  This paper outlines a method for improving the precision of atmospheric
neutrino oscillation measurements. One experimental signature for these
oscillations is an observed deficit in the rate of $\nu_{\mu}$ charged-current
interactions with an oscillatory dependence on $L_{\nu}/E_{\nu}$, where
$L_{\nu}$ is the neutrino propagation distance, and $E_{\nu}$ is the neutrino
energy. For contained-vertex atmospheric neutrino interactions, the
$L_{\nu}/E_{\nu}$ resolution varies significantly from event to event. The
precision of the oscillation measurement can be improved by incorporating
information on $L_{\nu}/E_{\nu}$ resolution into the oscillation analysis. In
the analysis presented here, a Bayesian technique is used to estimate the
$L_{\nu}/E_{\nu}$ resolution of observed atmospheric neutrinos on an
event-by-event basis. By separating the events into bins of $L_{\nu}/E_{\nu}$
resolution in the oscillation analysis, a significant improvement in
oscillation sensitivity can be achieved.
