  The behaviors of various confidence/credible interval constructions are
explored, particularly in the region of low statistics 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 behaviours 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 models 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.
