a discrete spatial grid, and at a fixed space point and at discrete time instances of a finite interval.
 
In the second part of the talk we will examine the statistical properties of stochastic evolution equations driven by space-only noise, either additive or multiplicative. We exploit the somewhat unusual structure of the observations coming from these equations that leads to an interesting interplay between classical and non-traditional statistical models. We derive several types of estimators for the drift and/or diffusion coefficients of these equations and prove their relevant properties.  The theoretical results will be illustrated via numerical examples.
 
November 13
Title: TBA
Alejandra Avalos Pacheco | Harvard Medical School
Abstract: TBA
 
November 20
Title: TBA
Jeffrey Kuan | Texas A&M
Abstract: TBA

November 27
Title: TBA
Speaker | INSTITUTION
Abstract: TBA
 
December 4
Title: TBA
Guillaume Remy | Columbia University
Abstract: TBA