14 papers
Mass Lumping and Numerical Quadrature for Approximation of Fractional Elliptic Differential Equations Driven by Gaussian White Noise
Kelvin J. R. Almeida-Sousa, David Bolin, Alexandre B. Simas
Fractional elliptic stochastic partial differential equations (SPDEs) are widely used in statistics and machine learning for computationally efficient and flexible modeling of Gaus…
Numerical approximation of fractional diffusion equations on metric graphs
David Bolin, Lenin Riera-Segura, Alexandre B. Simas
We study fractional diffusion equations on compact metric graphs, where the nonlocal dynamics is governed by fractional powers of the shifted Kirchhoff-Laplacian. Building on recen…
Finite element and box-method discretizations for fractional elliptic problems with quadrature and mass lumping
Kelvin J. R. Almeida-Sousa, David Bolin, Alexandre B. Simas
We analyze numerical approximation of the fractional elliptic problem , , where is a second-order self-adjoint elliptic operator with homogeneous Dirichlet or Ne…
A new class of non-stationary Gaussian fields with general smoothness on metric graphs
David Bolin, Lenin Riera-Segura, Alexandre B. Simas
The increasing availability of network data has driven the development of advanced statistical models specifically designed for metric graphs, where Gaussian processes play a pivot…
A Unified and Computationally Efficient Non-Gaussian Statistical Modeling Framework
David Bolin, Xiaotian Jin, Alexandre B. Simas +1
Datasets that exhibit non-Gaussian characteristics are common in many fields, while the current modeling framework and available software for non-Gaussian models is limited. We int…
Geometric ergodicity of Gibbs samplers for linear latent models with GIG variance mixtures
Elsiddig Awadelkarim, David Bolin, Xiaotian Jin +2
We study geometric ergodicity of the Gibbs sampler for linear latent non-Gaussian models (LLnGMs), a class of hierarchical models in which conditional Gaussian structure is preserv…