Abstract
In Bayesian statistics, the choice of prior distribution is often debatable, especially if prior knowledge is limited or data are scarce. In imprecise probability, sets of priors are used to accurately model and reflect prior knowledge. This has the advantage that prior-data conflict sensitivity can be modelled: Ranges of posterior inferences should be larger when prior and data are in conflict. We propose a new method for generating prior sets which, in addition to prior-data conflict sensitivity, allows to reflect strong prior-data agreement by decreased posterior imprecision.
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Notes
- 1.
We denote prior parameter values by upper index \({}^{(0)}\) and posterior parameter values, after n observations, by upper index\({}^{(n)}\).
- 2.
We treat s as a a real-value in [0, n] for convenience of our discussions; this does not affect the conclusions.
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Acknowledgements
Gero Walter was supported by the Dinalog project “Coordinated Advanced Maintenance and Logistics Planning for the Process Industries” (CAMPI).
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Walter, G., Coolen, F.P.A. (2016). Sets of Priors Reflecting Prior-Data Conflict and Agreement. In: Carvalho, J., Lesot, MJ., Kaymak, U., Vieira, S., Bouchon-Meunier, B., Yager, R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2016. Communications in Computer and Information Science, vol 610. Springer, Cham. https://doi.org/10.1007/978-3-319-40596-4_14
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