Related papers: Non-Gaussian bivariate modelling with application …
The properties of diffusion processes are drastically affected by heterogeneities of the medium that can induce non-Gaussian behavior of the propagator in contrast with the idealized realm of Brownian motion. In this paper we analyze the…
In many inverse problems, model parameters cannot be precisely determined from observational data. Bayesian inference provides a mechanism for capturing the resulting parameter uncertainty, but typically at a high computational cost. This…
Inverse problems constrained by partial differential equations are often ill-conditioned due to noisy and incomplete data or inherent non-uniqueness. A prominent example is full waveform inversion, which estimates Earth's subsurface…
We examine the multi--point velocity field for non--Gaussian models as a probe of non--Gaussian behavior. The two--point velocity correlation is not a useful indicator of a non--Gaussian density field, since it depends only on the power…
Numerical evidence of non-diffusive transport in three-dimensional, resistive pressure-gradient-driven plasma turbulence is presented. It is shown that the probability density function (pdf) of test particles' radial displacements is…
Fractal structures and non-Gaussian velocity distributions are characteristic properties commonly observed in virialized self-gravitating systems such as galaxies or interstellar molecular clouds. We study the origin of these properties…
A generalized covariant method of analysis applicable to frames for which time is not orthogonal to space, such as spacetime around a star possessing angular momentum or on a rotating disk, is presented. Important aspects of such an…
The non-Markovian continuous-time random walk model, featuring fat-tailed waiting times and narrow distributed displacements with a non-zero mean, is a well studied model for anomalous diffusion. Using an analytical approach, we recently…
In this paper we focus on a type of inverse problem in which the data is expressed as an unknown function of the sought and unknown model function (or its discretised representation as a model parameter vector). In particular, we deal with…
In many environmental applications involving spatially-referenced data, limitations on the number and locations of observations motivate the need for practical and efficient models for spatial interpolation, or kriging. A key component of…
Spatio-temporal systems exhibiting multi-scale behaviour are common in applications ranging from cyber-physical systems to systems biology, yet they present formidable challenges for computational modelling and analysis. Here we consider a…
We consider the statistical inverse problem of estimating a background flow field (e.g., of air or water) from the partial and noisy observation of a passive scalar (e.g., the concentration of a solute), a common experimental approach to…
Diffusion models have achieved remarkable success in generating samples from unknown data distributions. Most popular stochastic differential equation-based diffusion models perturb the target distribution by adding Gaussian noise,…
We describe a method for detecting, locating and quantifying sources of gas emissions to the atmosphere using remotely obtained gas concentration data; the method is applicable to gases of environmental concern. We demonstrate its…
Sampling conditional distributions is a fundamental task for Bayesian inference and density estimation. Generative models, such as normalizing flows and generative adversarial networks, characterize conditional distributions by learning a…
Gaussian Process state-space models capture complex temporal dependencies in a principled manner by placing a Gaussian Process prior on the transition function. These models have a natural interpretation as discretized stochastic…
The behavior of a bidisperse inelastic gas vertically shaken in a compartmentalized container is investigated using two different approaches: the first is a mean-field dynamical model, which treats the number of particles in the two…
Nonparametric Bayesian models are used routinely as flexible and powerful models of complex data. Many times, a statistician may have additional informative beliefs about data distribution of interest, e.g., its mean or subset components,…
Gaussian processes (GPs) are Bayesian nonparametric generative models that provide interpretability of hyperparameters, admit closed-form expressions for training and inference, and are able to accurately represent uncertainty. To model…
We present a numerical study of a model of pattern formation following a convective instability in a non-Boussinesq fluid. It is shown that many of the features observed in convection experiments conducted on $CO_{2}$ gas can be reproduced…