The series hosts a seminar every other week on current research topics. The seminar often features an invited guest speaker and occasionally local faculty members, students or others affiliated with the department. The usual time of the seminar is 3:30-4:30 pm on Fridays. Professors Tatiyana V Apanasovich (email@example.com), Qing Pan (firstname.lastname@example.org) and Emre Barut (email@example.com ) are the Seminar Series Coordinators.
Date: Friday, April 17th, 3:30-4:30pm
Location: Duques Hall, Room 251
Title: Statistically and Computationally Efficient Estimating Equations for Large Spatial Datasets
Speaker: Ying Sun, King Abdullah University of Science and Technology (KAUST), Saudi Arabia
Abstract: For Gaussian process models, likelihood based methods are often difficult to use with large irregularly spaced spatial datasets, because exact calculations of the likelihood for n observations require O(n3) operations and O(n2) memory. Various approximation methods have been developed to address the computational difficulties. In this work, we propose new unbiased estimating equations based on score equation approximations that are both computationally and statistically efficient. We replace the inverse covariance matrix that appears in the score equations by a sparse matrix to approximate the quadratic forms, then set the resulting quadratic forms equal to their expected values to obtain unbiased estimating equations. The sparse matrix is constructed by a sparse inverse Cholesky approach to approximate the inverse covariance matrix. The statistical efficiency of the resulting unbiased estimating equations are evaluated both in theory and by numerical studies. Our methods are applied to nearly 90,000 satellite-based measurements of water vapor levels over a region in the Southeast Pacific Ocean. This talk is based on a joint work with Michael Stein from the University of Chicago.
Date: Friday, April 24th, 3:30-4:30pm
Location: Duques Hall, Room 251
Title: Mixture of Inhomogeneous Matrix Models for Species-Rich Ecosystems
Speaker: Dr. Frédéric Mortier CIRAD, UPR Bsef, Montpellier, France
Abstract: Understanding how climate change could impact population dynamics is of primary importance for species conservation. Matrix population models are widely used to predict population dynamics. However, in species-rich ecosystems with many rare species, the small population sizes hinder a good fit of species-specific models. In addition, classical matrix models do not take into account environmental variability. We propose a mixture of regression models with variable selection allowing the simultaneous clustering of species into groups according to vital rate information (recruitment, growth, and mortality) and the identification of group-specific explicative environmental variables. We develop an inference method. We first highlight the effectiveness of the method on simulated datasets. Next, we apply it to data from a tropical rain forest in the Central African Republic. We demonstrate the accuracy of the inhomogeneous mixture matrix model in successfully reproducing stand dynamics and classifying tree species into well-differentiated groups with clear ecological interpretations.