13 papers
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…
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…
Whittle-Matérn Fields with Variable Smoothness
Hamza Ruzayqat, Wenyu Lei, David Bolin +2
We introduce and analyze a nonlocal generalization of Whittle--Matérn Gaussian fields in which the smoothness parameter varies in space through the fractional order, $s=s(x)\in[\un…
Fractional and Integer Order Sobolev Spaces for Compact Metric Graphs
Elsiddig Awadelkarim, David Bolin, Alexandre B. Simas
Given a compact metric graph and the Laplacian coupled with standard (Kirchhoff) vertex conditions, solutions to fractional elliptic partial differential equations of the…
Elliptic Bayesian Inverse Problems on Metric Graphs
David Bolin, Wenwen Li, Daniel Sanz-Alonso
This paper studies the formulation, well-posedness, and numerical solution of Bayesian inverse problems on metric graphs, in which the edges represent one-dimensional wires connect…
rSPDE: tools for statistical modeling using fractional SPDEs
David Bolin, Alexandre B. Simas
The R software package rSPDE contains methods for approximating Gaussian random fields based on fractional-order stochastic partial differential equations (SPDEs). A common example…
Log-Gaussian Cox Processes on General Metric Graphs
David Bolin, Damilya Saduakhas, Alexandre B. Simas
The modeling of spatial point processes has advanced considerably, yet extending these models to non-Euclidean domains, such as road networks, remains a challenging problem. We pro…
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…
Linear cost and exponentially convergent approximation of Gaussian Matérn processes on intervals
David Bolin, Vaibhav Mehandiratta, Alexandre B. Simas
The computational cost for inference and prediction of statistical models based on Gaussian processes with Matérn covariance functions scales cubicly with the number of observation…
Fast and robust cross-validation-based scoring rule inference for spatial statistics
Helga Kristin Olafsdottir, Holger Rootzén, David Bolin
Scoring rules are aimed at evaluation of the quality of predictions, but can also be used for estimation of parameters in statistical models. We propose estimating parameters of mu…
Enhanced spatial modeling on linear networks using Gaussian Whittle-Matérn fields
Somnath Chaudhuri, Maria A. Barceló, Pablo Juan +4
Spatial statistics is traditionally based on stationary models on like Matérn fields. The adaptation of traditional spatial statistical methods, originally designed…
Wasserstein complexity penalization priors: a new class of penalizing complexity priors
David Bolin, Alexandre B. Simas, Zhen Xiong
Penalizing complexity (PC) priors provide a principled framework for reducing model complexity by penalizing the Kullback--Leibler Divergence (KLD) between a ``simple'' base model…
Leveraging population information in brain connectivity via Bayesian ICA with a novel informative prior for correlation matrices
Amanda Mejia, David Bolin, Daniel Spencer +1
Brain functional connectivity (FC), the temporal synchrony between brain networks, is essential to understand the functional organization of the brain and to identify changes due t…