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

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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.

Details

Original languageEnglish
Title of host publicationProceedings of the 29th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2019
Publication statusPublished - 1 Oct 2019
MoE publication typeA4 Article in a conference publication
EventIEEE International Workshop on Machine Learning for Signal Processing - Pittsburgh, United States
Duration: 13 Oct 201916 Oct 2019
Conference number: 29

Publication series

NameIEEE International Workshop on Machine Learning for Signal Processing
PublisherIEEE
ISSN (Print)2161-0363
ISSN (Electronic)2161-0371

Workshop

WorkshopIEEE International Workshop on Machine Learning for Signal Processing
Abbreviated titleMLSP
CountryUnited States
CityPittsburgh
Period13/10/201916/10/2019

    Research areas

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

ID: 40550144