AI 中文总结
该研究针对系统发育网络的Metropolis-Hastings采样提出内部对称性校正方法，利用μ-向量简化自同构群计算，可加快采样速度，果园网络等无需校正。
AI 中文摘要
在系统发育学中，Metropolis-Hastings方法常用于采样系统发育树或网络，例如从贝叶斯后验分布中采样。这些方法通常使用能区分所有涉及节点的转移，因此需要系统发育网络的完全标记表示。我们认为，采样叶标记系统发育网络时，需要对叶标记网络的完全标记代表数量进行校正，或者等价地对其内部对称性进行校正。若不进行校正，存在对具有内部对称性的网络采样不足的风险。我们表明，该校正可通过对Metropolis-Hastings马尔可夫链的商构造实现，实际操作中需要计算网络自同构群的大小。利用μ-向量，我们证明果园网络的自同构群是平凡的，树孩子网络和树亦是如此。这意味着仅从这类网络类中采样时，无需进行对称性校正。更广泛地说，通过我们实现本文算法的Python代码，我们表明使用μ-向量可显著加快自同构群大小的计算，从而加快叶标记网络的Metropolis-Hastings采样速度。
英文摘要
In phylogenetics, Metropolis-Hastings methods are commonly used to sample phylogenetic trees or networks, for example from Bayesian posteriors. These methods generally use transitions that distinguish all nodes involved, and thus require fully labelled representations of phylogenetic networks. We argue that sampling leaf-labelled phylogenetic networks demands a correction for the number of fully labelled representatives of a leaf-labelled network, or, equivalently, for its internal symmetry. Without correction, there is a danger of undersampling networks with internal symmetries. We show that this correction can be realized by a quotient construction on the Metropolis-Hastings Markov chain, which, in practice, requires the calculation of the size of the network's automorphism group. Using $μ$-vectors, we show that the automorphism group is trivial for orchard networks, and thus also for tree-child networks and trees. This implies that a correction for symmetry is not needed when sampling only from such network classes. More generally, using our Python implementation of the algorithms in this paper, we show that using $μ$-vectors can significantly speed up calculations of automorphism group sizes and thus of Metropolis-Hastings sampling of leaf-labelled networks.
Comments33 pages, 6 figures
