Sampling from manifold-restricted distributions using tangent bundle projections
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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. The method can act as a multiplicative complement to any standard sampling algorithm, and is designed for the efficient production of approximate high-resolution histograms from manifold-restricted Gaussian distributions.
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