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The Minkowski functionals are useful statistics to quantify the morphology of various random fields. They have been applied to numerous analyses of geometrical patterns, including various types of cosmic fields, morphological image…
In this paper we consider probabilistic analogues of some classical integral geometric formulae: Weyl--Steiner tube formulae and the Chern--Federer kinematic fundamental formula. The probabilistic building blocks are smooth, real-valued…
Posterior computation for high-dimensional data with many parameters can be challenging. This article focuses on a new method for approximating posterior distributions of a low- to moderate-dimensional parameter in the presence of a…
Convex regularization techniques are now widespread tools for solving inverse problems in a variety of different frameworks. In some cases, the functions to be reconstructed are naturally viewed as realizations from random processes; an…
Large or very large spatial (and spatio-temporal) datasets have become common place in many environmental and climate studies. These data are often collected in non-Euclidean spaces (such as the planet Earth) and they often present…
Correlation matrices are fundamental summaries of functional brain networks, yet standard analyses often treat entries independently, ignoring the curved geometry of correlation space. Existing geometric methods frequently lack closed-form…
We propose a new method to define theories of random geometries, using an explicit and simple map between metrics and large hermitian matrices. We outline some of the many possible applications of the formalism. For example, a…
We study cosmological expansion in F(R) gravity using the trace of the field equations. High frequency oscillations in the Ricci scalar, whose amplitude increase as one evolves backward in time, have been predicted in recent works. We show…
Two algorithms are proposed to simulate space-time Gaussian random fields with a covariance function belonging to an extended Gneiting class, the definition of which depends on a completely monotone function associated with the spatial…
This paper investigates the approximation of Gaussian random variables in Banach spaces, focusing on the high-probability bounds for the approximation of Gaussian random variables using finitely many observations. We derive non-asymptotic…
Stochastic process models for spatiotemporal data underlying random fields find substantial utility in a range of scientific disciplines. Subsequent to predictive inference on the values of the random field (or spatial surface indexed…
The analysis of excursion sets in imaging data is essential to a wide range of scientific disciplines such as neuroimaging, climatology and cosmology. Despite growing literature, there is little published concerning the comparison of…
Analysis of brain imaging scans is critical to understanding the way the human brain functions, which can be leveraged to treat injuries and conditions that affect the quality of life for a significant portion of the human population. In…
Gaussian variational approximation is a popular methodology to approximate posterior distributions in Bayesian inference especially in high dimensional and large data settings. To control the computational cost while being able to capture…
We study random perturbations of Riemannian manifolds $(\mathsf{M},\mathsf{g})$ by means of so-called Fractional Gaussian Fields, which are defined intrinsically by the given manifold. The fields $h^\bullet: \omega\mapsto h^\omega$ will act…
Three-Dimensional Gaussian Splatting (3DGS) has shown substantial promise in the field of computer vision, but remains unexplored in the field of magnetic resonance imaging (MRI). This study explores its potential for the reconstruction of…
Gaussian processes are probabilistic models that are commonly used as functional priors in machine learning. Due to their probabilistic nature, they can be used to capture the prior information on the statistics of noise, smoothness of the…
Analytic expressions for the statistics of peaks of random fields with weak non-Gaussianity are provided. Specifically, the abundance and spatial correlation of peaks are represented by formulas which can be evaluated only by virtually…
Existing Bayesian spatial priors for functional magnetic resonance imaging (fMRI) data correspond to stationary isotropic smoothing filters that may oversmooth at anatomical boundaries. We propose two anatomically informed Bayesian spatial…
We examine a wide class of stochastic approximation algorithms for solving (stochastic) nonlinear problems on Riemannian manifolds. Such algorithms arise naturally in the study of Riemannian optimization, game theory and optimal transport,…