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

TL;DR

This paper introduces a novel non-stationary spatial modeling algorithm that combines geostatistics with Quantile Random Forests, enabling improved interpolation, uncertainty quantification, and the integration of simpler methods like Kriging.

Contribution

It presents a new embedding approach for non-stationary random functions using multiple secondary variables, with consistency guarantees similar to existing geostatistical and machine learning methods.

Findings

The method effectively estimates conditional distributions at target locations.

It enables spatial estimates, quantile calculation, and uncertainty assessment.

The algorithm supports conditional simulations influenced by secondary variables.

Abstract

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.