Lagged Exact Bayesian Online Changepoint Detection

Identifying changes in the generative process of sequential data, known as changepoint detection, has become an increasingly important topic for a wide variety of fields. A recently developed approach, which we call EXact Online Bayesian Changepoint Detection (EXO), has shown reasonable results with efficient computation for real time updates. However, when the changes are relatively small, EXO starts to have difficulty in detecting changepoints accurately. We propose a new algorithm called $\ell$-Lag EXact Online Bayesian Changepoint Detection (LEXO-$\ell$), which improves the accuracy of the detection by incorporating $\ell$ time lags in the inference. We prove that LEXO-1 finds the exact posterior distribution for the current run length and can be computed efficiently, with extension to arbitrary lag. Additionally, we show that LEXO-1 performs better than EXO in an extensive simulation study; this study is extended to higher order lags to illustrate the performance of the generalized methodology. Lastly, we illustrate applicability with two real world data examples comparing EXO and LEXO-1.