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