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How the Choice of Distance Measure Influences the Detection of Prior-Data Conflict

Department of Methods and Statistics, Utrecht University, 3584 CH 14 Utrecht, The Netherlands
Optentia Research Program, Faculty of Humanities, North-West University, Vanderbijlpark 1900, South Africa
Author to whom correspondence should be addressed.
Entropy 2019, 21(5), 446;
Received: 28 March 2019 / Revised: 16 April 2019 / Accepted: 23 April 2019 / Published: 29 April 2019
(This article belongs to the Special Issue Bayesian Inference and Information Theory)
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The present paper contrasts two related criteria for the evaluation of prior-data conflict: the Data Agreement Criterion (DAC; Bousquet, 2008) and the criterion of Nott et al. (2016). One aspect that these criteria have in common is that they depend on a distance measure, of which dozens are available, but so far, only the Kullback-Leibler has been used. We describe and compare both criteria to determine whether a different choice of distance measure might impact the results. By means of a simulation study, we investigate how the choice of a specific distance measure influences the detection of prior-data conflict. The DAC seems more susceptible to the choice of distance measure, while the criterion of Nott et al. seems to lead to reasonably comparable conclusions of prior-data conflict, regardless of the distance measure choice. We conclude with some practical suggestions for the user of the DAC and the criterion of Nott et al. View Full-Text
Keywords: prior-data conflict; distance measure; Kullback-Leibler; data agreement criterion prior-data conflict; distance measure; Kullback-Leibler; data agreement criterion

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Lek, K.; Van De Schoot, R. How the Choice of Distance Measure Influences the Detection of Prior-Data Conflict. Entropy 2019, 21, 446.

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