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

1
Department of Methods and Statistics, Utrecht University, 3584 CH 14 Utrecht, The Netherlands
2
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; https://doi.org/10.3390/e21050446
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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Abstract

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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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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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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