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Relative Maximum Likelihood Updating of Ambiguous Beliefs

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  • Xiaoyu Cheng

Abstract

This paper proposes and axiomatizes a new updating rule: Relative Maximum Likelihood (RML) 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 a 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.

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  • Xiaoyu Cheng, 2019. "Relative Maximum Likelihood Updating of Ambiguous Beliefs," Papers 1911.02678, arXiv.org, revised Oct 2021.
    • Handle: RePEc:arx:papers:1911.02678
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    References listed on IDEAS

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    Cited by:

    1. Xiaoyu Cheng, 2022. "Robust Data-Driven Decisions Under Model Uncertainty," Papers 2205.04573, arXiv.org.
    2. Xiaoyu Cheng, 2021. "Extended Relative Maximum Likelihood Updating of Choquet Beliefs," Papers 2109.02597, arXiv.org.

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