Estimation of Building Energy Demand Characteristics using Bayesian Statistics and Energy Signature Models

Abstract: This work presents a scalable Bayesian modeling framework for evaluating building energy performance using smart-meter data from 2,788 Danish single-family homes. The framework leverages Bayesian statistical inference integrated with Energy Signature (ES) models to characterize thermal performance in buildings. This approach quantifies key parameters such as the Heat Loss Coefficient (HLC), solar gain, and wind infiltration, while providing full posterior distributions to reflect parameter uncertainty. Three model variants are developed: a baseline ES model, an auto-regressive model (ARX-ES) to account for thermal inertia, and an auto-regressive moving average model (ARMAX-ES) that approximates stochastic gray-box dynamics. Results show that model complexity improves one-step-ahead predictive performance, with the ARMAX-ES model achieving a median Bayesian R^2 of 0.94 across the building stock. At the single-building level, the Bayesian approach yields credible intervals for yearly energy demand within $\pm1\%$, enabling more robust diagnostics than deterministic methods. Beyond improved accuracy, the Bayesian framework enhances decision-making by explicitly representing uncertainty in building performance parameters. This provides a more realistic foundation for investment prioritization, demand forecasting, and long-term energy planning. The method is readily applicable to other building typologies or geographies, offering a scalable tool for data-driven energy management under uncertainty.