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The accurate prediction of precipitation is important to allow for reliable warnings of flood or drought risk in a changing climate. However, to make trust-worthy predictions of precipitation, at a local scale, is one of the most difficult challenges for today's weather and climate models. This is because important features, such as individual clouds and high-resolution topography, cannot be resolved explicitly within simulations due to the significant computational cost of high-resolution simulations. Climate models are typically run at $\sim$50-100 km resolution which is insufficient to represent local precipitation events in satisfying detail. Here, we develop a method to make probabilistic precipitation predictions based on features that climate models can resolve well and that is not highly sensitive to the approximations used in individual models. To predict, we will use a temporal compound Poisson distribution dependent on the output of climate models at a location. We use the output of Earth System models at coarse resolution $\sim$50 km as input and train the statistical models towards precipitation observations over Wales at $\sim$10 km resolution. A Bayesian inferential scheme is provided so that the compound-Poisson model can be inferred using a Gibbs-within-Metropolis-Elliptic-Slice sampling scheme which enables us to quantify the uncertainty of our predictions. In addition, we use a Gaussian process regressor on the posterior samples of the model parameters, to infer a spatially coherent model and hence to produce spatially coherent rainfall prediction. We illustrate the prediction performance of our model by training over 5 years of the data up to 31st December 1999 and predicting precipitation for 20 years afterwards for Cardiff and Wales.