2014/05/31 by S. D. Biller, Steven D. Biller, Scott M. Oser
Decision Sciences · Mathematics · Physics and Astronomy · Psychology · #Aside #Computer science #Epistemology #Instinct #Linguistics #Philosophy #Political science #Probabilistic and Robust Engineering Design #Psychology #Relevance (law) #Statistical Methods in Clinical Trials #astro-ph.IM #hep-ex #hep-ph #physics.data-an
paper · pdf · doi:10.1016/j.nima.2014.11.081
published as Nuclear Instruments and methods in Physics Research A 774 (2015) 103-119 · 23 pages, 11 figures
openalex publication_date 2014/11/29 · arxiv created 2015/02/03 · arxiv updated 2015/02/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The behaviors of various confidence/credible interval constructions are explored, particularly in the region of low event numbers where methods diverge most. We highlight a number of challenges, such as the treatment of nuisance parameters, and common misconceptions associated with such constructions. An informal survey of the literature suggests that confidence intervals are not always defined in relevant ways and are too often misinterpreted and/or misapplied. This can lead to seemingly paradoxical behaviors and flawed comparisons regarding the relevance of experimental results. We therefore conclude that there is a need for a more pragmatic strategy which recognizes that, while it is critical to objectively convey the information content of the data, there is also a strong desire to derive bounds on model parameter values and a natural instinct to interpret things this way. Accordingly, we attempt to put aside philosophical biases in favor of a practical view to propose a more transparent and self-consistent approach that better addresses these issues.