  While gravitational waves have not yet been measured directly, data analysis
from detection experiments commonly includes an upper limit statement. Such
upper limits may be derived via a frequentist or Bayesian approach; the
theoretical implications are very different, and on the technical side, one
notable difference is that one case requires maximization of the likelihood
function over parameter space, while the other requires integration. Using a
simple example (detection of a sinusoidal signal in white Gaussian noise), we
investigate the differences in performance and interpretation, and the effect
of the "trials factor", or "look-elsewhere effect".
