Related papers: Bayesian modeling with spatial curvature processes

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…

Spatiotemporal dynamics models are fundamental for various domains, from heat propagation in materials to oceanic and atmospheric flows. However, currently available neural network-based spatiotemporal modeling approaches fall short when…

Quantifying changes in the probability and magnitude of extreme flooding events is key to mitigating their impacts. While hydrodynamic data are inherently spatially dependent, traditional spatial models such as Gaussian processes are poorly…

This paper describes an interdisciplinary approach to geometry modeling of geospatial boundaries. The objective is to extract surfaces from irregular spatial patterns using differential geometry and obtain coherent directional predictions…

We investigate the consequences of fluid flowing on a continuous surface upon the geometric and statistical distribution of the flow. We find that the ability of a surface to collect water by its mere geometrical shape is proportional to…

A common practice to account for psychophysical biases in vision is to frame them as consequences of a dynamic process relying on optimal inference with respect to a generative model. The present study details the complete formulation of…

Within the past two decades, Gaussian process regression has been increasingly used for modeling dynamical systems due to some beneficial properties such as the bias variance trade-off and the strong connection to Bayesian mathematics. As…

Understanding and predicting environmental phenomena often requires the construction of spatio-temporal statistical models, which are typically Gaussian processes. A common assumption made on Gaussian processes is that of covariance…

Sequential probabilistic inference from streaming observations requires modeling distributions over future trajectories as new observations arrive. Although diffusion and flow-matching models are effective at capturing high-dimensional,…

Learning-based behavior prediction methods are increasingly being deployed in real-world autonomous systems, e.g., in fleets of self-driving vehicles, which are beginning to commercially operate in major cities across the world. Despite…

We introduce a Bayesian Gaussian process latent variable model that explicitly captures spatial correlations in data using a parameterized spatial kernel and leveraging structure-exploiting algebra on the model covariance matrices for…

High resolution geospatial data are challenging because standard geostatistical models based on Gaussian processes are known to not scale to large data sizes. While progress has been made towards methods that can be computed more…

We develop an approach for Bayesian learning of spatiotemporal dynamical mechanistic models. Such learning consists of statistical emulation of the mechanistic system that can efficiently interpolate the output of the system from arbitrary…

The smoothing spline is one of the most popular curve-fitting methods, partly because of empirical evidence supporting its effectiveness and partly because of its elegant mathematical formulation. However, there are two obstacles that…

We develop a spatio-temporal model to forecast sensor output at five locations in North East England. The signal is described using coupled dynamic linear models, with spatial effects specified by a Gaussian process. Data streams are…

Spatial fields in the Earth and environmental sciences are often available at multiple scales or resolutions. While coarse-scale data (e.g., from global circulation models) are often abundant, they lack the local detail provided by…

The inverse problem which consists of determining the flow at the Earth's Core Mantle Boundary according to an outer core magnetic field and secular variation model, has been investigated through a Bayesian formalism. To circumvent the…

Calibration or parameter identification is used with computational mechanics models related to observed data of the modeled process to find model parameters such that good similarity between model prediction and observation is achieved. We…

In the era of climate change, the distribution of climate variables evolves with changes not limited to the mean value. Consequently, clustering algorithms based on central tendency could produce misleading results when used to summarize…

Multivariate spatial-statistical models are often used when modeling environmental and socio-demographic processes. The most commonly used models for multivariate spatial covariances assume both stationarity and symmetry for the…