Recent Advances in Changepoint Modeling

Changepoints—abrupt shifts in sequential data—are critical for understanding underlying structural variations. Bayesian models that incorporate position-specific prior probabilities for changepoints can substantially enhance inference quality. This strategy enables researchers to integrate domain knowledge through informative priors and share information across multiple samples via hierarchical modeling, thereby increasing sensitivity to subtle changepoints in noisy data. However, existing Bayesian changepoint methods either do not permit position-specific priors or rely on complex MCMC sampling procedures. In this work, we introduce a simple and efficient framework for Bayesian changepoint detection that supports position-specific priors while enabling fast, optimization-based inference. Our approach leverages novel dynamic programming techniques to compute the posterior distributions over changepoint indicators, segmentations, and local parameters. We also develop an approximate inference algorithm with time complexity linear in the sequence length. We demonstrate the effectiveness of our method on simulated data and consider the problem of identifying copy number alterations in cancer biopsy samples with low tumor fractions. 

In contrast with other fields, it is well accepted in Climatology that climate time series contain changes over time; whether as part of station moves, and/or evolving climate dynamics. There are many different (statistical) ways to model these changes over time. This talk introduces the field of changepoint detection as the simplest departure from the assumption of constant (statistical) properties over time. Following an introduction to the benefits and limitations of changepoint models we will touch on a recent development in detecting changepoints in spatio-temporal data motivated by air quality.

Air quality is an important measure for both ongoing public health and as part of climate modelling. Changes in the spatio-temporal distribution of air quality are important in the short term, e.g. for managing biohazards, and in the longer term for informing climate scenarios or predicting response to climate forcings. We present a spatio-temporal changepoint method that utilises a generalised additive model (GAM) dependent on the 2D spatial location and the observation time to account for the underlying spatio-temporal process.
 

We consider a high-dimensional dynamic pricing problem under non-stationarity, where a firm sells products to T sequentially arriving consumers that behave according to an unknown demand model with potential changes at unknown times. The demand model is assumed to be a high-dimensional generalized linear model (GLM), allowing for a feature vector in R^d that encodes products and consumer information. To achieve optimal revenue (i.e., least regret), the firm needs to learn and exploit the unknown GLMs while monitoring for potential change-points. To tackle such a problem, we first design a novel penalized likelihood-based online change-point detection algorithm for high-dimensional GLMs, which is the first algorithm in the change-point literature that achieves optimal minimax localization error rate for high-dimensional GLMs. A change-point detection assisted dynamic pricing (CPDP) policy is further proposed and achieves a near-optimal regret of order O(slog(Td)√MT)), where s is the sparsity level and M is the number of change-points. This regret is accompanied with a minimax lower bound, demonstrating the optimality of CPDP (up to logarithmic factors). In particular, the optimality with respect to M is seen for the first time in the dynamic pricing literature, and is achieved via a novel accelerated exploration mechanism. Extensive simulation experiments and a real data application on online lending illustrate the efficiency of the proposed policy and the importance and practical value of handling non-stationarity in dynamic pricing. 

Spatio-temporal areal data can be seen as a collection of time series which are spatially correlated, according to a specific neighboring structure. Motivated by a dataset on mobile phone usage in the Metropolitan area of Milan, Italy, we propose a semi-parametric hierarchical Bayesian model allowing for time-varying as well as spatial model-based clustering. To accommodate for changing patterns over work hours and weekdays/weekends, we incorporate a temporal change-point component that allows the specification of different hierarchical structures across time points. The change-points might occur within fixed time windows over the day. The model features a novel random partition prior that incorporates the desired spatial features and encourages co-clustering based on areal proximity. We discuss the application to the motivating data, where the main goal is to spatially cluster population patterns of mobile phone usage.  

Change point analyses are concerned with identifying positions of an ordered stochastic process that undergo abrupt local changes of some underlying distribution. When multiple processes are observed, it is often the case that information regarding the change point positions is shared across the different processes. This work describes a method that takes advantage of this type of information. Since the number and position of change points can be described through a partition with contiguous clusters, our approach develops a joint model for these types of partitions. We describe computational strategies associated with our approach and illustrate improved performance in detecting change points through a small simulation study. We then apply our method to a financial data set of emerging markets in Latin America and highlight interesting insights discovered due to the correlation between change point locations among these economies.