Adaptation of the tuning parameter in general Bayesian inference with robust divergence

Shouto Yonekura, Shonosuke Sugasawa

研究成果: Article査読


We introduce a novel methodology for robust Bayesian estimation with robust divergence (e.g., density power divergence or γ-divergence), indexed by tuning parameters. It is well known that the posterior density induced by robust divergence gives highly robust estimators against outliers if the tuning parameter is appropriately and carefully chosen. In a Bayesian framework, one way to find the optimal tuning parameter would be using evidence (marginal likelihood). However, we theoretically and numerically illustrate that evidence induced by the density power divergence does not work to select the optimal tuning parameter since robust divergence is not regarded as a statistical model. To overcome the problems, we treat the exponential of robust divergence as an unnormalisable statistical model, and we estimate the tuning parameter by minimising the Hyvarinen score. We also provide adaptive computational methods based on sequential Monte Carlo samplers, enabling us to obtain the optimal tuning parameter and samples from posterior distributions simultaneously. The empirical performance of the proposed method through simulations and an application to real data are also provided.

ジャーナルStatistics and Computing
出版ステータスPublished - 2023 4月

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • 統計学および確率
  • 統計学、確率および不確実性
  • 計算理論と計算数学


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