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Geostatistics is a branch of statistics concerned with stochastic processes over continuous domains, with Gaussian processes (GPs) providing a flexible and principled modelling framework. However, the high computational cost of simulating…
In this paper we first describe the class of log-Gaussian Cox processes (LGCPs) as models for spatial and spatio-temporal point process data. We discuss inference, with a particular focus on the computational challenges of likelihood-based…
Gaussian processes (GPs), or distributions over arbitrary functions in a continuous domain, can be generalized to the multi-output case: a linear model of coregionalization (LMC) is one approach. LMCs estimate and exploit correlations…
Gaussian processes (GPs) are commonplace in spatial statistics. Although many non-stationary models have been developed, there is arguably a lack of flexibility compared to equipping each location with its own parameters. However, the…
Some scenarios require the computation of a predictive distribution of a new value evaluated on an objective function conditioned on previous observations. We are interested on using a model that makes valid assumptions on the objective…
In the study of natural and artificial complex systems, responses that are not completely determined by the considered decision variables are commonly modelled probabilistically, resulting in response distributions varying across decision…
Spatial generalized linear mixed models (SGLMMs) are popular and flexible models for non-Gaussian spatial data. They are useful for spatial interpolations as well as for fitting regression models that account for spatial dependence, and are…
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…
Engineering disciplines often rely on extensive simulations to ensure that structures are designed to withstand harsh conditions while avoiding over-engineering for unlikely scenarios. Assessments such as Serviceability Limit State (SLS)…
Generative modeling of spatio-temporal fields is crucial for a variety of applications, including stochastic weather generators and climate-model surrogates. However, many such fields exhibit complex dependence structures that vary across…
Conditional density estimation is complicated by multimodality, heteroscedasticity, and strong non-Gaussianity. Gaussian processes (GPs) provide a principled nonparametric framework with calibrated uncertainty, but standard GP regression is…
Nonstationary Gaussian processes (GPs) are essential for modeling complex, locally heterogeneous spatial data. A common modeling approach is the spatial deformation method that warps the domain to recover isotropy. However, this static…
Gaussian processes (GPs) are distributions over functions, which provide a Bayesian nonparametric approach to regression and classification. In spite of their success, GPs have limited use in some applications, for example, in some cases a…
We propose a probabilistic model for inferring the multivariate function from multiple areal data sets with various granularities. Here, the areal data are observed not at location points but at regions. Existing regression-based models can…
Gaussian random field (GRF) models are widely used in spatial statistics to capture spatially correlated error. We investigate the results of replacing Gaussian processes with Laplace moving averages (LMAs) in spatial generalized linear…
Gaussian Process State Space Models (GP-SSM) are a data-driven stochastic model class suitable to represent nonlinear dynamics. They have become increasingly popular in non-parametric modeling approaches since they provide not only a…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
Models of spatial transition probabilities, or equivalently, transiogram models have been recently proposed as spatial continuity measures in categorical fields. In this paper, properties of transiogram models are examined analytically, and…
Multivariate spatial fields are of interest in many applications, including climate model emulation. Not only can the marginal spatial fields be subject to nonstationarity, but the dependence structure among the marginal fields and between…
We propose an extension of the non-homogeneous Gaussian regression (NGR) model by Gneiting et al. (2005) that yields locally calibrated probabilistic forecasts of tem- perature, based on the output of an ensemble prediction system (EPS).…