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Hierarchical models for regionally aggregated disease incidence data commonly involve region specific latent random effects that are modeled jointly as having a multivariate Gaussian distribution. The covariance or precision matrix…
An important aim of the analysis of agricultural field trials is to obtain good predictions for genotypic performance, by correcting for spatial effects. In practice these corrections turn out to be complicated, since there can be different…
Conditional autoregressive (CAR) models are commonly used to capture spatial correlation in areal unit data, and are typically specified as a prior distribution for a set of random effects, as part of a hierarchical Bayesian model. The…
Accurate spatial prediction and rigorous uncertainty quantification are central to modern spatial epidemiology and environmental risk analysis. We introduce a statistically principled hybrid modelling framework that integrates the…
We envision a system to continuously build and maintain a map based on earth-scale neural radiance fields (NeRF) using data collected from vehicles and drones in a lifelong learning manner. However, existing large-scale modeling by NeRF has…
Neural fields, a category of neural networks trained to represent high-frequency signals, have gained significant attention in recent years due to their impressive performance in modeling complex 3D data, such as signed distance (SDFs) or…
Automated sensing instruments on satellites and aircraft have enabled the collection of massive amounts of high-resolution observations of spatial fields over large spatial regions. If these datasets can be efficiently exploited, they can…
We study the nonparametric covariance estimation of a stationary Gaussian field X observed on a lattice. To tackle this issue, a neighborhood selection procedure has been recently introduced. This procedure amounts to selecting a…
We present Vector-Space Markov Random Fields (VS-MRFs), a novel class of undirected graphical models where each variable can belong to an arbitrary vector space. VS-MRFs generalize a recent line of work on scalar-valued, uni-parameter…
An explicit optimal linear spatial predictor is derived. The spatial correlations are imposed by means of Gibbs energy functionals with explicit coupling coefficients instead of covariance matrices. The model inference process is based on…
This work proposes an optimization-based manipulation planning framework where the objectives are learned functionals of signed-distance fields that represent objects in the scene. Most manipulation planning approaches rely on analytical…
The interpolation of spatial data can be of tremendous value in various applications, such as forecasting weather from only a few measurements of meteorological or remote sensing data. Existing methods for spatial interpolation, such as…
I present an approach for modeling areal spatial covariance by considering the stationary distribution of a spatio-temporal Markov random walk. In the areal data case, this stationary distribution corresponds to an intrinsic simultaneous…
Neural Radiance Fields (NeRF) has been applied to various tasks related to representations of 3D scenes. Most studies based on NeRF have focused on a small object, while a few studies have tried to reconstruct large-scale scenes although…
Centered Gaussian random fields (GRFs) indexed by compacta such as smooth, bounded Euclidean domains or smooth, compact and orientable manifolds are determined by their covariance operators. We consider centered GRFs given as variational…
Articulated objects and their representations pose a difficult problem for robots. These objects require not only representations of geometry and texture, but also of the various connections and joint parameters that make up each…
We present a method for transferring the artistic features of an arbitrary style image to a 3D scene. Previous methods that perform 3D stylization on point clouds or meshes are sensitive to geometric reconstruction errors for complex…
Spatial models for areal data are often constructed such that all pairs of adjacent regions are assumed to have near-identical spatial autocorrelation. In practice, data can exhibit dependence structures more complicated than can be…
Spatio-temporal data sets are rapidly growing in size. For example, environmental variables are measured with ever-higher resolution by increasing numbers of automated sensors mounted on satellites and aircraft. Using such data, which are…
Gaussian Markov random fields (GMRFs) are popular for modeling dependence in large areal datasets due to their ease of interpretation and computational convenience afforded by the sparse precision matrices needed for random variable…