\texttt{BayesBreak}: Generalized Hierarchical Bayesian Segmentation with Irregular Designs, Multi-Sample Hierarchies, and Grouped/Latent-Group Designs
This work addresses the need for more flexible and uncertainty-aware segmentation methods in fields like signal processing or genomics, though it appears incremental as it builds on existing Bayesian segmentation concepts.
The authors tackled the problem of Bayesian segmentation models being limited to narrow likelihood classes, single-sequence settings, or uniform designs by introducing BayesBreak, a modular offline framework that enables exact inference for posterior quantities like segment counts and boundary locations, with closed-form solutions for weighted exponential-family likelihoods and conjugate priors.
Bayesian change-point and segmentation models provide uncertainty-aware piecewise-constant representations of ordered data, but exact inference is often tied to narrow likelihood classes, single-sequence settings, or index-uniform designs. We present \texttt{BayesBreak}, a modular offline Bayesian segmentation framework built around a simple separation: each candidate block contributes a marginal likelihood and any required moment numerators, and a global dynamic program combines those block scores into posterior quantities over segment counts, boundary locations, and latent signals. For weighted exponential-family likelihoods with conjugate priors, block evidences and posterior moments are available in closed form from cumulative sufficient statistics, yielding exact sum-product inference for $P(y\mid k)$, $P(k\mid y)$, boundary marginals, and Bayes regression curves. We also distinguish these quantities from the \emph{joint} MAP segmentation, which is recovered by a separate max-sum backtracking recursion.