Geodesic Monte Carlo on Embedded Manifolds.
Geodesic Monte Carlo on Embedded Manifolds.
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DOI：
10.1111/sjos.12036
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发表时间：
2013-12
期刊：
影响因子：
--
通讯作者：
Girolami M
中科院分区：
文献类型：
--
作者：
Byrne S;Girolami M
最近已经建立了在概率分布的歧管上明确定义的蒙特卡洛方法。 Markov Chain Monte Carlo的进一步考虑方法，以模拟从歧管上定义的概率分布中模拟的方法常见的例子是描述方向统计的分布类别。
Markov chain Monte Carlo methods explicitly defined on the manifold of probability distributions have recently been established. These methods are constructed from diffusions across the manifold and the solution of the equations describing geodesic flows in the Hamilton–Jacobi representation. This paper takes the differential geometric basis of Markov chain Monte Carlo further by considering methods to simulate from probability distributions that themselves are defined on a manifold, with common examples being classes of distributions describing directional statistics. Proposal mechanisms are developed based on the geodesic flows over the manifolds of support for the distributions, and illustrative examples are provided for the hypersphere and Stiefel manifold of orthonormal matrices.
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