García-Portugués, E, Sørensen, M, Mardia, KV orcid.org/0000-0003-0090-6235 et al. (1 more author) (2019) Langevin diffusions on the torus: estimation and applications. Statistics and Computing, 29 (1). pp. 1-22. ISSN 0960-3174
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2017 Springer Nature. This is a post-peer-review, pre-copyedit version of an article published in Statistics and Computing. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11222-017-9790-2 |
Keywords: | Circular data Directional statistics Likelihood Protein structure Stochastic Differential Equation Wrapped normal |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 08 Nov 2017 14:49 |
Last Modified: | 11 Sep 2020 09:59 |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/s11222-017-9790-2 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:123576 |