Summarization: Sensing by proxy (SbP) is proposed in this paper as a sensing paradigm for occupancy detection, where the inference is based on 'proxy' measurements such as temperature and CO2 concentrations. The effects of occupants on indoor environments are captured by constitutive models comprising a coupled partial differential equation-ordinary differential equation system that exploits the spatial and physical features. Sensor fusion of multiple environmental parameters is enabled in the proposed framework. We report on experiments conducted under simulated conditions and real-life circumstances, when the variation of occupancy follows a schedule as the ground truth. The inference of the number of occupants in the room based on CO2 co...