Many empirical models have been developed that use sunshine hours (SSH) data to estimate global solar radiation. Most of these models use the Angstrom-Prescott equation to produce deterministic estimates of monthly radiation and do not provide uncertainty estimates in their predictions. This study develops five stochastic models that use daily SSH data to produce probabilistic simulations of global radiation, including associated uncertainties. These models can be used to estimate historical daily radiation or to estimate radiation without the use of satellite data. Two sources of predictive uncertainty are considered: (1) the timing of the SSH during the day (estimated using Monte Carlo simulation) and (2) external errors such as variability in cloud type and amount (estimated using residual error modelling). The models differ in the parameterization of the diffuse and direct radiation, using either no scaling, linear or quadratic scaling of the radiation by the daily SSH fraction to account for cloud attenuation. The models are calibrated under several residual error assumptions, including constant, linear and quadratic variances dependent on the SSH fraction and simulated radiation. The five models perform equally well in simulating global radiation, with an average error of approximately 9% for all locations studied. The results suggest that SSH uncertainty does not dominate predictive errors in global radiation. The residual errors appear to be best described by a linear heteroscedastic structure with larger variance during cloudy days and smaller variance during sunny days. The developed methodology provides a novel approach for estimating the uncertainty in radiation estimates based on SSH data.