On the second order random walk model for irregular locations
(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:
https://lup.lub.lu.se/record/912666
- author
- Lindgren, Finn LU and Rue, Håvard
- organization
- publishing date
- 2008
- 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
- 2016-04-04 12:15:03
- date last changed
- 2022-03-16 00:30:04
@article{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}},
keywords = {{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 = {{Wiley-Blackwell}},
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}},
doi = {{10.1111/j.1467-9469.2008.00610.x}},
volume = {{35}},
year = {{2008}},
}