17 papers
Local asymptotic normality for spectral-tail likelihoods under fixed-domain sampling
Alexandre B. Simas, Jonas Wallin
We establish local asymptotic normality (LAN) for joint inference on scale and roughness in stationary Gaussian random fields observed on increasingly dense regular grids in a fixe…
A bridge representation of Gaussian Whittle-Matérn fields on compact metric graphs
David Bolin, Alexandre B. Simas, Jonas Wallin
Gaussian Whittle-Matérn fields form a flexible class of Gaussian processes on compact metric graphs, where spatial dependence is governed by the geometry and connectivity of the ne…
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 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…
Forecasting the Term Structure of Interest Rates with SPDE-Based Models
Qihao Duan, Alexandre B. Simas, David Bolin +1
The Dynamic Nelson--Siegel (DNS) model is a widely used framework for term structure forecasting. We propose a novel extension that models DNS residuals as a Gaussian random field,…
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…
Incorporating Correlated Nugget Effects in Multivariate Spatial Models: An Application to Argo Ocean Data
Damilya Saduakhas, David Bolin, Xiaotian Jin +2
Accurate analysis of global oceanographic data, such as temperature and salinity profiles from the Argo program, requires geostatistical models capable of capturing complex spatial…
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…
An explicit link between graphical models and Gaussian Markov random fields on metric graphs
David Bolin, Alexandre B. Simas, Jonas Wallin
We derive an explicit link between Gaussian Markov random fields on metric graphs and graphical models, and in particular show that a Markov random field restricted to the vertices…
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…
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…
Statistical inference for Gaussian Whittle-Matérn fields on metric graphs
David Bolin, Alexandre Simas, Jonas Wallin
Whittle-Matérn fields are a recently introduced class of Gaussian processes on metric graphs, which are specified as solutions to a fractional-order stochastic differential equatio…