An approximately unbiased (AU) test that   uses a newly devised multiscale   bootstrap technique was developed for general hypothesis testing of   regions in an attempt to reduce test bias. It was applied to   maximum-likelihood tree selection for obtaining the confidence set of trees.   The AU test is based on the theory of Efron et al. (Proc. Natl. Acad. Sci.   USA 93:13429-13434; 1996), but the new method provides higher-order accuracy   yet simpler implementation. The AU test, like the Shimodaira-Hasegawa (SH)   test, adjusts the selection bias overlooked in the standard use of the   bootstrap probability and Kishino-Hasegawa tests. The selection bias comes   from comparing many trees at the same time and often leads to overconfidence   in the wrong trees. The SH test, though safe to use, may exhibit another type   of bias such that it appears conservative. Here I show that the AU test is   less biased than other methods in typical cases of tree selection. These   points are illustrated in a simulation study as well as in the analysis of   mammalian mitochondrial protein sequences. The theoretical argument provides   a simple formula that covers the bootstrap probability test, the   Kishino-Hasegawa test, the AU test, and the Zharkikh-Li test. A practical suggestion   is provided as to which test should be used under particular circumstances.

为了减少多区域通用假设检验偏差，近无偏检验（AU test）这一多尺度自举检验技术被开发了出来。它应用于最大似然树选择，以得到树的置信集。AU检验基于Efron等人的理论（Proc. Natl.   Acad. Sci. USA 93:13429-13434; 1996），但新方法精度更高，操作更简便。AU检验，像Shimodaira-Hasegawa（SH）检验一样，调整了选择偏差，而这些偏差是被标准自举检验概率方法和Kishino-Hasegawa检验所忽略的。选择偏差来自于同时比较多棵树，并且常常导致错误树的过度自信。虽然使用SH检验较为保险，但它可能会显示出另一种类型的偏差，即偏保守。在这里，我证明了在典型的树选择情况下，AU检验比其他方法的偏差更小。这些观点在模拟研究和哺乳动物线粒体蛋白序列分析中得到了说明。理论论证提供了一个简单的公式，涵盖了自举概率检验、Kishino-Hasegawa检验、AU检验和Zharkikh-Li检验。本研究还提出了在特殊情况下应采用何种检验的实用建议。