Combining machine learning quantile regression and Gaussian random fields: A general framework for modeling and simulating space–time processes

Modeling and simulating space–time random fields while accounting for possibly misaligned covariates is crucial for many applications requiring uncertainty quantification and risk assessment. To achieve this, we propose a flexible framework that couples machine-learning quantile regression with space–time Gaussian random fields. In this framework, the target variable is modeled as a combination of a latent Gaussian random field and transformed marginals obtained by Machine learning quantile regression conditionally on a set of covariates. We illustrate the approach on a synthetic experiment and on a case study that considers daily maximum temperature over north-east Switzerland conditional on seasonal cycle and large-scale geopotential height.