PMID: 22587067May 17, 2012Paper

Optimal estimates of the diffusion coefficient of a single Brownian trajectory

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Denis BoyerGleb Oshanin

Abstract

Modern developments in microscopy and image processing are revolutionizing areas of physics, chemistry, and biology as nanoscale objects can be tracked with unprecedented accuracy. The goal of single-particle tracking is to determine the interaction between the particle and its environment. The price paid for having a direct visualization of a single particle is a consequent lack of statistics. Here we address the optimal way to extract diffusion constants from single trajectories for pure Brownian motion. It is shown that the maximum likelihood estimator is much more efficient than the commonly used least-squares estimate. Furthermore, we investigate the effect of disorder on the distribution of estimated diffusion constants and show that it increases the probability of observing estimates much smaller than the true (average) value.

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Citations

Apr 14, 2016·Annual Review of Physical Chemistry·Ji Yu
Oct 16, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Denis S Grebenkov
Jan 24, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·David S Dean, Thomas Guérin
Jun 13, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Aljaž Godec, Ralf Metzler
Sep 3, 2016·Physical Review Letters·Olivier BénichouGleb Oshanin
Sep 20, 2018·Physical Review Letters·Daniel Nickelsen, Hugo Touchette
Oct 4, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Thiago G MattosGleb Oshanin
Feb 2, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Denis BoyerGleb Oshanin
Sep 13, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·David S Dean, Gleb Oshanin
Feb 7, 2013·Physical Review Letters·Johannes H P SchulzRalf Metzler
Feb 16, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Iddo Eliazar, Morrel H Cohen
May 16, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Juan Duque RodríguezCarlos Mejía-Monasterio

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