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Pathwise concentration bounds for Bayesian beliefs

Author

Listed:
  • Fudenberg, Drew

    (Department of Economics, Massachusetts Institute of Technology)

  • Lanzani, Giacomo

    (Department of Economics, Massachusettes Institute of Technology)

  • Strack, Philipp

    (Department of Economics, Yale University)

Abstract
We show that Bayesian posteriors concentrate on the outcome distributions that approximately minimize the Kullback-Leibler divergence from the empirical distribution, uniformly over sample paths, even when the prior does not have full support. This generalizes Diaconis and Freedman (1990)'s uniform convergence result to e.g., priors that have finite support, are constrained by independence assumptions, or have a parametric form that cannot match some probability distributions. The concentration result lets us provide a rate of convergence for Berk (1996)’s result on the limiting behavior of posterior beliefs when the prior is misspecified. We provide a bound on approximation errors in “anticipated-utility” models, and extend our analysis to outcomes that are perceived to follow a Markov proces

Suggested Citation

  • Fudenberg, Drew & Lanzani, Giacomo & Strack, Philipp, 2023. "Pathwise concentration bounds for Bayesian beliefs," Theoretical Economics, Econometric Society, vol. 18(4), November.
    • Handle: RePEc:the:publsh:5206
    as

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    References listed on IDEAS

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    More about this item

    Keywords

    Learning; misspecification; Bayesian updating; consistency; concentration of beliefs;
    All these keywords.

    JEL classification:

    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General

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