  Confidence is a fundamental concept in statistics, but there is a tendency to
misinterpret it as probability. In this paper, I argue that an intuitively and
mathematically more appropriate interpretation of confidence is through
belief/plausibility functions, in particular, those that satisfy a certain
validity property. Given their close connection with confidence, it is natural
to ask how a valid belief/plausibility function can be constructed directly.
The inferential model (IM) framework provides such a construction, and here I
prove a complete-class theorem stating that, for every nominal confidence
region, there exists a valid IM whose plausibility regions are contained by the
given confidence region. This characterization has implications for statistics
understanding and communication, and highlights the importance of belief
functions and the IM framework.
