A generalized Bayesian approach to multiple changepoint analysis

Abstract

We introduce a generalized Bayesian method for multiple changepoint analysis with a loss function inspired by multinomial logistic regression. The method does not require a specification of the data-generating process and avoids restrictive assumptions on the nature of changepoints. From the joint posterior distribution, we can make simultaneous inference on the locations of changepoints and the coefficients of a multinomial logistic regression model for distinguishing data across homogeneous segments. The multinomial logistic regression coefficients provide a familiar means of interpreting potentially complex changes. To select the number of changepoints, we leverage posterior summaries that measure whether the multinomial logistic classifier can distinguish data from either side of a potential changepoint. To simulate from the generalized posterior distribution, we present a Gibbs sampler based on Pólya-Gamma data augmentation. We assess the accuracy and flexibility of our method through simulation studies featuring different types of changes and demonstrate its interpretability through applications to financial network data and topological data derived from nanoparticle videos.

Figures (10)

• Figure 1: The DJIA network statistics with posterior mode estimates of changepoints (blue dashed lines) along with 95% credible intervals (blue bands) obtained from applying bcmlr.
• Figure 2: The posterior distribution of the number of 10 fitted changepoints that correspond to true changepoints based on 5000 posterior samples (after 10000 burn-in samples) obtained from applying the approach in Section \ref{['Sec. select num of CPs']} to select the number of changepoints on the DJIA series.
• Figure 3: Each plot shows 95% credible intervals for difference $\bm{\beta}_{l+1}-\bm{\beta}_{l}$ for $l \in \{1, \dots, 3\}$. The three dimensions of each difference vector relate to edges, triangles, and homophily for risk orientation. The black dots represent posterior means.
• Figure 4: Each plot shows posterior means of $\bm{x}_i^{\top}\left(\bm{\beta}_{l+1}-\bm{\beta}_l\right)$, along with 95% pointwise credible intervals (blue bands), based on the data in neighboring segments on either side of the changepoint $\kappa_l$. The blue dashed lines represent the posterior mode estimates of the changepoints.
• Figure 5: Plot of 6 of the 7 features used to detect nanoparticle activity and tilt in the denoised video from Figure 4 of crozier2025. Blue dashed lines are posterior modes and blue bands are 95% credible intervals.