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Pseudo‐Bayesian updating
Author(s) -
Zhao Chen
Publication year - 2022
Publication title -
theoretical economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.404
H-Index - 32
eISSN - 1555-7561
pISSN - 1933-6837
DOI - 10.3982/te4535
Subject(s) - axiom , event (particle physics) , bayesian probability , computer science , mathematical economics , prior probability , artificial intelligence , divergence (linguistics) , kullback–leibler divergence , bayesian inference , stochastic game , probabilistic logic , mathematics , machine learning , linguistics , philosophy , physics , geometry , quantum mechanics
I propose an axiomatic framework for belief revision when new information is qualitative, of the form “event A is at least as likely as event B .” My decision maker need not have beliefs about the joint distribution of the signal she will receive and the payoff‐relevant states. I propose three axioms, Exchangeability , Stationarity , and Reduction , to characterize the class of pseudo‐Bayesian updating rules. The key axiom, Exchangeability , requires that the order in which the information arrives does not matter if the different pieces of information neither reinforce nor contradict each other. I show that adding one more axiom, Conservatism , which requires that the decision maker adjust her beliefs just enough to embrace new information, yields Kullback–Leibler minimization: The decision maker selects the posterior closest to her prior in terms of Kullback–Leibler divergence from the probability measures consistent with newly received information. I show that pseudo‐Bayesian agents are susceptible to recency bias, which may be mitigated by repetitive learning.

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