A study on asymptotic analysis for robust quasi-posterior distributions

2022 Fiscal Year Final Research Report

• Project/Area Number: 19K14597
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 12040:Applied mathematics and statistics-related
• Research Institution: Tokyo University of Science
• Principal Investigator: Nakagawa Tomoyuki 東京理科大学, 理工学部情報科学科, 嘱託特別講師 (70822526)
• Project Period (FY): 2019-04-01 – 2023-03-31
• Keywords: ベイズ統計 / ロバスト統計 / 漸近理論

Outline of Final Research Achievements

When dealing with large amounts of data, issues such as outliers and model misspecification can be very serious. Outliers are data points that deviate greatly from the data generating process and can have a significant impact on inference. On the other hand, outliers can also suggest model misspecification, making it important to handle them appropriately. The problem of model misspecification and the presence of outliers has been discussed in Bayesian statistics for a long time. In this study, we developed a Bayesian method that is robust to outliers and investigated its theoretical properties. Specifically, we constructed a robust Bayesian estimator using a pseudo-distance between distributions called divergence and derived its asymptotic properties when performing inference using methods such as MCMC.

Free Research Field

数理統計

Academic Significance and Societal Importance of the Research Achievements

近年は膨大な数のデータが取れるため, その中から外れ値を見つけることは大変困難である. また外れ値に影響されるような手法は, しばしば誤った解析結果を誘導することがある. 一方で外れ値を含む場合は仮定したモデルが誤っている可能性もあるため, 外れ値の扱いは重要である. 特に外れ値に影響を受けにくい解析は, 現在のモデルとデータで説明できる部分の結果を返してくれる. そのため本研究は, データに外れ値が含まれていても影響を受けにくいベイズ法とその理論的性質の導出を行ったことで, 推定だけでなく予測や不確実性の評価も外れ値の影響を受けにくくすることができる.