# Posterior Integration on a Riemannian Manifold

arXiv: https://arxiv.org/abs/1712.01793 · HTML: https://mlsanity.com/paper/1712.01793/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Dec 2017.

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

- [Kernel Stein Discrepancy thinning: a theoretical perspective of pathologies and a practical fix with regularization](https://mlsanity.com/paper/2301.13528/) (2023)

## Abstract (arXiv)

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 = mathbbS2 × ℝ_+.