Backward Simulation of Stochastic Process Using a Time Reverse Monte Carlo Method

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 found 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.