Parameter Estimation For Subdiffusive Processes With Applications To Microrheology

Open Access
Bernstein, Jason
Graduate Program:
Master of Science
Document Type:
Master Thesis
Date of Defense:
Committee Members:
  • John Fricks, Thesis Advisor
  • Subdiffusion
  • parameter estimation
The statistical analysis of complex biological fluids is a research area of active interest. In a general microrheology experiment, probes are embedded in fluids and their positions tracked over time with a camera. An important statistical problem that arises from these experiments is how to estimate the parameters characterizing the subdiffusive behavior of the probes. We begin this thesis by reviewing the background and literature on diffusive behavior in complex biological fluids, leading to a description of subdiffusion in viscoelastic fluids, a phenomenon observed widely in biology experiments. The local Whittle, wavelet and pathwise mean-squared displacement methods for parameter estimation are described, and their performance compared in a simulation study. Lastly, the R package physdiff is presented that contains functions to perform the simulations herein.