Multivariate Gaussian processes: definitions, examples and applications

Zexun Chen (), Jun Fan and Kuo Wang
Additional contact information
Zexun Chen: University of Edinburgh Business School
Jun Fan: University of Nottingham Ningbo China
Kuo Wang: Jiaxing university

METRON, 2023, vol. 81, issue 2, No 4, 191 pages

Abstract: Abstract Gaussian processes occupy one of the leading places in modern statistics and probability theory due to their importance and a wealth of strong results. The common use of Gaussian processes is in connection with problems related to estimation, detection, and many statistical or machine learning models. In this paper, we propose a precise definition of multivariate Gaussian processes based on Gaussian measures on vector-valued function spaces, and provide an existence proof. In addition, several fundamental properties of multivariate Gaussian processes, such as stationarity and independence, are introduced. We further derive two special cases of multivariate Gaussian processes, including multivariate Gaussian white noise and multivariate Brownian motion, and present a brief introduction to multivariate Gaussian process regression as a useful statistical learning method for multi-output prediction problems.

Keywords: Gaussian measure; Gaussian process; Multivariate Gaussian process; Multivariate Gaussian distribution; Matrix-variate Gaussian distribution; Brownian motion (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s40300-023-00238-3 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:metron:v:81:y:2023:i:2:d:10.1007_s40300-023-00238-3

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/40300

DOI: 10.1007/s40300-023-00238-3

Access Statistics for this article

METRON is currently edited by Marco Alfo'

More articles in METRON from Springer, Sapienza Università di Roma
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().