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

2021/04/07 by Mai Ngoc Bui, Bui, Mai Ngoc, Yvo Pokern +3
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Computation (stat.CO) #FOS: Computer and information sciences #Markov Chains and Monte Carlo Methods #Methodology (stat.ME) #Statistical Methods and Bayesian Inference

paper · pdf · doi:10.48550/arxiv.2104.03193

openalex publication_date 2021/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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