Uncertainty in sensor data (e.g., weather, occupancy) complicates the construction of baseline models for measurement and verification (M&V). We present a Monte Carlo expectation maximization (MCEM) framework for constructing baseline Gaussian process (GP) models under uncertain input data. We demonstrate that the GP-MCEM framework yields more robust predictions and confidence levels compared with standard GP training approaches that neglect uncertainty. We argue that the approach can also reduce data needs because it implicitly expands the data range used for training and can thus be used as a mechanism to reduce data collection and sensor installation costs in M&V processes. We analyze the numerical behavior of the framework and conclude that robust predictions can be obtained with relatively few samples. (C) 2014 Elsevier B.V. All rights reserved.