Formal guarantees for BKP-based decision processes

Establish formal theoretical guarantees for decision processes based on the Beta Kernel Process (BKP).

Background

The Beta Kernel Process (BKP) is a nonparametric, Bayesian-inspired framework that combines kernel-weighted local likelihoods with conjugate beta priors to model spatially varying binomial probabilities, yielding closed-form posterior updates without latent variables or approximate inference.

Despite practical advantages and demonstrated performance, the theoretical properties of BKP have not been thoroughly developed. In particular, prior work has highlighted that BKP-based decision procedures currently lack formal guarantees, motivating the need for rigorous analysis to support reliability and principled use in applications.