论文标题
几何嵌套抽样：来自非平凡几何形状的分布采样
Geometric nested sampling: sampling from distributions defined on non-trivial geometries
论文作者
论文摘要
大都会黑斯廷斯（Metropolis Hastings）嵌套的采样发展了马尔可夫链，并根据大都会黑斯廷斯（Hastings）的接受率接受链条沿链的新点，该版本已经过修改以满足嵌套的采样可能约束。我在这里提出的几何嵌套采样算法是基于大都会的Hastings方法，但是将参数视为代表某些几何对象上的点，即圆圈，Tori和球体。对于代表圆或圆环上点的参数，试验分布在后验分布的域“包裹”，因此在评估大都市比率时，由于在采样域之外，不能自动拒绝样品。此外，这增强了采样器的迁移率。对于表示球体表面坐标的参数，该算法将参数转换为笛卡尔坐标系统，然后再进行采样，这再次确保不会自动拒绝样品，并提供了对参数空间采样的物理直觉的方式。
Metropolis Hastings nested sampling evolves a Markov chain, accepting new points along the chain according to a version of the Metropolis Hastings acceptance ratio, which has been modified to satisfy the nested sampling likelihood constraint. The geometric nested sampling algorithm I present here is based on the Metropolis Hastings method, but treats parameters as though they represent points on certain geometric objects, namely circles, tori and spheres. For parameters which represent points on a circle or torus, the trial distribution is "wrapped" around the domain of the posterior distribution such that samples cannot be rejected automatically when evaluating the Metropolis ratio due to being outside the sampling domain. Furthermore, this enhances the mobility of the sampler. For parameters which represent coordinates on the surface of a sphere, the algorithm transforms the parameters into a Cartesian coordinate system before sampling which again makes sure no samples are automatically rejected, and provides a physically intuitive way of the sampling the parameter space.
