Learning under misspecified likelihoods

Determine whether the convergence results for heterogeneous and time-varying non-Bayesian social learning remain valid under likelihood misspecification when the likelihood associated with the true state is the closest to the actual signal distribution.

Background

The analysis assumes a correctly specified finite state space and correctly specified likelihoods: the actual signal distribution is exactly the likelihood associated with the true state. This ensures that Bayesian updating is calibrated to the data-generating process.

The unresolved question is whether the paper’s learning conclusions persist under misspecification when no likelihood is exactly correct, but the likelihood corresponding to the true state remains closest to the real signal distribution.

References

Do these results hold when this equality no longer holds but the likelihood under the true state remains the closest to the real signal distribution?

— Non-Bayesian Social Learning with Heterogeneous and Time-Varying Aggregation Rules  (2610.13611 - Oukaci et al., 9 Oct 2026) in Section 5, Discussion and Future Work, paragraph “Misspecification”