  The estimation of signal frequency count in the presence of background noise
has had much discussion in the recent physics literature, and Mandelkern [1]
brings the central issues to the statistical community, leading in turn to
extensive discussion by statisticians. The primary focus however in [1] and the
accompanying discussion is on the construction of a confidence interval. We
argue that the likelihood function and $p$-value function provide a
comprehensive presentation of the information available from the model and the
data. This is illustrated for Gaussian and Poisson models with lower bounds for
the mean parameter.
