Uncertainty affects all aspects of building performance: from the identification of models, through the implementation of model-based control, to the operation of the deployed systems. Learning models of buildings from sensor data has a fundamental property that the model can only be as accurate and reliable as the data on which it was trained. For small and medium size buildings, a low-cost method for model capture is necessary to take advantage of optimal model-based supervisory control schemes. We present IMpACT, a methodology and a toolbox for analysis of uncertainty propagation for building inverse modeling and controls. Given a plant model and real input data, IMpACT automatically evaluates the effect of the uncertainty propagation from sensor data to model accuracy and control performance. We also present a statistical method to quantify the bias in the sensor measurement and to determine near optimal sensor placement and density for accurate signal measurements. In our previous work, we considered the end-to-end propagation of uncertainty in the form of fixed bias in the sensor data. In this paper, we extend the method to work with random errors in the sensor data, which is more realistic. Using a real building test-bed, we show how performing an uncertainty analysis can reveal trends about inverse model accuracy and control performance, which can be used to make informed decisions about sensor requirements and data accuracy.