In many Scientific studies, hypotheses to be tested are often determined by the data. Once the test for the generated hypothesis is conducted by using the same data, the test become no more valid due to the fact that the p-value is underestimated, which causes selection bias. In order to address such problems, we have been studied post-selection inference to make valid testing even when the same data is used for both stages.

A gene expression data and an example of the change point common to several patients. The p-value of the test for the change point detected exploratory from the data becomes 0.00 after properly taking into account the selection bias.

It is important to extract relevant variables from the data, such as gene expression data, for which the number of variables may be exponentially larger than the sample size. Such methods are useful at least of the point of view of computational efficiency and estimation accuracy for the inference after variable selection. On the other hand, it becomes difficult to extract relevant variables when there are nonlinear dependency between the variables. We are developing methods to extract such nonlinear dependency effectively.