Efficient MCMC algorithms for Bayesian changepoint detection in overdispersed autoregressive count data

Standard Bayesian changepoint models for count data assume independent Poisson observations. However, epidemiological time series data possess temporal dependence and overdispersion. We develop an enhanced Bayesian framework that integrates changepoint detection with AR(1) structure and a negative binomial likelihood to address both issues simultaneously. The model allows regime-specific dynamics, enabling different temporal correlation patterns and dispersion levels before and after changepoints. We present a Metropolis-within-Gibbs Markov chain Monte Carlo algorithm with efficient proposal mechanisms for discrete changepoint updates, utilizing an adaptive Metropolis scheme that eliminates manual tuning. Through simulation studies across twelve scenarios varying sample size (n = 100, 200), temporal dependence (ϕ=0,0.5), overdispersion (r=5,20), and data-generating processes, we demonstrate that the model achieves 96–100% credible interval coverage in eleven of twelve scenarios with near-perfect changepoint recovery (RMSE <1 day) when n≥200. Comparison with standard Poisson changepoint models shows our approach reduces RMSE by 9% and exhibits superior numerical stability. Application to COVID-19 daily case data from the United States, Italy, and Germany successfully identifies epidemiologically meaningful changepoints corresponding to policy interventions and epidemic waves during March–December 2020. The algorithm demonstrates near-linear computational scaling, making it practical for routine epidemiological surveillance.