  The current and upcoming generation of Very Large Volume Neutrino
Telescopes---collecting unprecedented quantities of neutrino events---can be
used to explore subtle effects in oscillation physics, such as (but not
restricted to) the neutrino mass ordering. The sensitivity of an experiment to
these effects can be estimated from Monte Carlo simulations. With the high
number of events that will be collected, there is a trade-off between the
computational expense of running such simulations and the inherent statistical
uncertainty in the determined values. In such a scenario, it becomes
impractical to produce and use adequately-sized sets of simulated events with
traditional methods, such as Monte Carlo weighting. In this work we present a
staged approach to the generation of binned event distributions in order to
overcome these challenges. By combining multiple integration and smoothing
techniques which address limited statistics from simulation it arrives at
reliable analysis results using modest computational resources.
