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A multivariate distribution can be described by a triangular transport map from the target distribution to a simple reference distribution. We propose Bayesian nonparametric inference on the transport map by modeling its components using…
Motivated by the subordinated Brownian motion, we define a new class of (in general discontinuous) random fields on higher-dimensional parameter domains: the subordinated Gaussian random field. We investigate the pointwise marginal…
In many applications it is important to be able to sample paths of SDEs conditional on observations of various kinds. This paper studies SPDEs which solve such sampling problems. The SPDE may be viewed as an infinite dimensional analogue of…
Generative modeling of spatio-temporal fields is crucial for a variety of applications, including stochastic weather generators and climate-model surrogates. However, many such fields exhibit complex dependence structures that vary across…
Unique existence of analytically strong solutions to stochastic partial differential equations (SPDE) with drift given by the subdifferential of a quasi-convex function and with general multiplicative noise is proven. The proof applies a…
We introduce a novel paradigm for learning non-parametric drift and diffusion functions for stochastic differential equation (SDE). The proposed model learns to simulate path distributions that match observations with non-uniform time…
This paper generalizes stochastic collocation methods to handle correlated non-Gaussian random parameters. The key challenge is to perform a multivariate numerical integration in a correlated parameter space when computing the coefficient…
We survey some of our recent results on existence, uniqueness and regularity of function solutions to parabolic and transport type partial differential equations driven by non-differentiable noises. When applied pathwise to random…
In the task of predicting spatio-temporal fields in environmental science using statistical methods, introducing statistical models inspired by the physics of the underlying phenomena that are numerically efficient is of growing interest.…
In this paper we investigate the numerical solution of stochastic partial differential equations (SPDEs) for a wider class of stochastic equations. We focus on non-diagonal colored noise instead of the usual space-time white noise. By…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and…
In this paper we consider a network of spatially distributed sensors which collect measurement samples of a spatial field, and aim at estimating in a distributed way (without any central coordinator) the entire field by suitably fusing all…
We derive posterior contraction rates (PCRs) and finite-sample Bernstein von Mises (BvM) results for non-parametric Bayesian models by extending the diffusion-based framework of Mou et al. (2024) to the infinite-dimensional setting. The…
This article proposes for stochastic partial differential equations (SPDEs) driven by additive noise, a novel approach for the approximate parameterizations of the ``small'' scales by the ``large'' ones, along with the derivaton of the…
Stochastic partial differential equations (SPDEs) are the mathematical tool of choice for modelling spatiotemporal PDE-dynamics under the influence of randomness. Based on the notion of mild solution of an SPDE, we introduce a novel neural…
Large classes of multi-dimensional Gaussian processes can be enhanced with stochastic Levy area(s). In a previous paper, we gave sufficient and essentially necessary conditions, only involving variational properties of the covariance.…
This paper develops a fractional stochastic partial differential equation (SPDE) to model the evolution of a random tangent vector field on the unit sphere. The SPDE is governed by a fractional diffusion operator to model the L\'{e}vy-type…
Stochastic symmetries and related invariance properties of finite dimensional SDEs driven by general c\`adl\`ag semimartingales taking values in Lie groups are defined and investigated. In order to enlarge the class of possible symmetries…
Current statistics literature on statistical inference of random fields typically assumes that the fields are stationary or focuses on models of non-stationary Gaussian fields with parametric/semiparametric covariance families, which may…