Bui, Mai Ngoc;
Pokern, Yvo;
Dellaportas, Petros;
(2023)
Inference for partially observed Riemannian Ornstein–Uhlenbeck diffusions of covariance matrices.
Bernoulli: a journal of mathematical statistics and probability
, 29
(4)
pp. 2961-2986.
10.3150/22-BEJ1570.
Preview |
Text
Bui_Inference for partially observed Riemannian Orstein Uhlenbeck diffusion process.pdf - Accepted Version Download (4MB) | Preview |
Abstract
We construct a generalization of the Ornstein–Uhlenbeck processes on the cone of covariance matrices endowed with the Log-Euclidean and the Affine-Invariant metrics. Our development exploits the Riemannian geometric structure of symmetric positive definite matrices viewed as a differential manifold. We then provide Bayesian inference for discretely observed diffusion processes of covariance matrices based on an MCMC algorithm built with the help of a novel diffusion bridge sampler accounting for the geometric structure. Our proposed algorithm is illustrated with a real data financial application.
| Type: | Article |
|---|---|
| Title: | Inference for partially observed Riemannian Ornstein–Uhlenbeck diffusions of covariance matrices |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.3150/22-BEJ1570 |
| Publisher version: | https://doi.org/10.3150/22-BEJ1570 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Affine-Invariant metric; Log-Euclidean metric; Ornstein–Uhlenbeck process; Riemannian manifold; Partially observed diffusion |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Population Health Sciences > Institute of Epidemiology and Health UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Population Health Sciences > Institute of Epidemiology and Health > Applied Health Research |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10161285 |
Archive Staff Only
 |
View Item |
