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dc.contributor.authorKleppe, Tore Selland
dc.identifier.citationKleppe, T.S. (2023) Log-density gradient covariance and automatic metric tensors for Riemann manifold Monte Carlo methods. Scandinavian Journal of Statisticsen_US
dc.description.abstractA metric tensor for Riemann manifold Monte Carlo particularly suited for nonlinear Bayesian hierarchical models is proposed. The metric tensor is built from symmetric positive semidefinite log-density gradient covariance (LGC) matrices, which are also proposed and further explored here. The LGCs generalize the Fisher information matrix by measuring the joint information content and dependence structure of both a random variable and the parameters of said variable. Consequently, positive definite Fisher/LGC-based metric tensors may be constructed not only from the observation likelihoods as is current practice, but also from arbitrarily complicated nonlinear prior/latent variable structures, provided the LGC may be derived for each conditional distribution used to construct said structures. The proposed methodology is highly automatic and allows for exploitation of any sparsity associated with the model in question. When implemented in conjunction with a Riemann manifold variant of the recently proposed numerical generalized randomized Hamiltonian Monte Carlo processes, the proposed methodology is highly competitive, in particular for the more challenging target distributions associated with Bayesian hierarchical models.en_US
dc.publisherJohn Wiley & Sons Ltd on behalf of The Board of the Foundation of the Scandinavian Journal of Statistics.en_US
dc.rightsNavngivelse 4.0 Internasjonal*
dc.titleLog-density gradient covariance and automatic metric tensors for Riemann manifold Monte Carlo methodsen_US
dc.typePeer revieweden_US
dc.typeJournal articleen_US
dc.rights.holder© 2023 The Author.en_US
dc.subject.nsiVDP::Matematikk og Naturvitenskap: 400en_US
dc.source.journalScandinavian Journal of Statisticsen_US

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Navngivelse 4.0 Internasjonal
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