Finite-sample Bayesian posterior concentration for preference elicitation

Determine whether the finite-sample identifiability, minimax, MLE-existence, and error-bound theory for linear-in-parameter utility elicitation under the Bradley–Terry–Luce model can be extended to Bayesian learning approaches so as to characterize posterior concentration rates, including posterior inference based on Jeffreys’ invariant prior.

Background

The paper analyzes the canonical MLE and uses the Firth correction for numerical comparison, while Bayesian priors are discussed as an alternative external stabilization mechanism. The existing results do not characterize posterior behavior or concentration rates for Bayesian estimators.

The authors explicitly leave open whether their finite-sample theoretical results can be transferred to Bayesian learning approaches. They identify posterior inference based on Jeffreys’ invariant prior as a particularly relevant case because its posterior mode yields the Firth correction.

References

An important direction for future work is to investigate whether the theoretical results can be extended to Bayesian learning approaches to describe posterior concentration rates with finite samples, which may also include posterior based on Jeffreys' invariant prior, whose mode yields the Firth correction, as one special case.

— Error Bounds for Statistical Estimators in BTL Model with Parametric Multivariate Utility Functions  (2609.26326 - Li et al., 22 Sep 2026) in Section 6, “Concluding Remarks”