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Relative Maximum Likelihood updating of ambiguous beliefs

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  • Cheng, Xiaoyu

Abstract

This paper proposes and axiomatizes a new updating rule: Relative Maximum Likelihood (RML) updating for ambiguous beliefs represented by a set of priors (C). This rule takes the form of applying Bayes’ rule to a subset of C. This subset is a linear contraction of C towards its subset ascribing the maximal probability to the observed event. The degree of contraction captures the extent of willingness to discard priors based on likelihood when updating. Two well-known updating rules of multiple priors, full Bayesian (FB) and Maximum Likelihood (ML), are included as special cases of RML. An axiomatic characterization of conditional preferences generated by RML updating is provided when the preferences admit Maxmin Expected Utility representations. The axiomatization relies on weakening the axioms characterizing FB and ML. The axiom characterizing ML is identified for the first time in this paper, addressing a long-standing open question in the literature.

Suggested Citation

  • Cheng, Xiaoyu, 2022. "Relative Maximum Likelihood updating of ambiguous beliefs," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    • Handle: RePEc:eee:mateco:v:99:y:2022:i:c:s0304406821001488
    DOI: 10.1016/j.jmateco.2021.102587
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    References listed on IDEAS

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    Cited by:

    1. Phoebe Koundouri & Nikitas Pittis & Panagiotis Samartzis, 2023. "Counterfactual Priors: A Bayesian Response to Ellsberg's Paradox," DEOS Working Papers 2307, Athens University of Economics and Business.
    2. Yi-Hsuan Lin & Fernando Payró Chew, 2024. "Updating Under Imprecise Information," Working Papers 1424, Barcelona School of Economics.

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