\texttt{BayesBreak}: Generalized Hierarchical Bayesian Segmentation with Irregular Designs, Multi-Sample Hierarchies, and Grouped/Latent-Group Designs

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.