About the book
Confidence regions is one of the most frequently used statistical measures, due to their simple interpretation. Built on the concept of probability of success for repeated testing, they seem natural in many contexts in medicine, natural and social sciences, as well as technology, despite that single testing prevails. Nevertheless, estimation of confidence or coverage is non-trivial as it relates to ordering of outcomes, rather than statistical expectations, which are more regular and well-behaved. Indeed, confidence boundaries are often hypothetically related to expectations by assumed coverage factors. Truthful assessment of confidence regions based on ordering rather than expectations and assumptions, however, is especially challenging for multi-modal and multi-variate distributions reflecting strong non-uniformity of samples and parametric dependency. The achieved level of confidence may have a potentially large impact on society at large, especially in the fields of medicine, safety, and election polling where the notion of confidence regions is the standard behind the apparently contradictory formulation of statistical certainty. Disputable credibility of presented confidence or coverage levels may have unprecedented consequences, most recently actualized in the quest for credible long term predictions of the COVID-19 pandemic.