# Inference for partially observed Riemannian Ornstein-Uhlenbeck diffusions of covariance matrices

arXiv: https://arxiv.org/abs/2104.03193 · HTML: https://mlsanity.com/paper/2104.03193/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Apr 2021.

## Built on by (most cited first, 1 of 1)

- [Score matching for sub-Riemannian bridge sampling](https://mlsanity.com/paper/2404.15258/) (2024)

## Abstract (arXiv)

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.