• Corpus ID: 88518751

Spatial Mat\'ern fields driven by non-Gaussian noise

  title={Spatial Mat\'ern fields driven by non-Gaussian noise},
  author={David Bolin},
  journal={arXiv: Methodology},
  • D. Bolin
  • Published 4 June 2012
  • Computer Science
  • arXiv: Methodology
The article studies non-Gaussian extensions of a recently discovered link between certain Gaussian random fields, expressed as solutions to stochastic partial differential equations (SPDEs), and Gaussian Markov random fields. The focus is on non-Gaussian random fields with Mat\'ern covariance functions, and in particular we show how the SPDE formulation of a Laplace moving average model can be used to obtain an efficient simulation method as well as an accurate parameter estimation technique… 

Figures and Tables from this paper

Spatial modeling with system of stochastic partial differential equations
An overview of the current state of spatial modeling with systems of SPDEs is given and some of the interesting topics for further research are described.
Multivariate spatial modelling through a convolution-based skewed process
A multivariate version of the Gaussian-log Gaussian convolution process is developed which, by virtue of its capacity for capturing skewness, is potentially more flexible than symmetric ones.
Weak convergence of Galerkin approximations for fractional elliptic stochastic PDEs with spatial white noise
The numerical approximation of the solution to a stochastic partial differential equation with additive spatial white noise on a bounded domain is considered. The differential operator is assumed to
Mixtures of Shifted AsymmetricLaplace Distributions
This work marks an important step in the non-Gaussian model-based clustering and classification direction, and a variant of the EM algorithm is developed for parameter estimation by exploiting the relationship with the generalized inverse Gaussian distribution.


A class of non-Gaussian second order random fields
Non-Gaussian stochastic fields are introduced by means of integrals with respect to independently scattered stochastic measures distributed according to generalized Laplace laws. In particular, we
Gaussian Markov Random Fields: Theory and Applications
This volume is essential reading for statisticians working in spatial theory and its applications, as well as quantitative researchers in a wide range of science fields where spatial data analysis is important.
In order to make spatial statistics computationally feasible, we need to forget about the covariance function
This paper compares two approximations to GRFs with Matérn covariance functions: the kernel convolution approximation and the Gaussian Markov random field representation of an associated stochastic partial differential equation.
An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach
It is shown that, using an approximate stochastic weak solution to (linear) stochastically partial differential equations, some Gaussian fields in the Matérn class can provide an explicit link, for any triangulation of , between GFs and GMRFs, formulated as a basis function representation.
Spatial models generated by nested stochastic partial differential equations, with an application to global ozone mapping
A new class of stochastic field models is constructed using nested stochastic partial differential equations (SPDEs). The model class is computationally efficient, applicable to data on general
T-distributed Random Fields : A Parametric Model for Heavy-tailed Random Fields
The T -distributed random field model is defined and the conditional model is developed, which provides algorithms for conditional simulation and prediction, so-called T -kriging, which compares favourably with most previously defined random field models.
EM-based maximum likelihood parameter estimation for multivariate generalized hyperbolic distributions with fixed λ
This article proposes a simple EM-based ML estimation procedure to estimate parameters of the distribution when the subclass is known regardless of the dimensionality, which relies on the ability to numerically evaluate modified Bessel functions of the third kind and their logarithms, which is made possible by currently available software.
Estimation for Stochastic Models Driven by Laplace Motion
Laplace motion is a Lévy process built upon Laplace distributions. Non Gaussian stochastic fields that are integrals with respect to this process are considered and methods for their model fitting
Krylov subspace methods for approximating functions of symmetric positive definite matrices with applications to applied statistics and anomalous diffusion
This thesis proves the convergence of the matrix transfer technique for the solution of the fractional Poisson equation and gives conditions by which the finite difference discretisation can be replaced by other methods for discretising the Laplacian.