Related papers: Spatial random field models based on L\'evy indica…
Solutions of the bivariate, linear errors-in-variables estimation problem with unspecified errors are expected to be invariant under interchange and scaling of the coordinates. The appealing model of normally distributed true values and…
Gaussian processes are arguably the most important class of spatiotemporal models within machine learning. They encode prior information about the modeled function and can be used for exact or approximate Bayesian learning. In many…
Filter banks are a popular tool for the analysis of piecewise smooth signals such as natural images. Motivated by the empirically observed properties of scale and detail coefficients of images in the wavelet domain, we propose a…
Subordinate diffusions are constructed by time changing diffusion processes with an independent L\'{e}vy subordinator. This is a rich family of Markovian jump processes which exhibit a variety of jump behavior and have found many…
Diffusion models offer stable training and state-of-the-art performance for deep generative modeling tasks. Here, we consider their use in the context of multivariate subsurface modeling and probabilistic inversion. We first demonstrate…
Upper estimates of densities of convolution semigroups of probability measures are given under explicit assumptions on the corresponding L\'evy measure and the L\'evy--Khinchin exponent.
The estimation of the L\'{e}vy density, the infinite-dimensional parameter controlling the jump dynamics of a L\'{e}vy process, is considered here under a discrete-sampling scheme. In this setting, the jumps are latent variables, the…
Motivated by limits of critical inhomogeneous random graphs, we construct a family of sequences of measured metric spaces that we call continuous multiplicative graphs, that are expected to be the universal limit of graphs related to the…
In this paper, we survey some recent results on statistical inference (parametric and nonparametric statistical estimation, hypotheses testing) about the spectrum of stationary models with tapered data, as well as, a question concerning…
Statistical inference for spatial processes from partially realized or scattered data has seen voluminous developments in diverse areas ranging from environmental sciences to business and economics. Inference on the associated rates of…
We study the problem of parameter estimation for discretely observed stochastic processes driven by additive small L\'{e}vy noises. We do not impose any moment condition on the driving L\'{e}vy process. Under certain regularity conditions…
A key task in Bayesian machine learning is sampling from distributions that are only specified up to a partition function (i.e., constant of proportionality). One prevalent example of this is sampling posteriors in parametric distributions,…
In this work stochastic integration with respect to cylindrical Levy processes with weak second moments is introduced. It is well known that a deterministic Hilbert-Schmidt operator radonifies a cylindrical random variable, i.e. it maps a…
This work provide a thorough study of L\'evy or heavy-tailed random matrices (LM). By analysing the self-consistent equation on the probability distribution of the diagonal elements of the resolvent we establish the equation determining the…
In this article, we first review the connection between L\'evy processes and infinitely divisible random variables, and the classification of infinitely divisible distributions. Using this connection and the L\'evy-Khinchine representation…
The paper addresses one-dimensional transport in a Goupillaud medium (a layered medium in which the layer thickness is proportional to the propagation speed), as a prototypical case of wave propagation in random media. Suitable stochastic…
Doubly-stochastic point processes model the occurrence of events over a spatial domain as an inhomogeneous Poisson process conditioned on the realization of a random intensity function. They are flexible tools for capturing spatial…
Gaussian processes are arguably the most important class of spatiotemporal models within machine learning. They encode prior information about the modeled function and can be used for exact or approximate Bayesian learning. In many…
Graphical models for structured domains are powerful tools, but the computational complexities of combinatorial prediction spaces can force restrictions on models, or require approximate inference in order to be tractable. Instead of…
We develop Bayesian predictive stacking for geostatistical models, where the primary inferential objective is to provide inference on the latent spatial random field and conduct spatial predictions at arbitrary locations. We exploit…