Applications of time reverse Monte Carlo method and its relation to data analysis

2019 Fiscal Year Final Research Report

• Project/Area Number: 16K00345
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Soft computing
• Research Institution: The Institute of Statistical Mathematics
• Principal Investigator: Iba Yukito 統計数理研究所, モデリング研究系, 教授 (30213200)
• Project Period (FY): 2016-04-01 – 2020-03-31
• Keywords: 時間逆転 / モンテカルロ法 / 逐次モンテカルロ法 / 確率過程 / レアイベント

Outline of Final Research Achievements

We improved "Time reverse Monte Carlo method" for calculating rare event probabilities, which is proposed in our previous study. In this method, the probability of rare events under the assumed stochastic difference equation is calculated by stochastic dynamics that traces a time-reversed path from the target region to the initial state. We tested the following improvements of the algorithm and showed that they improve the efficiency of computation without introducing bias of the estimated probabilities: (1) Use of the sequential Monte Carlo method that splits/erases paths according to the weight of paths, (2) Improvement of the transition probability for generating time-reversed paths, (3) Introduction of "guiding field" that controls the direction of paths.

Free Research Field

統計学，統計物理学

Academic Significance and Societal Importance of the Research Achievements

確率が極端に低い事象（たとえば、東京に台風が直撃する）について通常のシミュレーションの繰り返しで生起確率を計算すると多くの計算量を要する。これに対し、本研究では、前回の科研費で提案した「出発点から経路を逆にたどる」という発想にもとづいた手法を発展させ、いくつかの重要な改良を加えた。こうしたタイプの問題はさまざまなな分野で応用があり、提案手法の学術的・社会的意義は大きいと考えられる。