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The Wasserstein Impact Measure (WIM): A practical tool for quantifying prior impact in Bayesian statistics

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  • Ghaderinezhad, Fatemeh
  • Ley, Christophe
  • Serrien, Ben

Abstract

The prior distribution is a crucial building block in Bayesian analysis, and its choice will impact the subsequent inference. It is therefore important to have a convenient way to quantify this impact, as such a measure of prior impact will help to choose between two or more priors in a given situation. To this end a new approach, the Wasserstein Impact Measure (WIM), is introduced. In three simulated scenarios, the WIM is compared to two competitor prior impact measures from the literature, and its versatility is illustrated via two real datasets.

Suggested Citation

  • Ghaderinezhad, Fatemeh & Ley, Christophe & Serrien, Ben, 2022. "The Wasserstein Impact Measure (WIM): A practical tool for quantifying prior impact in Bayesian statistics," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:csdana:v:174:y:2022:i:c:s0167947321001869
    DOI: 10.1016/j.csda.2021.107352
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    References listed on IDEAS

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    1. Holger Dette & Christophe Ley & Francisco Rubio, 2018. "Natural (Non†)Informative Priors for Skew†symmetric Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 45(2), pages 405-420, June.
    2. Satoshi Morita & Peter F. Thall & Peter Müller, 2008. "Determining the Effective Sample Size of a Parametric Prior," Biometrics, The International Biometric Society, vol. 64(2), pages 595-602, June.
    3. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
    4. A. Racine & A. P. Grieve & H. Flühler & A. F. M. Smith, 1986. "Bayesian Methods in Practice: Experiences in the Pharmaceutical Industry," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 35(2), pages 93-120, June.
    5. Ghaderinezhad, Fatemeh & Ley, Christophe, 2019. "Quantification of the impact of priors in Bayesian statistics via Stein’s Method," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 206-212.
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