Selective inference for testing trees and edges in hierarchical clustering and phylogeny

Bootstrap resampling is quite useful for computing “confidence values” or “p-values” of trees and edges. However, they are biased and may lead to false positives (too many wrong discoveries) or false negatives (too few correct discoveries) depending on the “curvature” of the boundary surface of a hypothesis region in the data space. In addition, we face the issue of selection bias because we tend to use the dataset twice for hypothesis selection and its evaluation. I will explain these two types of bias and show methods to adjust the confidence values.