Martin Lysy

Department of Statistics and Actuarial Science, University of Waterloo

“Comparison and Assessment of Models for Particle Diffusion in Biological Fluids”

Date: Friday, November 7, 2014

Rapidly progressing particle tracking techniques have revealed that foreign particles in biological fluids exhibit rich and at times unexpected behavior, with important consequences for drug delivery. Yet, there remains a frustrating lack of coherence in the description of these particles' motion. Largely this is due to a reliance on functional statistics (e.g., mean-squared displacement) to perform model selection and assess goodness-of-fit. However, not only are these functional characteristics typically estimated with substantial variability, but they are shared by many stochastic processes -- each making fundamentally different predictions for important quantities of scientific interest.

Here, we conduct a detailed Bayesian analysis of leading candidate models for subdiffusive particle trajectories in human pulmonary mucus. Model selection is achieved by way of intrinsic Bayes factors, which avoid both noninformative priors and "using the data twice". Goodness-of-fit is evaluated via several second-order criteria along with exact model residuals. Our findings suggest that a simple model of fractional Brownian motion describes the data just as well as a first-principles physical model of viscoelastic subdiffusion.

Upcoming Seminars

Statistics seminar: Miroslaw Pawlak: “Nearest Neighbor Estimates for Nonlinear Time Series Systems” — Thursday, November 23 at 2:45 p.m., 301 Biological Sciences.

PIMS lecture: Anthony Bonato — Thursday, November 30 at 4 p.m., Robert Schultz Theatre.

Interdisciplinary seminar: Lena Kourkoutis — Friday, December 1 at 4 p.m., Robert Schultz Theatre.

Where are they now?

Yung-Ming Chang, Ph.D. (2002)

Jeffrey Alan Sloan, Ph.D. (1991)