Building continuous performance monitoring is becoming a cornerstone in ensuring energy efficiency and sobriety of existing, retrofitted and newly built buildings. Although it may help convince investors in energy efficiency projects or bridge the gap between expected and actual performance, continuous monitoring-sometimes referred to as "Advanced M&V" or continuous commissioning-is still the exception rather than the rule. Recent efforts to continuously characterize building performance usually rely on building-level analyses: previous works include leveraging a Building Energy Model (BEM), monthly calibrated on building heating, ventilation and lighting consumption using real weather data and fine grain occupancy data, for daily monitoring. While BEM calibration against sub-daily frequency data has been increasingly studied in recent years, it is, to our knowledge, seldom used for building continuous monitoring. It is, however, particularly tailored for this task, to the extent it extracts embedded physics within the BEM into actionable insights for fault detection and diagnosis. Fine grain calibration of BEM faces a number of challenges in the recent literature, among which are (i) accounting for time varying dependent functional inputs-e.g. electric equipment and lighting energy consumption altogether with building occupancy-but for sensor data in the calibration algorithm, and (ii) treating functional outputs as functional stochastic variables when comparing simulation outputs with real data. Our contribution is to enhance building-level performance monitoring by introducing a stochastic model inversion scheme, also referred to as stochastic calibration, to support robust preventive fault detection and diagnosis. Our approach extends the current state-of-the-art on Bayesian calibration of BEM by accounting for dependent functional inputs and outputs in both selecting the most influential parameters and calibrating the model, and deals with uncertainties in functional inputs such as daily profiles of lighting and electric equipment energy consumption. This methodology is illustrated against a medium-size real secondary school building, located in Rennes, France, and equipped with an Advanced Meter Infrastructure (AMI) with hundreds of sensors. A comparison between a classic calibration process and the described methodology is presented and the benefits of accounting for the functional nature of the inputs and outputs in both the Design of Experiment (DoE) and the calibration process are illustrated against this case study.