A Robust Conflict Measure of Inconsistencies in Bayesian Hierarchical Models |
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Authors: | FREDRIK A DAHL JØRUND GÅSEMYR BENT NATVIG |
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Institution: | Health Services Research Unit, Akershus University Hospital, and Department of Mathematics, University of Oslo; Department of Mathematics, University of Oslo |
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Abstract: | 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. |
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Keywords: | double use of data Markov chain Monte Carlo simulations model evaluation one-way analysis of variance |
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