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Conditioning on uncertain event: Extensions to bayesian inference

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Abstract

In this paper the alternative procedure for updating probabilities (that is, to calculate the posterior distribution from the prior distribution) proposed by Richard Jeffrey is considered, which allows the addition of new information to the prior distribution under more circumstances than with the Bayesian conditioning. A predictivistic approach for the Jeffrey’s rule is introduced and a definition of conjugacy according to this rule (named Jeffrey-conjugacy) is established. Results for Jeffrey-conjugacy in the exponential family are also presented. As a by-product, these results provide full predictivistic characterizations of some predictive distributions. By using both the predictivistic Jeffrey’s rule and Jeffrey-conjugacy, a forecasting procedure which is applied to the Chilean stock market, data is also developed. The Jeffrey’s rule with the Bayesian conditioning according to their capability of incorporating unpredictable information in the forecast is compared.

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Authors and Affiliations

  1. Departmento de Estatística, Pontifícia Universidad Católica de Chile, Chile

    Pilar Loreto Iglesias & Rinaldo Boris Arellano-Valle

  2. Departmento de Estatística, Universidade Federal de Minas Gerais, Caixa Postal 702 CEP 30123-970, Belo Horizonte/MG, Brazil

    Rosangela Helena Loschi

Authors
  1. Rosangela Helena Loschi
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  2. Pilar Loreto Iglesias
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  3. Rinaldo Boris Arellano-Valle
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Correspondence to Rosangela Helena Loschi.

Additional information

Research support in part by FAPEMIG, grant CEX 795/00; PRPq-UFMG, grant 40-UFMG/RTR/FUNDO/PRPq/99; and CAPES (Brazil): FONDECYT, grants 8000004, 1971128 and 1990431; and Fundación Andes (Chile).

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Loschi, R.H., Iglesias, P.L. & Arellano-Valle, R.B. Conditioning on uncertain event: Extensions to bayesian inference. Test 11, 365–383 (2002). https://doi.org/10.1007/BF02595712

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