Energy Measurement and Verification (M&V) aims to make inferences about the savings achieved in energy projects, given the data and other information at hand. Traditionally, a frequentist approach has been used to quantify these savings and their associated uncertainties. We demonstrate that the Bayesian paradigm is an intuitive, coherent, and powerful alternative framework within which M&V can be done. Its advantages and limitations are discussed, and two examples from the industry-standard International Performance Measurement and Verification Protocol (IPMVP) are solved using the framework. Bayesian analysis is shown to describe the problem more thoroughly and yield richer information and uncertainty quantification than the standard methods while not sacrificing model simplicity. We also show that Bayesian methods can be more robust to outliers. Bayesian alternatives to standard M&V methods are listed, and examples from literature are cited.