November 2023 Inference for partially observed Riemannian Ornstein–Uhlenbeck diffusions of covariance matrices
Mai Ngoc Bui, Yvo Pokern, Petros Dellaportas
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Bernoulli 29(4): 2961-2986 (November 2023). DOI: 10.3150/22-BEJ1570

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.

Acknowledgements

Mai Ngoc Bui acknowledges financial support from the UCL Overseas Research Scholarship. The authors would like to thank Stephan Huckemann for helpful discussions.

Citation

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Mai Ngoc Bui. Yvo Pokern. Petros Dellaportas. "Inference for partially observed Riemannian Ornstein–Uhlenbeck diffusions of covariance matrices." Bernoulli 29 (4) 2961 - 2986, November 2023. https://doi.org/10.3150/22-BEJ1570

Information

Received: 1 April 2021; Published: November 2023
First available in Project Euclid: 22 August 2023

MathSciNet: MR4632127
Digital Object Identifier: 10.3150/22-BEJ1570

Keywords: Affine-Invariant metric , log-Euclidean metric , Ornstein–Uhlenbeck process , partially observed diffusion , Riemannian manifold

Vol.29 • No. 4 • November 2023
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