Sampling from manifold-restricted distributions using tangent bundle projections. (arXiv:1811.05494v1 [stat.CO])
<a href="http://arxiv.org/find/stat/1/au:+Chua_A/0/1/0/all/0/1">Alvin J. K. Chua</a>
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.
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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