Stat Cafe - Toryn Schafer

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Innovative Bayesian Approaches for Robust Trend Filtering and Changepoint Detection in Complex Time Series

Time: Monday 3/17/2025 from 10:00 AM to 11:00 AM
Location: BLOC 503

Description

Accurately detecting trends and changepoints in time series is essential across many fields. This talk synthesizes advanced methodologies for detecting trends and changepoints in complex time series data, highlighting both fully Bayesian and decoupled approaches. We present the Adaptive Bayesian Changepoints with Outliers (ABCO) model, which utilizes dynamic global-local shrinkage priors within a Bayesian dynamic linear model with extensions to simultaneously estimate changepoints and local outliers. ABCO effectively handles heteroscedastic noise and measurement errors by incorporating additional local parameters, ensuring robustness in identifying unspecified changepoints amidst complex series interruptions. Complementing this, the Drift versus Shift methodology introduces a novel decoupled approach that separates trend (drift) estimation from changepoint (shift) detection. By integrating Bayesian trend filtering with posterior regularization, this method leverages the strengths of Bayesian dynamic linear models for smooth trend estimation and penalized likelihood estimators for discrete changepoint inference. Additionally, we present the generalization of the methodology for count time series, the Negative Binomial Bayesian Trend Filter (NB-BTF). Through extensive simulations and applications ranging from economic indicators to power outage frequencies, these approaches demonstrate superior performance and flexibility compared to existing methods. This synthesis underscores the complementary nature of fully Bayesian and decoupled strategies, offering robust solutions for trend and changepoint analysis across diverse scientific domains.