Abstract
A predictive distribution over a sequence of \(N+1\) events is said to be “frequency mimicking” whenever the probability for the final event conditioned on the outcome of the first N events equals the relative frequency of successes among them. Exchangeable distributions that exhibit this feature universally are known to have several annoying concomitant properties. We motivate frequency mimicking assertions over a limited subdomain in practical problems of finite inference, and we identify their computable coherent implications. We provide some examples using reference distributions, and we introduce computational software to generate any complete specification desired. Theorems on reduction and extendability of frequency mimicking assertions delineate the extent of the usefulness of such distributions.
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Acknowledgements
We thank a guest editor and the anonymous reviewers for their careful reading of our manuscript and their helpful suggestions. Thanks to James O’Malley, Wes Johnson, Val Johnson, Andrea Piesse, and Angelo Gilio for helpful comments on earlier drafts of this article during the many years of its development, and to Jay Kadane for a helpful reference.
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Lad, F., Sanfilippo, G. Predictive distributions that mimic frequencies over a restricted subdomain. Decisions Econ Finan 43, 17–41 (2020). https://doi.org/10.1007/s10203-020-00281-z
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DOI: https://doi.org/10.1007/s10203-020-00281-z
Keywords
- Probability elicitation
- Conditional probability
- Probability bounds
- Extendable exchangeability
- \(A_n\) and \(H_n\) distributions