Building simulation requires a large number of uncertain inputs and parameters. These include quantities that may be known with reasonable confidence, like the thermal properties of materials and building dimensions, but also inputs whose correct values cannot be known with absolute certainty, notably weather and occupancy. A simulation run is not, strictly, a prediction. Since the parameters and calculations are approximations of real-world phenomena and materials, the exercise is essentially uncertain. Regardless of whether simulation is interpreted as a prediction or an approximation indicative of average behaviour, including explicit bounds of uncertainty is more informative for a decision-maker than a single point estimate. This thesis presents results for two related but independent proposals for sensitivity and uncertainty analyses in building simulation, particularly to weather. The first is a novel, generalisable procedure for generating synthetic weather data to carry out a Monte Carlo experiment with a building simulation model. The second is a technique for training emulators or response surfaces to rapidly obtain estimates of performance outputs from simulation models, using Gaussian Process regression on small training data sets. The two parts, together and separately, enable the quantification of the lack of knowledge about an input, and the impact of this uncertainty on the final results. The synthetic weather time series developed are an ensemble of realistic hourly data whose mean statistical characteristics are close to the typical year used to generate them. The procedures developed are generalisable with minimal expert input. We avoid presenting a unified model for all climates, leaving some tuning parameters like the extent of correlation, and the unknown coefficients of stationary time series models, to be calculated empirically (based on the typical file of a given climate). The emulators are created using regression, comparing the performance of classical parametric regression with a non-linear technique based on Gaussian random processes. Our proposal trains reliable models on small samples, reducing the computational burden, and gives an explicit estimate of the uncertainty for a prediction, since the response at any sampled point is modelled as a Normally-distributed random process. Once again, we avoid a unified emulator or regression model because the response from one building (defined by its geometry and usage in this case) is not necessarily an appropriate description of the response of another. This work is a step towards practical tools for the use of building simulation in a stochastic paradigm. Both elements of the thesis contribute toward explicitly estimating the uncertainty in the results of building simulation, using empirical or data-driven techniques. The types of the time series and emulator models are general enough to work on any climate or building, with parameters obtained from the simulated/typical sample at hand, but the importance of different aspects and the nature of a building’s response are determined uniquely (i.e., parameter values). The work is easily extensible to the analysis of the sensitivity of a building, or groups of buildings, to any inputs. The concepts proposed in this thesis may also be used for stochastic optimisation and models to predict performance metrics other than the annual sum of energy.