Asymptotics of Maximum Likelihood Parameter Estimates For Gaussian Processes: The Ornstein–Uhlenbeck Prior
(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:
https://lup.lub.lu.se/record/0d337a0a-580e-42b6-a717-84bd4212a51e
- author
- Tronarp, Filip LU ; Särkkä, Simo and Karvonen, Toni
- publishing date
- 2019
- 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}}, }