Langevin diffusions on the torus: estimation and applications

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Standard

Langevin diffusions on the torus : estimation and applications. / García-Portugués, Eduardo; Sørensen, Michael; Mardia, Kanti V.; Hamelryck, Thomas.

I: Statistics and Computing, 2019, s. 1-22.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningfagfællebedømt

Harvard

García-Portugués, E, Sørensen, M, Mardia, KV & Hamelryck, T 2019, 'Langevin diffusions on the torus: estimation and applications' Statistics and Computing, s. 1-22. https://doi.org/10.1007/s11222-017-9790-2

APA

García-Portugués, E., Sørensen, M., Mardia, K. V., & Hamelryck, T. (2019). Langevin diffusions on the torus: estimation and applications. Statistics and Computing, 1-22. https://doi.org/10.1007/s11222-017-9790-2

Vancouver

García-Portugués E, Sørensen M, Mardia KV, Hamelryck T. Langevin diffusions on the torus: estimation and applications. Statistics and Computing. 2019;1-22. https://doi.org/10.1007/s11222-017-9790-2

Author

García-Portugués, Eduardo ; Sørensen, Michael ; Mardia, Kanti V. ; Hamelryck, Thomas. / Langevin diffusions on the torus : estimation and applications. I: Statistics and Computing. 2019 ; s. 1-22.

Bibtex

@article{77d640d70e6b4898a175b3b4fd9affff,
title = "Langevin diffusions on the torus: estimation and applications",
abstract = "We introduce stochastic models for continuous-time evolution of angles and develop their estimation. We focus on studying Langevin diffusions with stationary distributions equal to well-known distributions from directional statistics, since such diffusions can be regarded as toroidal analogues of the Ornstein–Uhlenbeck process. Their likelihood function is a product of transition densities with no analytical expression, but that can be calculated by solving the Fokker–Planck equation numerically through adequate schemes. We propose three approximate likelihoods that are computationally tractable: (i) a likelihood based on the stationary distribution; (ii) toroidal adaptations of the Euler and Shoji–Ozaki pseudo-likelihoods; (iii) a likelihood based on a specific approximation to the transition density of the wrapped normal process. A simulation study compares, in dimensions one and two, the approximate transition densities to the exact ones, and investigates the empirical performance of the approximate likelihoods. Finally, two diffusions are used to model the evolution of the backbone angles of the protein G (PDB identifier 1GB1) during a molecular dynamics simulation. The software package sdetorus implements the estimation methods and applications presented in the paper.",
keywords = "Circular data, Directional statistics, Likelihood, Protein structure, Stochastic Differential Equation, Wrapped normal",
author = "Eduardo Garc{\'i}a-Portugu{\'e}s and Michael S{\o}rensen and Mardia, {Kanti V.} and Thomas Hamelryck",
year = "2019",
doi = "10.1007/s11222-017-9790-2",
language = "English",
pages = "1--22",
journal = "Statistics and Computing",
issn = "0960-3174",
publisher = "Springer",

}

RIS

TY - JOUR

T1 - Langevin diffusions on the torus

T2 - estimation and applications

AU - García-Portugués, Eduardo

AU - Sørensen, Michael

AU - Mardia, Kanti V.

AU - Hamelryck, Thomas

PY - 2019

Y1 - 2019

N2 - We introduce stochastic models for continuous-time evolution of angles and develop their estimation. We focus on studying Langevin diffusions with stationary distributions equal to well-known distributions from directional statistics, since such diffusions can be regarded as toroidal analogues of the Ornstein–Uhlenbeck process. Their likelihood function is a product of transition densities with no analytical expression, but that can be calculated by solving the Fokker–Planck equation numerically through adequate schemes. We propose three approximate likelihoods that are computationally tractable: (i) a likelihood based on the stationary distribution; (ii) toroidal adaptations of the Euler and Shoji–Ozaki pseudo-likelihoods; (iii) a likelihood based on a specific approximation to the transition density of the wrapped normal process. A simulation study compares, in dimensions one and two, the approximate transition densities to the exact ones, and investigates the empirical performance of the approximate likelihoods. Finally, two diffusions are used to model the evolution of the backbone angles of the protein G (PDB identifier 1GB1) during a molecular dynamics simulation. The software package sdetorus implements the estimation methods and applications presented in the paper.

AB - We introduce stochastic models for continuous-time evolution of angles and develop their estimation. We focus on studying Langevin diffusions with stationary distributions equal to well-known distributions from directional statistics, since such diffusions can be regarded as toroidal analogues of the Ornstein–Uhlenbeck process. Their likelihood function is a product of transition densities with no analytical expression, but that can be calculated by solving the Fokker–Planck equation numerically through adequate schemes. We propose three approximate likelihoods that are computationally tractable: (i) a likelihood based on the stationary distribution; (ii) toroidal adaptations of the Euler and Shoji–Ozaki pseudo-likelihoods; (iii) a likelihood based on a specific approximation to the transition density of the wrapped normal process. A simulation study compares, in dimensions one and two, the approximate transition densities to the exact ones, and investigates the empirical performance of the approximate likelihoods. Finally, two diffusions are used to model the evolution of the backbone angles of the protein G (PDB identifier 1GB1) during a molecular dynamics simulation. The software package sdetorus implements the estimation methods and applications presented in the paper.

KW - Circular data

KW - Directional statistics

KW - Likelihood

KW - Protein structure

KW - Stochastic Differential Equation

KW - Wrapped normal

UR - http://www.scopus.com/inward/record.url?scp=85034638368&partnerID=8YFLogxK

U2 - 10.1007/s11222-017-9790-2

DO - 10.1007/s11222-017-9790-2

M3 - Journal article

SP - 1

EP - 22

JO - Statistics and Computing

JF - Statistics and Computing

SN - 0960-3174

ER -

ID: 192389083