On the meaning of coverage probabilities. http://dx.doi.org/doi:10.1088/0026-1394/46/6/002

Abstract

It has been argued that the probability associated with a coverage interval calculated following the procedure proposed in Supplement 1 to the GUM should be about equal to the proportion of independent intervals reckoned over time that contain the measurand (Willink 2006 Metrologia 43 L39–42, Hall 2008 Metrologia 45 L5–8, Possolo et al 2009 Metrologia 46
L1–7). The opposite point of view maintains that a coverage probability can only be interpreted as the degree of belief in the quoted interval containing the unknown value of the
measurand (Lira 2008 Metrologia 45 L21–3). In this paper, two simple examples are presented to reinforce the latter interpretation.