Posterior Integration on a Riemannian Manifold

Chris. J. Oates; Alessandro Barp; Mark Girolami

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arXiv · 1712.01793

Posterior Integration on a Riemannian Manifold

Chris. J. Oates·Alessandro Barp·Mark Girolami

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Abstract

The geodesic Markov chain Monte Carlo method and its variants enable computation of integrals with respect to a posterior supported on a manifold. However, for regular integrals, the convergence rate of the ergodic average will be sub-optimal. To fill this gap, this paper extends the efficient posterior integration method of Oates et al. (2017) to the case of a Riemannian manifold. In contrast to the original Euclidean case, no non-trivial boundary conditions are needed for a closed manifold. The method is assessed through simulation and deployed to compute posterior integrals for an Australian Mesozoic paleomagnetic pole model, whose parameters are constrained to lie on the manifold $M = \mathbb{S}^2 \times \mathbb{R}_+$.

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Chris. J. Oates, Alessandro Barp, Mark Girolami. 2018-10-14. Posterior Integration on a Riemannian Manifold. https://arxiv.org/abs/1712.01793

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