Sampling from manifold-restricted distributions using tangent bundle projections

Understand

A common problem in Bayesian inference is the sampling of target probability distributions at sufficient resolution and accuracy to estimate the probability density, and to compute credible regions.

• Often by construction, many target distributions can be expressed as some higher-dimensional closed-form distribution with parametrically constrained variables, i.e., one that is restricted to a smooth submanifold of Euclidean space.
• I propose a derivative-based importance sampling framework for such distributions.
• A base set of $n$ samples from the target distribution is used to map out the tangent bundle of the manifold, and to seed $nm$ additional points that are projected onto the tangent bundle and weighted appropriately.