Simulation-based Bayesian analysis for multiple changepoints

This paper presents a Markov chain Monte Carlo method to generate approximate posterior samples in retrospective multiple changepoint problems where the number of changes is not known in advance. The method uses conjugate models whereby the marginal likelihood for the data between consecutive changepoints is tractable. Inclusion of hyperpriors gives a near automatic algorithm providing a robust alternative to popular filtering recursions approaches in cases which may be sensitive to prior information. Three real examples are used to demonstrate the proposed approach.

💡 Research Summary

The paper introduces a Bayesian framework for detecting an unknown number of changepoints in a retrospective setting, employing a Markov chain Monte Carlo (MCMC) algorithm that leverages conjugate models to obtain closed‑form marginal likelihoods for data segments between successive changepoints. The core idea is to treat the changepoint locations and the number of changepoints as random variables and to place hyper‑priors on these quantities, thereby reducing sensitivity to the choice of prior parameters and allowing the algorithm to operate in a near‑automatic fashion.

Model formulation: The observed series (y_{1:n}) is partitioned by changepoints (\tau_1,\dots,\tau_K) into (K+1) contiguous blocks. Within each block the data follow a parametric likelihood (f(y|\theta_k)) with a conjugate prior (\pi(\theta_k|\eta)). Because of conjugacy, the block‑wise marginal likelihood (\int f(y_{a:b}|\theta)\pi(\theta|\eta)d\theta) can be computed analytically, eliminating the need to sample the block‑specific parameters (\theta_k) during the MCMC run.

Hyper‑prior structure: A prior on the number of changepoints (K) (e.g., Poisson or geometric) and on the minimal spacing between changepoints is introduced, together with a prior on the hyper‑parameters (\eta). This hierarchical construction enables the algorithm to learn appropriate prior scales from the data, making the method robust when prior knowledge is vague or unavailable.

MCMC moves: The sampler explores the trans‑dimensional space of changepoint configurations using three reversible moves—birth (add a changepoint), death (remove a changepoint), and shift (relocate an existing changepoint). For each proposed move, the Metropolis–Hastings acceptance probability is computed as

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