ArticleJournal of statistical computation and simulation2018
Geodesic Lagrangian Monte Carlo over the space of positive definite matrices: with application to Bayesian spectral density estimation.
Article in Journal of statistical computation and simulation, 2018. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
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3 citing papers in PubMed.
- Massive parallelization boosts big Bayesian multidimensional scaling.Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America · 2021Article
- Flexible Bayesian Dynamic Modeling of Correlation and Covariance Matrices.Bayesian analysis · 2020Article
- A Bayesian Approach for Estimating Dynamic Functional Network Connectivity in fMRI Data.Journal of the American Statistical Association · 2018Article
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4 authors.
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Abstract
We present geodesic Lagrangian Monte Carlo, an extension of Hamiltonian Monte Carlo for sampling from posterior distributions defined on general Riemannian manifolds. We apply this new algorithm to Bayesian inference on symmetric or Hermitian positive definite matrices. To do so, we exploit the Riemannian structure induced by Cartan's canonical metric. The geodesics that correspond to this metric are available in closed-form and-within the context of Lagrangian Monte Carlo-provide a principled way to travel around the space of positive definite matrices. Our method improves Bayesian inference on such matrices by allowing for a broad range of priors, so we are not limited to conjugate priors only. In the context of spectral density estimation, we use the (non-conjugate) complex reference prior as an example modeling option made available by the algorithm. Results based on simulated and real-world multivariate time series are presented in this context, and future directions are outlined.
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