  The high computational expense of simulating light through ray-tracing in
large, sparsely instrumented particle detectors such as IceCube and Antares is
a critical outstanding problem in particle physics. When the detector is
sparsely instrumented, ray tracing is inefficient, as nearly all of these rays
are either lost in the bulk of the detector due to absorption or simply fail to
end on a detector. Particle astrophysics experiments face a similar problem
when they simulate cosmic ray muon fluxes in their detectors. Many fields of
science face calculations that involve constrained initial and final states,
with stochastic processes between. Taking the case of ray-tracing of light as
our example, this paper describes a new and highly computationally efficient
approach to the problem. By specifying the problem as a path integral, the
final state of these rays can be constrained to land on a light sensitive
element. The path integral can then be efficiently sampled using Reversible
Jump Markov Chain Monte-Carlo, yielding performance improvements of up to 1,000
times faster on a realistic test scenario.
