Asymptotics of Maximum Likelihood Parameter Estimates for Gaussian Processes: The Ornstein-Uhlenbeck Prior

Toni Karvonen; Filip Tronarp; Simo Särkkä

doi:10.1109/MLSP.2019.8918767

Asymptotics of Maximum Likelihood Parameter Estimates for Gaussian Processes: The Ornstein-Uhlenbeck Prior

Toni Karvonen, Filip Tronarp, Simo Särkkä

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

3 Citations (Scopus)

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.

Original language	English
Title of host publication	Proceedings of the 29th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2019
Publisher	IEEE
Number of pages	6
ISBN (Electronic)	9781728108247
DOIs	https://doi.org/10.1109/MLSP.2019.8918767
Publication status	Published - 1 Oct 2019
MoE publication type	A4 Conference publication
Event	IEEE International Workshop on Machine Learning for Signal Processing - Pittsburgh, United States Duration: 13 Oct 2019 → 16 Oct 2019 Conference number: 29

Publication series

Name	IEEE International Workshop on Machine Learning for Signal Processing
Publisher	IEEE
ISSN (Print)	2161-0363
ISSN (Electronic)	2161-0371

Workshop

Workshop	IEEE International Workshop on Machine Learning for Signal Processing
Abbreviated title	MLSP
Country/Territory	United States
City	Pittsburgh
Period	13/10/2019 → 16/10/2019

Keywords

Gaussian process regression
Maximum likelihood estimation
Ornstein- Uhlenbeck process
Probabilistic numerics

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10.1109/MLSP.2019.8918767

Cite this

Karvonen, T., Tronarp, F., & Särkkä, S. (2019). Asymptotics of Maximum Likelihood Parameter Estimates for Gaussian Processes: The Ornstein-Uhlenbeck Prior. In Proceedings of the 29th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2019 Article 8918767 (IEEE International Workshop on Machine Learning for Signal Processing). IEEE. https://doi.org/10.1109/MLSP.2019.8918767

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Karvonen, T, Tronarp, F & Särkkä, S 2019, Asymptotics of Maximum Likelihood Parameter Estimates for Gaussian Processes: The Ornstein-Uhlenbeck Prior. in Proceedings of the 29th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2019., 8918767, IEEE International Workshop on Machine Learning for Signal Processing, IEEE, IEEE International Workshop on Machine Learning for Signal Processing, Pittsburgh, Pennsylvania, United States, 13/10/2019. https://doi.org/10.1109/MLSP.2019.8918767

Asymptotics of Maximum Likelihood Parameter Estimates for Gaussian Processes: The Ornstein-Uhlenbeck Prior. / Karvonen, Toni; Tronarp, Filip; Särkkä, Simo.
Proceedings of the 29th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2019. IEEE, 2019. 8918767 (IEEE International Workshop on Machine Learning for Signal Processing).

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

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AB - 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.

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Karvonen T, Tronarp F, Särkkä S. Asymptotics of Maximum Likelihood Parameter Estimates for Gaussian Processes: The Ornstein-Uhlenbeck Prior. In Proceedings of the 29th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2019. IEEE. 2019. 8918767. (IEEE International Workshop on Machine Learning for Signal Processing). doi: 10.1109/MLSP.2019.8918767

Asymptotics of Maximum Likelihood Parameter Estimates for Gaussian Processes: The Ornstein-Uhlenbeck Prior

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