A method and system for inferring airborne contaminant concentrations in rooms without contaminant sensors, based on data collected by contaminant sensors in other rooms of a building, using known airflow interconnectivity data. The method solves a least squares problem that minimizes the difference between measured and predicted contaminant sensor concentrations with respect to an unknown contaminant release time. Solutions are constrained to providing non-negative initial contaminant concentrations in all rooms. The method can be used to identify a near-optimal distribution of sensors within the building, when then number of available sensors is less than the total number of rooms. This is achieved by having a system-sensor matrix that is non-singular, and by selecting that distribution which yields the lowest condition number of all the distributions considered. The method can predict one or more contaminant initial release points from the collected data.