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A Robust Conflict Measure of Inconsistencies in Bayesian Hierarchical Models

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  • FREDRIK A. DAHL
  • JØRUND GÅSEMYR
  • BENT NATVIG

Abstract

. O'Hagan (Highly Structured Stochastic Systems, Oxford University Press, Oxford, 2003) introduces some tools for criticism of Bayesian hierarchical models that can be applied at each node of the model, with a view to diagnosing problems of model fit at any point in the model structure. His method relies on computing the posterior median of a conflict index, typically through Markov chain Monte Carlo simulations. We investigate a Gaussian model of one‐way analysis of variance, and show that O'Hagan's approach gives unreliable false warning probabilities. We extend and refine the method, especially avoiding double use of data by a data‐splitting approach, accompanied by theoretical justifications from a non‐trivial special case. Through extensive numerical experiments we show that our method detects model mis‐specification about as well as the method of O'Hagan, while retaining the desired false warning probability for data generated from the assumed model. This also holds for Student's‐t and uniform distribution versions of the model.

Suggested Citation

  • Fredrik A. Dahl & Jørund Gåsemyr & Bent Natvig, 2007. "A Robust Conflict Measure of Inconsistencies in Bayesian Hierarchical Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(4), pages 816-828, December.
    • Handle: RePEc:bla:scjsta:v:34:y:2007:i:4:p:816-828
    DOI: 10.1111/j.1467-9469.2007.00560.x
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    Cited by:

    1. Jørund Gåsemyr, 2016. "Uniformity of Node Level Conflict Measures in Bayesian Hierarchical Models Based on Directed Acyclic Graphs," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 20-34, March.
    2. Jørund Gåsemyr & Bent Natvig, 2009. "Extensions of a Conflict Measure of Inconsistencies in Bayesian Hierarchical Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(4), pages 822-838, December.
    3. Gunnhildur Högnadóttir Steinbakk & Geir Olve Storvik, 2009. "Posterior Predictive p‐values in Bayesian Hierarchical Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 320-336, June.
    4. Ying Yuan & Valen E. Johnson, 2012. "Goodness-of-Fit Diagnostics for Bayesian Hierarchical Models," Biometrics, The International Biometric Society, vol. 68(1), pages 156-164, March.

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