Related papers: A Multi-Resolution Model for Non-Gaussian Random F…
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.…
Non-Gaussianity in the cosmic microwave background and the large-scale structure of galaxies provides an increasingly powerful probe of the universe. I implement an algorithm to generate realisations of fields that possess an arbitrary…
State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference \emph{and learning} (i.e. state estimation and system…
This work is concerned with the study of the adaptivity properties of nonparametric regression estimators over the $d$-dimensional sphere within the global thresholding framework. The estimators are constructed by means of a form of…
This letter describes an incremental multimodal surface mapping methodology, which represents the environment as a continuous probabilistic model. This model enables high-resolution reconstruction while simultaneously compressing spatial…
In this work, we study probability functions associated with Gaussian mixture models. Our primary focus is on extending the use of spherical radial decomposition for multivariate Gaussian random vectors to the context of Gaussian mixture…
These days we live in a world with a permanent electromagnetic field. This raises many questions about our health and the deployment of new equipment. The problem is that these fields remain difficult to visualize easily, which only some…
We consider evidence integration from potentially dependent observation processes under varying spatio-temporal sampling resolutions and noise levels. We develop a multi-resolution multi-task (MRGP) framework while allowing for both…
This paper provides quantitative Central Limit Theorems for nonlinear transforms of spherical random fields, in the high frequency limit. The sequences of fields that we consider are represented as smoothed averages of spherical Gaussian…
We propose a new modeling framework for highly-multivariate spatial processes that synthesizes ideas from recent multiscale and spectral approaches with graphical models. The basis graphical lasso writes a univariate Gaussian process as a…
Gaussian processes are popular and flexible models for spatial, temporal, and functional data, but they are computationally infeasible for large datasets. We discuss Gaussian-process approximations that use basis functions at multiple…
We study non-parametric regression estimates for random fields. The data satisfies certain strong mixing conditions and is defined on the regular $N$-dimensional lattice structure. We show consistency and obtain rates of convergence. The…
Quantifying spatial and/or temporal associations in multivariate geolocated data of different types is achievable via spatial random effects in a Bayesian hierarchical model, but severe computational bottlenecks arise when spatial…
Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…
We develop Bayesian nonparametric models for spatially indexed data of mixed type. Our work is motivated by challenges that occur in environmental epidemiology, where the usual presence of several confounding variables that exhibit complex…
Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…
Gaussian processes have been successful in both supervised and unsupervised machine learning tasks, but their computational complexity has constrained practical applications. We introduce a new approximation for large-scale Gaussian…
Sparse Multi-view Images can be Learned to predict explicit radiance fields via Generalizable Gaussian Splatting approaches, which can achieve wider application prospects in real-life when ground-truth camera parameters are not required as…
Identifying an appropriate covariance function is one of the primary interests in spatial and spatio-temporal statistics because it allows researchers to analyze the dependence structure of the random process. For this purpose, spatial…
Many problems arising in applications result in the need to probe a probability distribution for functions. Examples include Bayesian nonparametric statistics and conditioned diffusion processes. Standard MCMC algorithms typically become…