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Asymptotics of Maximum Likelihood Parameter Estimates For Gaussian Processes: The Ornstein–Uhlenbeck Prior

Tronarp, Filip LU ; Särkkä, Simo and Karvonen, Toni (2019) IEEE 29th International Workshop on Machine Learning for Signal Processing (MLSP)
Abstract
This article studies the maximum likelihood estimates of magnitude and scale parameters for a Gaussian process of Ornstein-Uhlenbeck type used to model a deterministic function that does not have to be a realisation of an Ornstein- Uhlenbeck process. Specifically, we derive explicit expressions for the limiting values of the maximum likelihood estimates as the number of observations increases. The results demonstrate that the function typically needs to be sufficiently similar to a sample path of an Ornstein-Uhlenbeck process or have discontinuities if the variance of the model is to remain non-zero. Numerical examples illustrate the behaviour of the estimates when the function is not a sample path of any Ornstein-Uhlenbeck process.
Please use this url to cite or link to this publication:
author
; and
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
IEEE 29th International Workshop on Machine Learning for Signal Processing (MLSP)
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
conference name
IEEE 29th International Workshop on Machine Learning for Signal Processing (MLSP)
conference location
Pittsburgh, United States
conference dates
2019-10-13 - 2019-10-16
external identifiers
  • scopus:85077712808
ISBN
978-1-7281-0824-7
978-1-7281-0823-0
978-1-7281-0825-4
DOI
10.1109/MLSP.2019.8918767
language
English
LU publication?
no
id
0d337a0a-580e-42b6-a717-84bd4212a51e
date added to LUP
2023-08-20 22:54:12
date last changed
2024-06-01 05:30:04
@inproceedings{0d337a0a-580e-42b6-a717-84bd4212a51e,
  abstract     = {{This article studies the maximum likelihood estimates of magnitude and scale parameters for a Gaussian process of Ornstein-Uhlenbeck type used to model a deterministic function that does not have to be a realisation of an Ornstein- Uhlenbeck process. Specifically, we derive explicit expressions for the limiting values of the maximum likelihood estimates as the number of observations increases. The results demonstrate that the function typically needs to be sufficiently similar to a sample path of an Ornstein-Uhlenbeck process or have discontinuities if the variance of the model is to remain non-zero. Numerical examples illustrate the behaviour of the estimates when the function is not a sample path of any Ornstein-Uhlenbeck process.}},
  author       = {{Tronarp, Filip and Särkkä, Simo and Karvonen, Toni}},
  booktitle    = {{IEEE 29th International Workshop on Machine Learning for Signal Processing (MLSP)}},
  isbn         = {{978-1-7281-0824-7}},
  language     = {{eng}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  title        = {{Asymptotics of Maximum Likelihood Parameter Estimates For Gaussian Processes: The Ornstein–Uhlenbeck Prior}},
  url          = {{http://dx.doi.org/10.1109/MLSP.2019.8918767}},
  doi          = {{10.1109/MLSP.2019.8918767}},
  year         = {{2019}},
}