When can finite testing ensure infinite trustworthiness? (English) Zbl 06657078

Singpurwalla, Nozer D.; Wilson, Philip

J. Iran. Stat. Soc. JIRSS 3, No. 1, 1-37 (2004).

Summary: In this paper we contribute to the general philosophical question as to whether empirical testing can ever prove a physical law. Problems that lead to this question arise under several contexts, and the matter has been addressed by the likes of Bayes and Laplace. After pointing out that a Bayesian approach is the proper way to address this problem, we show that the answer depends on what we start with. Namely, under certain prior assumptions, a finite amount of testing can lead to the conclusion of total trustworthiness, though such priors could be unrealistic. However, we do produce a new class of priors under which a finite amount of testing can lead to a high degree of trustworthiness, at a relatively fast pace. We use the scenario of software testing as a way to motivate and discuss our development.

MSC:

62A01

Foundations and philosophical topics in statistics

Keywords:

Bayes’ law; discrete priors; Jeffreys’ prior; reliability; sample size; software testing; stockpile stewardship