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On the second order random walk model for irregular locations

Lindgren, Finn LU and Rue, Håvard (2008) In Scandinavian Journal of Statistics 35(4). p.691-700
Abstract
The second order random walk (RW2) model is commonly used for smoothing data and for modelling response functions. It is computationally efficient due to the Markov properties of the joint (intrinsic) Gaussian density. For evenly spaced locations the RW2 model is well established, whereas for irregularly spaced locations there is no well established construction in the literature. By considering the RW2 model as the solution of a stochastic differential equation (SDE), a discretely observed integrated Wiener process, it is possible to derive the density preserving the Markov properties by augmenting the state-space with the velocities. Here, we derive a computationally more efficient RW2 model for irregular locations using a Galerkin... (More)
The second order random walk (RW2) model is commonly used for smoothing data and for modelling response functions. It is computationally efficient due to the Markov properties of the joint (intrinsic) Gaussian density. For evenly spaced locations the RW2 model is well established, whereas for irregularly spaced locations there is no well established construction in the literature. By considering the RW2 model as the solution of a stochastic differential equation (SDE), a discretely observed integrated Wiener process, it is possible to derive the density preserving the Markov properties by augmenting the state-space with the velocities. Here, we derive a computationally more efficient RW2 model for irregular locations using a Galerkin approximation to the solution of the SDE without the need of augmenting the state-space. Numerical comparison with the exact solution demonstrates that the error in the Galerkin approximation is small and negligible in applications. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Numerical methods for sparse matrices, Second order random walk., Intrinsic Gaussian Markov random fields, Galerkin approximation, Integrated Wiener process
in
Scandinavian Journal of Statistics
volume
35
issue
4
pages
691 - 700
publisher
Wiley-Blackwell
external identifiers
  • WOS:000260824400008
  • Scopus:55849090666
ISSN
1467-9469
DOI
10.1111/j.1467-9469.2008.00610.x
language
English
LU publication?
yes
id
4f425b0d-cf79-48d7-8102-399f8f019d71 (old id 912666)
date added to LUP
2008-01-10 14:53:31
date last changed
2016-10-13 04:50:30
@misc{4f425b0d-cf79-48d7-8102-399f8f019d71,
  abstract     = {The second order random walk (RW2) model is commonly used for smoothing data and for modelling response functions. It is computationally efficient due to the Markov properties of the joint (intrinsic) Gaussian density. For evenly spaced locations the RW2 model is well established, whereas for irregularly spaced locations there is no well established construction in the literature. By considering the RW2 model as the solution of a stochastic differential equation (SDE), a discretely observed integrated Wiener process, it is possible to derive the density preserving the Markov properties by augmenting the state-space with the velocities. Here, we derive a computationally more efficient RW2 model for irregular locations using a Galerkin approximation to the solution of the SDE without the need of augmenting the state-space. Numerical comparison with the exact solution demonstrates that the error in the Galerkin approximation is small and negligible in applications.},
  author       = {Lindgren, Finn and Rue, Håvard},
  issn         = {1467-9469},
  keyword      = {Numerical methods for sparse matrices,Second order random walk.,Intrinsic Gaussian Markov random fields,Galerkin approximation,Integrated Wiener process},
  language     = {eng},
  number       = {4},
  pages        = {691--700},
  publisher    = {ARRAY(0x9527f48)},
  series       = {Scandinavian Journal of Statistics},
  title        = {On the second order random walk model for irregular locations},
  url          = {http://dx.doi.org/10.1111/j.1467-9469.2008.00610.x},
  volume       = {35},
  year         = {2008},
}