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Large spatial and spatio-temporal data sets lead to challenging statistical modelling and computational problems. In some cases one can use a low dimensional model, which allows a very large number of observations to be used. Unfortunately, a common situation is that the increased data size is coupled with a desire to perform analysis on finer scales, e.g. in global and regional temperature reconstruction. I will discuss a method for stochastic multiscale modelling via combinations of stochastic PDEs, and how numerical methods for sparse linear systems might be used to construct direct prediction and conditional sampling methods, avoiding the more costly MCMC approaches that are traditionally used to quantify estimation uncertainty.