Bayesian Spatio-Temporal Modeling and Change-Point Detection of Energy Consumption in the Midwestern United States

Abstract

Understanding structural changes in regional energy consumption is critical for designing effective energy policies and anticipating future demand patterns. This study develops a Bayesian spatio-temporal framework to analyze structural shifts in energy consumption across Midwestern states of the United States. Annual state-level energy consumption data from 1960 to 2023 were analyzed to identify temporal dynamics and spatial dependencies among neighboring states, with monthly data from 2000 to 2024 used for high-resolution structural break detection. A Bayesian hierarchical model was employed to jointly capture spatial effects, temporal evolution, and structural change points in energy consumption patterns. Spatial dependence between states was modeled using a conditional autoregressive (CAR) prior based on a first-order queen contiguity spatial adjacency matrix. Temporal dynamics were represented through a stochastic random-walk process, while structural changes were identified using a Bayesian Online Change Point Detection (BOCPD) mechanism embedded within the hierarchical framework.
Model performance and validation were evaluated using posterior predictive checks (PPC), the Widely Applicable Information Criterion (WAIC), and Leave-One-Out Cross-Validation (LOO-CV), with the Pettitt test used as a classical benchmark for structural break detection. The results reveal several statistically significant change points across states, particularly around the 2008-2009 financial crisis, the 2012 Midwest drought, and during the expansion of renewable energy policies. The proposed Bayesian spatio-temporal framework provides a flexible approach for identifying regional structural shifts in energy consumption while accounting for spatial interdependencies among states. These findings offer valuable insights for energy planners and policymakers seeking to understand long-term changes in regional energy demand and the potential impacts of economic shocks and policy transitions.