Scalable Bayesian changepoint inference with position-specific priors

Music City Center 

Changepoints—abrupt shifts in sequential data—are critical for understanding underlying structural variations. Bayesian models that incorporate position-specific prior probabilities for changepoints can substantially enhance inference quality. This strategy enables researchers to integrate domain knowledge through informative priors and share information across multiple samples via hierarchical modeling, thereby increasing sensitivity to subtle changepoints in noisy data. However, existing Bayesian changepoint methods either do not permit position-specific priors or rely on complex MCMC sampling procedures. In this work, we introduce a simple and efficient framework for Bayesian changepoint detection that supports position-specific priors while enabling fast, optimization-based inference. Our approach leverages novel dynamic programming techniques to compute the posterior distributions over changepoint indicators, segmentations, and local parameters. We also develop an approximate inference algorithm with time complexity linear in the sequence length. We demonstrate the effectiveness of our method on simulated data and consider the problem of identifying copy number alterations in cancer biopsy samples with low tumor fractions.