Scalable Bayesian Multiple Changepoint Detection via Auxiliary Uniformisation

In this paper, we perform a sparse filtering recursion for efficient changepoint detection for discrete‐time observations. We attach auxiliary event times to the chronologically ordered observations and formulate multiple changepoint problems of discrete‐time observations into continuous‐time observations. Ideally, both the computational and memory costs of the proposed auxiliary uniformisation forward‐filtering backward‐sampling algorithm can be quadratically scaled down to the number of changepoints instead of the number of observations, which would otherwise be prohibitive for a long sequence of observations. To avoid model bias, a time‐varying changepoint recurrence rate across different segments is assumed to characterise diverse scales of run lengths of the changepoints. We demonstrate the methods through simulation studies and real data analysis.