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Expectation maximisation (EM) is an unsupervised learning method for estimating the parameters of a finite mixture distribution. It works by introducing "hidden" or "latent" variables via Baum's auxiliary function $Q$ that allow the joint…
We construct a Gaussian random field (GRF) that combines fractional smoothness with spatially varying anisotropy. The GRF is defined through a stochastic partial differential equation (SPDE), where the range, marginal variance, and…
We introduce inferential methods for prediction based on functional random effects in generalized functional mixed effects models. This is similar to the inference for random effects in generalized linear mixed effects models (GLMMs), but…
Due to spatial dependence -- often characterized as complex and non-linear -- model misspecification is a prevalent and critical issue in spatial data analysis and prediction. As the data, and thus model performance, is heterogeneous,…
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…
A non-stationary spatial Gaussian random field (GRF) is described as the solution of an inhomogeneous stochastic partial differential equation (SPDE), where the covariance structure of the GRF is controlled by the coefficients in the SPDE.…
Recent developments in non-ergodic ground-motion models (GMMs) explicitly model systematic spatial variations in source, site, and path effects, reducing standard deviation to 30-40% of ergodic models and enabling more accurate…
Quantifying predictive uncertainty is essential for real world machine learning applications, especially in scenarios requiring reliable and interpretable predictions. Many common parametric approaches rely on neural networks to estimate…
In this chapter, we show how to efficiently model high-dimensional extreme peaks-over-threshold events over space in complex non-stationary settings, using extended latent Gaussian Models (LGMs), and how to exploit the fitted model in…
This paper introduces a method for spatial interpolation of extreme values, and in particular targets the case in which conventional data, resulting from a measurement for example, are available at only a few locations. To overcome this the…
The last decade has seen an explosion in data sources available for the monitoring and prediction of environmental phenomena. While several inferential methods have been developed that make predictions on the underlying process by combining…
Expectation Maximization (EM) is among the most popular algorithms for estimating parameters of statistical models. However, EM, which is an iterative algorithm based on the maximum likelihood principle, is generally only guaranteed to find…
Additive smooth models, such as Generalized additive models (GAMs) of location, scale, and shape (GAMLSS), are a popular choice for modeling experimental data. However, software available to fit such models is usually not tailored…
Additive spatial statistical models with weakly stationary process assumptions have become standard in spatial statistics. However, one disadvantage of such models is the computation time, which rapidly increases with the number of data…
The Expectation Maximization (EM) algorithm is of key importance for inference in latent variable models including mixture of regressors and experts, missing observations. This paper introduces a novel EM algorithm, called…
Dramatic increases in the size and dimensionality of many recent data sets make crucial the need for sophisticated methods that can exploit inherent structure and handle missing values. In this article we derive an expectation-maximization…
This work highlights an approach for incorporating realistic uncertainties into scientific computing workflows based on finite elements, focusing on applications in computational mechanics and design optimization. We leverage Mat\'ern-type…
In this paper we consider a network of spatially distributed sensors which collect measurement samples of a spatial field, and aim at estimating in a distributed way (without any central coordinator) the entire field by suitably fusing all…
To address the dual challenges of inherent stochasticity and non-differentiable metrics in physical spatiotemporal forecasting, we propose Spatiotemporal Forecasting as Planning (SFP), a new paradigm grounded in Model-Based Reinforcement…
Statistical methods for inference on spatial extremes of large datasets are yet to be developed. Motivated by standard dimension reduction techniques used in spatial statistics, we propose an approach based on empirical basis functions to…