OCTOBER 16 | 3:00-5:00pm
Ballard Room | 503 | HMS Countway Library
Itai Dattner, PhD
Statistical Learning of Dynamic Systems – a Direct Approach
Lecturer, Department of Statistics
University of Haifa
Abstract: Dynamic systems are ubiquitous in nature and are used to model many processes in biology, chemistry, physics, medicine, and engineering. In particular, systems of (deterministic or stochastic) differential equations as well as discrete models are commonly used for the mathematical modeling of dynamic processes. These systems describe the interrelationships between the variables involved, and depend in a complicated way on unknown quantities (e.g., initial values, constants or time dependent parameters). Modern dynamic systems are typically very complex: nonlinear, high dimensional and only partly measured. Moreover, data may be sparse and noisy. Thus, statistical learning (inference, prediction) of dynamical systems is not a trivial task in practice.
In the first part of the talk we will present the direct integral method, a novel approach for estimating the parameters of systems of ordinary differential equations. We will discuss some theoretical results such as identifiability and consistency for both, fully and partially observed systems.
The second part of the talk will be concerned with applications of the direct method. We will consider examples from infectious diseases and biology. In particular, we will present a recent study where we experimentally monitored the temporal dynamic of a predatory-prey system and demonstrated the ability to obtain realistic parameter estimates given sparse and noisy data. Next, we will discuss the statistical learning of age-dependent dynamics which is an important characteristic of many infectious diseases. We examine the estimation of the so called next-generation matrix using incidence data of influenza-like-illness. Unlike previous studies, using our estimation method we do not have to assume any constraints regarding the structure of the matrix.
Biostatistics Work in Progress Session
MGH Biostatistics Center, 50 Staniford Street, Suite 560
Douglas Hayden, Assistant Professor of Medicine at Harvard Medical School, MGH, will lead the October meeting of the Harvard Catalyst Biostatistics Work-in-Progress, Composite Outcomes in Critical Care Research.
Please contact Jai Vartikar for call-in information.