Title: Backward Simulation of Stochastic Process using a Time Reverse Monte Carlo method,
Abstract: The "backward simulation" of a stochastic process is defined as the
stochastic dynamics that trace a time-reversed path from the target region to
the initial configuration. If the probabilities calculated by the original
simulation are easily restored from those obtained by backward dynamics, we can
use it as a computational tool. It is shown that the naive approach to backward
simulation does not work as expected. As a remedy, the Time Reverse Monte Carlo
method (TRMC) based on the ideas of Sequential Importance Sampling (SIS) and
Sequential Monte Carlo (SMC) is proposed and successfully tested with a
stochastic typhoon model and the Lorenz 96 model. TRMC with SMC, which contains
resampling steps, is shown to be more efficient for simulations with a larger
number of time steps. A limitation of TRMC and its relation to the Bayes
formula are also discussed.