The comparison of the confidence regions in phylogeny

In this paper, several different procedures for constructing confidence regions for the true evolutionary tree are evaluated both in terms of coverage and size without considering model misspecification. The regions are constructed on the basis of tests of hypothesis using six existing tests: Shimodaira Hasegawa (SH), SOWH, star form of SOWH (SSOWH), approximately unbiased (AU), likelihood weight (LW), generalized least squares, plus two new tests proposed in this paper: single distribution nonparametric bootstrap (SDNB) and single distribution parametric bootstrap (SDPB). The procedures are evaluated on simulated trees both with small and large number of taxa. Overall, the SH, SSOWH, AU, and LW tests led to regions with higher coverage than the nominal level at the price of including large numbers of trees. Under the specified model, the SOWH test gives accurate coverage and relatively small regions. The SDNB and SDPB tests led to the small regions with occasional undercoverage. These two procedures have a substantial computational advantage over the SOWH test. Finally, the cutoff levels for the SDNB test are shown to be more variable than those for the SDPB test.