Next generation Monte Carlo methods based on reversible proposal Metropolis-Hastings algorithms

2019 Fiscal Year Final Research Report

• Project/Area Number: 16K00046
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Statistical science
• Research Institution: Osaka University
• Principal Investigator: Kamatani Kengo 大阪大学, 基礎工学研究科, 准教授 (00569767)
• Project Period (FY): 2016-04-01 – 2020-03-31
• Keywords: ベイズ統計学 / マルコフ連鎖 / モンテカルロ法 / 確率過程

Outline of Final Research Achievements

I worked on Monte Carlo methods for the integral evaluations that appear in Bayesian statistics. We focused on the simplest class of Markov kernels for Monte Carlo methods. I showed that a minor generalization of a simple method worked quite well in both high-dimensional and heavy-tailed target distributions. No other method of having the same properties is known. Another result is the non-reversible Markov process. In collaboration with the UK and Netherlands' researchers, we obtained quantitative results for non-reversible Markov processes in a Monte Carlo context.

Free Research Field

統計科学

Academic Significance and Societal Importance of the Research Achievements

対称なマルコフ連鎖の研究の成果により，研究開始以前に提案していた手法が，高次元にも，裾の重い分布にも有効に働くことがわかった．おなじ性質を持つ手法は知られていない．また，研究開始前後に，非対称なマルコフ過程の重要性がベイズ統計学者に認識され始めていた．我々がはじめて定量的な評価をしたことによって実際にどの程度有効であるか，どんな場合に有効であるかがよりはっきりわかった．