Optimal estimation of drift and diffusion coefficients in the presence of static localization error

Research output: Contribution to journalArticle

Abstract

We consider the inference of the drift velocity and the diffusion coefficient of a particle undergoing a directed random walk in the presence of static localization error. A weighted least-squares fit to mean-square displacement (MSD) data is used to infer the parameters of the assumed drift-diffusion model. For experiments which cannot be repeated we show that the quality of the inferred parameters depends on the number of MSD points used in the fitting. An optimal number of fitting points popt is shown to exist which depends on the time interval between frames Δt and the unknown parameters. We therefore also present a simple iterative algorithm which converges rapidly toward popt. For repeatable experiments the quality depends crucially on the measurement time interval over which measurements are made, reflecting the different timescales associated with drift and diffusion. An optimal measurement time interval Topt exists, which depends on the number of measurement points and the unknown parameters, and so again we present an iterative algorithm which converges quickly toward Topt and is shown to be robust to initial parameter guesses.

LanguageEnglish
Article number022134
Number of pages14
JournalPhysical Review E
Volume100
Issue number2
DOIs
Publication statusPublished - 23 Aug 2019

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Optimal Estimation
Diffusion Coefficient
diffusion coefficient
coefficients
Unknown Parameters
Mean Square
Iterative Algorithm
Interval
intervals
Converge
Drift-diffusion Model
time measurement
Weighted Least Squares
Guess
Experiment
Random walk
Time Scales
inference
random walk

Keywords

  • drift velocity
  • diffusion coefficient
  • static localization error
  • drift-diffusion model

Cite this

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title = "Optimal estimation of drift and diffusion coefficients in the presence of static localization error",
abstract = "We consider the inference of the drift velocity and the diffusion coefficient of a particle undergoing a directed random walk in the presence of static localization error. A weighted least-squares fit to mean-square displacement (MSD) data is used to infer the parameters of the assumed drift-diffusion model. For experiments which cannot be repeated we show that the quality of the inferred parameters depends on the number of MSD points used in the fitting. An optimal number of fitting points popt is shown to exist which depends on the time interval between frames Δt and the unknown parameters. We therefore also present a simple iterative algorithm which converges rapidly toward popt. For repeatable experiments the quality depends crucially on the measurement time interval over which measurements are made, reflecting the different timescales associated with drift and diffusion. An optimal measurement time interval Topt exists, which depends on the number of measurement points and the unknown parameters, and so again we present an iterative algorithm which converges quickly toward Topt and is shown to be robust to initial parameter guesses.",
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Optimal estimation of drift and diffusion coefficients in the presence of static localization error. / Devlin, J.; Husmeier, D.; MacKenzie, J. A.

In: Physical Review E, Vol. 100, No. 2, 022134, 23.08.2019.

Research output: Contribution to journalArticle

TY - JOUR

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AU - Devlin, J.

AU - Husmeier, D.

AU - MacKenzie, J. A.

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AB - We consider the inference of the drift velocity and the diffusion coefficient of a particle undergoing a directed random walk in the presence of static localization error. A weighted least-squares fit to mean-square displacement (MSD) data is used to infer the parameters of the assumed drift-diffusion model. For experiments which cannot be repeated we show that the quality of the inferred parameters depends on the number of MSD points used in the fitting. An optimal number of fitting points popt is shown to exist which depends on the time interval between frames Δt and the unknown parameters. We therefore also present a simple iterative algorithm which converges rapidly toward popt. For repeatable experiments the quality depends crucially on the measurement time interval over which measurements are made, reflecting the different timescales associated with drift and diffusion. An optimal measurement time interval Topt exists, which depends on the number of measurement points and the unknown parameters, and so again we present an iterative algorithm which converges quickly toward Topt and is shown to be robust to initial parameter guesses.

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