I think that up to now I haven’t seen a completely unbiased overview of how statistical tests of different types should be applied to a data from astronomy. If I will see such a paper, I will post the link here.

In general, I have an impression that there are still some powerful tests that weren’t used in statistical problems of astronomy yet. Also, I think that there are still many statistical problems in astronomy such that the statisticians haven’t constructed optimal tests for these problems. In principle, it is the aim of the theory of statistical inverse problems to provide such testing procedures. But this theory is still under development. There remains a lot of work both for theoreticians and practitioners.

—[hlee response] Thank you for your comment and promise for sharing information. It would be very valuable to know theoretical perspective of applying goodness-of-fit tests incorporating information from data. Relying on my impression, there’s not much understanding of powerful tests or optimal tests in the astronomical community mainly due to the complexity of physical models and data process.