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The Gaussian process is an indispensable tool for spatial data analysts. The onset of the "big data" era, however, has lead to the traditional Gaussian process being computationally infeasible for modern spatial data. As such, various…
In the last few decades, the size of spatial and spatio-temporal datasets in many research areas has rapidly increased with the development of data collection technologies. As a result, classical statistical methods in spatial statistics…
Spatial data display correlation between observations collected at neighboring locations. Generally, machine and deep learning methods either do not account for this correlation or do so indirectly through correlated features and thereby…
Gaussian Processes have become an indispensable part of the spatial statistician's toolbox but are unsuitable for analyzing large dataset because of the significant time and memory needed to fit the associated model exactly. Vecchia…
Data-driven forecasts of air quality have recently achieved more accurate short-term predictions. Despite their success, most of the current data-driven solutions lack proper quantifications of model uncertainty that communicate how much to…
We discuss the experiences and results of the AppStatUZH team's participation in the comprehensive and unbiased comparison of different spatial approximations conducted in the Competition for Spatial Statistics for Large Datasets. In each…
A key challenge in spatial statistics is the analysis for massive spatially-referenced data sets. Such analyses often proceed from Gaussian process specifications that can produce rich and robust inference, but involve dense covariance…
Many scientific phenomena are studied using computer experiments consisting of multiple runs of a computer model while varying the input settings. Gaussian processes (GPs) are a popular tool for the analysis of computer experiments,…
Gaussian processes (GPs) are highly flexible function estimators used for geospatial analysis, nonparametric regression, and machine learning, but they are computationally infeasible for large datasets. Vecchia approximations of GPs have…
Recent advances in data collection technologies have led to the emergence of massive spatial datasets, with measurements obtained at millions of spatial locations. Geostatistical models typically employ Gaussian processes (GPs) to capture…
Strong Lensing is a powerful probe of the matter distribution in galaxies and clusters and a relevant tool for cosmography. Analyses of strong gravitational lenses with Deep Learning have become a popular approach due to these astronomical…
Machine learning models have become increasingly popular for predicting the results of soccer matches, however, the lack of publicly-available benchmark datasets has made model evaluation challenging. The 2023 Soccer Prediction Challenge…
With the development of new remote sensing technology, large or even massive spatial datasets covering the globe become available. Statistical analysis of such data is challenging. This article proposes a semiparametric approach to model…
The topic of deep learning has seen a surge of interest in recent years both within and outside of the field of Statistics. Deep models leverage both nonlinearity and interaction effects to provide superior predictions in many cases when…
Two fundamental research tasks in science and engineering are forward predictions and data inversion. This article introduces a recent R package RobustCalibration for Bayesian data inversion and model calibration by experiments and field…
The availability of reliable, high-resolution climate and weather data is important to inform long-term decisions on climate adaptation and mitigation and to guide rapid responses to extreme events. Forecasting models are limited by…
Recent developments in engineering techniques for spatial data collection such as geographic information systems have resulted in an increasing need for methods to analyze large spatial data sets. These sorts of data sets can be found in…
Gaussian processes (GPs) are flexible, probabilistic, nonparametric models widely used in fields such as spatial statistics and machine learning. A drawback of Gaussian processes is their computational cost, with $O(N^3)$ time and $O(N^2)$…
Uncertainty quantification for deep learning is a challenging open problem. Bayesian statistics offer a mathematically grounded framework to reason about uncertainties; however, approximate posteriors for modern neural networks still…
Deep Gaussian processes (DGPs) upgrade ordinary GPs through functional composition, in which intermediate GP layers warp the original inputs, providing flexibility to model non-stationary dynamics. Two DGP regimes have emerged in recent…