贝叶斯与维里定理：从运动学快照推断星系的势能
Bayes versus the virial theorem: inferring the potential of a galaxy from a kinematical snapshot
摘要：
我们提出了一个新的框架来估计星系的引力势，Phi（x），从它的恒星运动学通过采用一个完全非参数模型的星系的未知的作用空间分布函数，f（J）。有一个表达式的联合可能性的Φ和f，Φ的可能性计算使用Dirichlet过程的混合物，以表示先验的f和边缘化。我们证明，使用这个框架构建的建模机器是成功的恢复潜力的一些简单的系统从完美的离散运动学数据，这种情况下毫不费力地处理传统的基于矩的方法，如维里定理，但在其他更现代的方法是不令人满意的。我们将展示如何概括的机械占现实的观测误差和选择功能。一个实际的实现可能会提出一些有趣的算法和计算的挑战。
英文摘要：
We present a new framework for estimating a galaxy's gravitational potential, Phi(x), from its stellar kinematics by adopting a fully non-parametric model for the galaxy's unknown action-space distribution function, f(J). Having an expression for the joint likelihood of Phi and f, the likelihood of Phi is calculated by using a Dirichlet process mixture to represent the prior on f and marginalising. We demonstrate that modelling machinery constructed using this framework is successful at recovering the potentials of some simple systems from perfect discrete kinematical data, a situation handled effortlessly by traditional moment-based methods, such as the virial theorem, but in which other, more modern, methods are less than satisfactory. We show how to generalise the machinery to account for realistic observational errors and selection functions. A practical implementation is likely to raise some interesting algorithmic and computational challenges.
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