Bayesian inference of scaled versus fractional Brownian motion

Samudrajit Thapa; Seongyu Park; Yeongjin Kim; Jae Hyung Jeon; Ralf Metzler; Michael A. Lomholt

doi:10.1088/1751-8121/ac60e7

Bayesian inference of scaled versus fractional Brownian motion

Samudrajit Thapa, Seongyu Park, Yeongjin Kim, Jae Hyung Jeon, Ralf Metzler, Michael A. Lomholt^*

^*Corresponding author for this work

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Abstract

We present a Bayesian inference scheme for scaled Brownian motion, and investigate its performance on synthetic data for parameter estimation and model selection in a combined inference with fractional Brownian motion. We include the possibility of measurement noise in both models. We find that for trajectories of a few hundred time points the procedure is able to resolve well the true model and parameters. Using the prior of the synthetic data generation process also for the inference, the approach is optimal based on decision theory. We include a comparison with inference using a prior different from the data generating one.

Original language	English
Article number	194003
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	55
Issue number	19
ISSN	1751-8113
DOIs	https://doi.org/10.1088/1751-8121/ac60e7
Publication status	Published - 13. May 2022

Keywords

Bayesian inference
scaled Brownian motion
single particle tracking

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10.1088/1751-8121/ac60e7

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title = "Bayesian inference of scaled versus fractional Brownian motion",

abstract = "We present a Bayesian inference scheme for scaled Brownian motion, and investigate its performance on synthetic data for parameter estimation and model selection in a combined inference with fractional Brownian motion. We include the possibility of measurement noise in both models. We find that for trajectories of a few hundred time points the procedure is able to resolve well the true model and parameters. Using the prior of the synthetic data generation process also for the inference, the approach is optimal based on decision theory. We include a comparison with inference using a prior different from the data generating one.",

keywords = "Bayesian inference, scaled Brownian motion, single particle tracking",

author = "Samudrajit Thapa and Seongyu Park and Yeongjin Kim and Jeon, {Jae Hyung} and Ralf Metzler and Lomholt, {Michael A.}",

note = "Funding Information: S Thapa acknowledges support in the form of a Sackler postdoctoral fellowship and funding from the Pikovsky-Valazzi matching scholarship, Tel Aviv University. J-H Jeon acknowledges support from the National Research Foundation (NRF) of Korea (No. 2020R1A2C4002490). R Metzler acknowledges funding from the German Science Foundation (DFG, Grant No. ME 1525/12-1) and the Foundation for Polish Science (Fundacja na rzecz Nauki Polskiej, FNR) within an Alexander von Humboldt Honorary Polish Research Scholarship. Publisher Copyright: {\textcopyright} 2022 IOP Publishing Ltd.",

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doi = "10.1088/1751-8121/ac60e7",

language = "English",

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T1 - Bayesian inference of scaled versus fractional Brownian motion

AU - Thapa, Samudrajit

AU - Park, Seongyu

AU - Kim, Yeongjin

AU - Jeon, Jae Hyung

AU - Metzler, Ralf

AU - Lomholt, Michael A.

N1 - Funding Information: S Thapa acknowledges support in the form of a Sackler postdoctoral fellowship and funding from the Pikovsky-Valazzi matching scholarship, Tel Aviv University. J-H Jeon acknowledges support from the National Research Foundation (NRF) of Korea (No. 2020R1A2C4002490). R Metzler acknowledges funding from the German Science Foundation (DFG, Grant No. ME 1525/12-1) and the Foundation for Polish Science (Fundacja na rzecz Nauki Polskiej, FNR) within an Alexander von Humboldt Honorary Polish Research Scholarship. Publisher Copyright: © 2022 IOP Publishing Ltd.

PY - 2022/5/13

Y1 - 2022/5/13

N2 - We present a Bayesian inference scheme for scaled Brownian motion, and investigate its performance on synthetic data for parameter estimation and model selection in a combined inference with fractional Brownian motion. We include the possibility of measurement noise in both models. We find that for trajectories of a few hundred time points the procedure is able to resolve well the true model and parameters. Using the prior of the synthetic data generation process also for the inference, the approach is optimal based on decision theory. We include a comparison with inference using a prior different from the data generating one.

AB - We present a Bayesian inference scheme for scaled Brownian motion, and investigate its performance on synthetic data for parameter estimation and model selection in a combined inference with fractional Brownian motion. We include the possibility of measurement noise in both models. We find that for trajectories of a few hundred time points the procedure is able to resolve well the true model and parameters. Using the prior of the synthetic data generation process also for the inference, the approach is optimal based on decision theory. We include a comparison with inference using a prior different from the data generating one.

KW - Bayesian inference

KW - scaled Brownian motion

KW - single particle tracking

U2 - 10.1088/1751-8121/ac60e7

DO - 10.1088/1751-8121/ac60e7

M3 - Journal article

AN - SCOPUS:85129189800

SN - 1751-8113

VL - 55

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 19

M1 - 194003

ER -

Bayesian inference of scaled versus fractional Brownian motion

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Keywords

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