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

Shouto Yonekura, Shonosuke Sugasawa

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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.

Original languageEnglish
Article number39
JournalStatistics and Computing
Issue number2
Publication statusPublished - 2023 Apr
Externally publishedYes


  • Density power divergence
  • General Bayes
  • Robustness
  • Sequential Monte Carlo
  • Tuning parameter estimation

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Computational Theory and Mathematics


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