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 essentially acts as an upsampling complement to any standard algorithm. It is designed for the efficient production of approximate high-resolution histograms from manifold-restricted Gaussian distributions and can provide large computational savings when sampling directly from the target distribution is expensive.

中文翻译：

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使用切线束投影从歧管限制分布中采样

贝叶斯推理中的一个常见问题是以足够的分辨率和精度对目标概率分布进行采样，以估计概率密度并计算可信区域。通常，通过构造，许多目标分布可以表示为具有参数约束变量的某些高维封闭形式分布，即，仅限于欧氏空间的光滑子流形。我为这种分布提出了一个基于导数的重要性抽样框架。来自目标分布的n个样本的基集用于绘制歧管的切线束并为nm设定种子投影到切线束上并适当加权的其他点​​。该方法实质上是对任何标准算法的上采样补充。它是为从歧管限制的高斯分布中高效生成近似高分辨率直方图而设计的，当直接从目标分布中进行采样非常昂贵时，可以节省大量计算量。