Aidan D. Bindoff | Searcharxiv

arXiv2026

smoothbp: Fast Bayesian Hierarchical Piecewise Regression with Smoothed Transitions and Spike-and-Slab Model Selection

Piecewise regression models are essential for identifying structural changes in longitudinal or spatial data across diverse scientific domains. While standard approaches often assume sharp, instantaneous transitions and single, non-hierarchical breakpoints, many real-world phenomena exhibit gradual, smoothed transitions that vary systematically across groups. We introduce smoothbp, an R package for fast, Bayesian hierarchical piecewise regression featuring logistic-smoothed transitions. By implementing a bespoke Metropolis-within-Gibbs sampler in Rust, smoothbp combines exact conjugate updates for linear terms with Hamiltonian Monte Carlo (HMC) transitions for non-linear location and sharpness parameters. smoothbp natively supports multiple change-points, random intercepts, random change-point timing, and structural covariates on all segment parameters. It also incorporates Kuo and Mallick (1998) spike-and-slab priors for automatic inference on the number of active breakpoints via the smoothbp_ss function. We document the sampler, validate parameter recovery and calibration through simulation-based calibration and interval-coverage studies, and contrast smoothbp against the existing software landscape across R, Python, Julia, and MATLAB, demonstrating its competitive efficiency against general-purpose probabilistic programming languages like brms and specialized packages like mcp.

stat.CO↗

arXiv2026

A Flat Connection: The Pooling Factor and the Geometry of Centring in Hierarchical MCMC

Standard MCMC diagnostics ($\hat{R}$, effective sample size, divergence counts) detect whether a chain has mixed, but not why it has not. We ask whether the centring/non-centring obstruction in hierarchical models has a geometric cause beyond the metric. The joint parameter space is a fiber bundle (hyperparameters the base, group-level parameters the fibers), and the Fisher information metric induces an Ehresmann connection $A = -G_{FF}^{-1}G_{BF}$; the natural hypothesis is that the obstruction is its curvature, felt by the sampler as holonomy. We prove this false. The connection is flat for any smooth hierarchical posterior, not only the Gaussian case, because its horizontal leaves are the level sets of the fiber score $\partial_α\log p$: there is no geometric obstruction above the metric. What remains is statistical, not geometric, and the flat connection identifies it as a single quantity: the conditional dependence of fiber on base, governed per group by the prior fraction $π_j$, the classical pooling factor. From it the framework recovers the established picture, that prior-dominated groups mix slowly and that the optimal per-group non-centring weight follows in closed form, and a simulation study separates this base-fiber coupling from the funnel, a distinct base-space pathology, by their opposite dependence on the hierarchical variance. A direct attribution test confirms that NUTS does not transport the fiber: the chain-level footprint is excess conditional autocorrelation in prior-dominated groups, exactly as $π_j$ predicts. Genuine, even rotational, curvature does appear, but only for connections built from a sampler's working metric (a fixed mass matrix), where holonomy re-enters as an algorithmic rather than geometric phenomenon. The prior-fraction diagnostic is distributed as the R package fibr, with the geometric methods as accompanying reproduction code.

stat.CO↗