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An algorithm for non-stationary spatial modelling using multiple secondaryvariables is developed. It combines Geostatistics with Quantile Random Foreststo give a new interpolation and stochastic simulation algorithm. This paperintroduces the method and shows that it has consistency results that aresimilar in nature to those applying to geostatistical modelling and to QuantileRandom Forests. The method allows for embedding of simpler interpolationtechniques, such as Kriging, to further condition the model. The algorithmworks by estimating a conditional distribution for the target variable at eachtarget location. The family of such distributions is called the envelope of thetarget variable. From this, it is possible to obtain spatial estimates,quantiles and uncertainty. An algorithm to produce conditional simulations fromthe envelope is also developed. As they sample from the envelope, realizationsare therefore locally influenced by relative changes of importance of secondaryvariables, trends and variability.

An Embedded Model Estimator for Non-Stationary Random Functions using Multiple Secondary Variables