Limited confidence in cosmological confidence contours

There is a certain longstanding tradition of slightly doubting posteriors reported by cosmological experiments: slight tensions between parameters inferred from the early and late Universe, or different cosmological probes, spark this slight doubt time and time again. With the advent of observatories operating at the precision of LSST/Euclid/SKA, the currently mild tensions can rapidly turn into drastic tensions. It would then be beneficial to be fully certain about whether these tensions originate from new physics or an agglomeration of human-made small mistakes (approximations, biases). In this talk I will summarize a series of results from my research on how to tell apart new physics and human-made mistakes.