arXiv subjects

Thomas Suesse

Publications and source records attributed to Thomas Suesse.

5 recordsLinked to original sources

arXiv2026

Aligning Validation with Deployment in Spatial Prediction: Target-Weighted Cross-Validation

Reliable estimation of predictive performance is essential for spatial environmental modeling, where machine-learning models are used to generate maps from unevenly distributed observations. Standard cross-validation (CV) assumes that validation data are representative of prediction conditions across the target domain. In practice, this assumption is often violated due to preferential or clustered sampling, leading to biased performance and uncertainty estimates. We introduce a deployment-oriented validation framework based on weighted CV that aligns validation tasks with the distribution of prediction tasks across a specified domain. The framework includes importance-weighted cross-validation (IWCV) and a calibration-based approach, Target-Weighted Cross-Validation (TWCV), which uses spatially meaningful task descriptors such as environmental covariates and prediction distance. Simulation experiments show that conventional non-spatial and spatial CV strategies can exhibit substantial bias under realistic sampling designs, whereas weighted CV approaches substantially reduce this bias when validation tasks adequately cover the deployment-task space. A case study on mapping nitrogen dioxide (NO$_2$) concentrations across Germany demonstrates that standard CV can overestimate prediction error due to sampling bias, while weighted CV yields estimates more consistent with deployment conditions. The framework separates validation task generation from risk estimation and provides a practical approach for improving performance assessment in spatial prediction settings where sample distributions differ from prediction domains.

cs.LG↗

arXiv2025

Bayesian Inference for Non-Gaussian Simultaneous Autoregressive Models with Missing Data

Standard simultaneous autoregressive (SAR) models typically assume normally distributed errors, an assumption often violated in real-world datasets that frequently exhibit non-normal, skewed, or heavy-tailed characteristics. New SAR models are proposed to capture these non-Gaussian features. The spatial error model (SEM), a widely used SAR-type model, is considered. Three novel SEMs are introduced, extending the standard Gaussian SEM. These extensions incorporate Student's $t$-distributed errors to accommodate heavy-tailed behaviour, one-to-one transformations of the response variable to address skewness, or a combination of both. Variational Bayes (VB) estimation methods are developed for these models, and the framework is further extended to handle missing response data under the missing not at random (MNAR) mechanism. Standard VB methods perform well with complete datasets; however, handling missing data requires a hybrid VB (HVB) approach, which integrates a Markov chain Monte Carlo (MCMC) sampler to generate missing values. The proposed VB methods are evaluated using both simulated and real-world datasets, demonstrating their robustness and effectiveness in dealing with non-Gaussian data and missing data in spatial models. Although the method is demonstrated using SAR models, the proposed model specifications and estimation approaches are widely applicable to various types of models for handling non-Gaussian data with missing values.

stat.ME↗

arXiv2024

Variational Bayes Inference for Spatial Error Models with Missing Data

The spatial error model (SEM) is a type of simultaneous autoregressive (SAR) model for analysing spatially correlated data. Markov chain Monte Carlo (MCMC) is one of the most widely used Bayesian methods for estimating SEM, but it has significant limitations when it comes to handling missing data in the response variable due to its high computational cost. Variational Bayes (VB) approximation offers an alternative solution to this problem. Two VB-based algorithms employing Gaussian variational approximation with factor covariance structure are presented, joint VB (JVB) and hybrid VB (HVB), suitable for both missing at random and not at random inference. When dealing with many missing values, the JVB is inaccurate, and the standard HVB algorithm struggles to achieve accurate inferences. Our modified versions of HVB enable accurate inference within a reasonable computational time, thus improving its performance. The performance of the VB methods is evaluated using simulated and real datasets.

stat.ME↗

arXiv2024

A Marginal Maximum Likelihood Approach for Hierarchical Simultaneous Autoregressive Models with Missing Data

Efficient estimation methods for simultaneous autoregressive (SAR) models with missing data in the response variable have been well-explored in the literature. A common practice is to introduce measurement error into SAR models to separate the noise component from the spatial process. However, prior research has not considered incorporating measurement error into SAR models with missing data. Maximum likelihood estimation for such models, especially with large datasets, poses significant computational challenges. This paper proposes an efficient likelihood-based estimation method, the marginal maximum likelihood (ML), for estimating SAR models on large datasets with measurement errors and a high percentage of missing data in the response variable. The spatial error model (SEM) and the spatial autoregressive model (SAM), two popular SAR model types, are considered. The missing data mechanism is assumed to follow a missing at random (MAR) pattern. We propose a fast method for marginal ML estimation with a computational complexity of $O(n^{3/2})$, where $n$ is the total number of observations. This complexity applies when the spatial weight matrix is constructed based on a local neighbourhood structure. The effectiveness of the proposed methods is demonstrated through simulations and real-world data applications.

stat.ME↗

arXiv2015

Capturing Multivariate Spatial Dependence: Model, Estimate and then Predict

Physical processes rarely occur in isolation, rather they influence and interact with one another. Thus, there is great benefit in modeling potential dependence between both spatial locations and different processes. It is the interaction between these two dependencies that is the focus of Genton and Kleiber's paper under discussion. We see the problem of ensuring that any multivariate spatial covariance matrix is nonnegative definite as important, but we also see it as a means to an end. That "end" is solving the scientific problem of predicting a multivariate field. [arXiv:1507.08017].

stat.ME↗