Scalable Bayesian Multiple Changepoint Detection via Auxiliary Uniformisation

Abstract

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.