Estimation of building energy demand characteristics using bayesian statistics and energy signature models

• Scalable Bayesian Energy Signature model for evaluating building energy performance. • Probabilistic estimates of the HTC, solar and wind effects for 2,788 homes. • ARMAX extension captures thermal inertia and improves predictive accuracy. • Uncertainty quantification enables robust diagnostics and planning decisions. Energy Signature (ES) models are widely used in building energy performance assessment due to their simplicity, scalability, and physical interpretability. Nevertheless, conventional ES formulations are deterministic and provide limited insight into parameter uncertainty, constraining their value for robust performance evaluation and decision-making under real-world data variability. This work addresses this gap by investigating how scalable Bayesian statistical inference can be systematically integrated into the ES framework to enable probabilistic, scalable assessments of building thermal performance at both individual building and building stock level. The research examines whether Bayesian ES models improve predictive performance while providing transparent uncertainty quantification for key thermal parameters, such as the effective heat transfer coefficient, solar gain, and wind infiltration. A scalable Bayesian modelling framework is developed and applied to smart-meter data from 2,788 Danish single-family houses. Three model variants are formulated and compared: a baseline ES model, an auto-regressive ES model (ARX-ES) capturing thermal inertia, and an auto-regressive moving average ES model (ARMAX-ES) approximating stochastic grey-box dynamics. The models estimate the effective heat transfer coefficients, solar gains, and wind infiltration, yielding full posterior distributions to reflect parameter uncertainty. Results show that increased model complexity enhances one-step-ahead predictive performance, with the ARMAX-ES model achieving a median Bayesian R² of 0.94 across the building stock. At the single-building level, the yearly energy demand is estimated with credibility intervals within ± 1%, showcasing more robust diagnostics than deterministic methods. Overall, the proposed Bayesian ES framework enhances robustness and interpretability in building energy performance assessment, offering a scalable tool to complement energy certification, investment prioritisation, demand forecasting and data-driven energy planning.