An Embedded Model Estimator for Non-Stationary Random Functions using Multiple Secondary Variables
This work addresses spatial modeling challenges in fields like geostatistics by offering a novel approach for handling multiple secondary variables, though it appears incremental as it builds on existing methods.
The paper tackled the problem of non-stationary spatial modeling by developing an algorithm that combines Geostatistics with Quantile Random Forests for interpolation and stochastic simulation, resulting in a method that provides spatial estimates, quantiles, and uncertainty with consistency results similar to established techniques.
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.