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Predictive distributions that mimic frequencies over a restricted subdomain

Author

Listed:
  • Frank Lad

    (University of Canterbury)

  • Giuseppe Sanfilippo

    (University of Palermo)

Abstract

A predictive distribution over a sequence of $$N+1$$ 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.

Suggested Citation

  • Frank Lad & Giuseppe Sanfilippo, 2020. "Predictive distributions that mimic frequencies over a restricted subdomain," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 17-41, June.
    • Handle: RePEc:spr:decfin:v:43:y:2020:i:1:d:10.1007_s10203-020-00281-z
    DOI: 10.1007/s10203-020-00281-z
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    References listed on IDEAS

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    1. Capotorti, Andrea & Lad, Frank & Sanfilippo, Giuseppe, 2007. "Reassessing Accuracy Rates of Median Decisions," The American Statistician, American Statistical Association, vol. 61, pages 132-138, May.
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    Cited by:

    1. Gianluca Cassese & Pietro Rigo & Barbara Vantaggi, 2020. "A special issue on the mathematics of subjective probability," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 1-2, June.

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      More about this item

      Keywords

      Probability elicitation; Conditional probability; Probability bounds; Extendable exchangeability; $$A_n$$ A n and $$H_n$$ H n distributions;
      All these keywords.

      JEL classification:

      • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
      • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General

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