Idioma:

explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach

Lindgren, Finn ; Rue, Håvard ; Lindström, Johan

Journal of the Royal Statistical Society. Series B, Statistical methodology, 2011-09, Vol.73 (4), p.423-498 [Periódico revisado por pares]

Oxford, UK: Blackwell Publishing Ltd

Texto completo disponível

Citações Citado por

Enviar para

Título:
explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach
Autor: Lindgren, Finn ; Rue, Håvard ; Lindström, Johan
Assuntos: Algorithms ; Approximate Bayesian inference ; Approximation ; Bayesian analysis ; Computation ; Computational methods ; Covariance ; Covariance functions ; Covariance matrices ; equations ; Exact sciences and technology ; Gaussian ; Gaussian fields ; Gaussian Markov random fields ; General topics ; Geostatistics ; Global warming ; Inference from stochastic processes; time series analysis ; ingredients ; Latent Gaussian models ; Markov chain ; Markov models ; Markov processes ; Markovian processes ; Matematik ; Mathematical analysis ; Mathematical functions ; Mathematical models ; Mathematics ; Modeling ; Natural Sciences ; Naturvetenskap ; Parametric models ; Parametrization ; Partial differential equations ; Probability and statistics ; Probability Theory and Statistics ; Probability theory and stochastic processes ; Sannolikhetsteori och statistik ; Sciences and techniques of general use ; Sparse matrices ; Spatial analysis ; Spatial models ; Statistical methods ; statistical models ; Statistics ; Stochastic analysis ; Stochastic models ; Stochastic partial differential equations ; Stochastic processes ; Stochasticity ; Studies ; temperature ; Triangulation
É parte de: Journal of the Royal Statistical Society. Series B, Statistical methodology, 2011-09, Vol.73 (4), p.423-498
Notas: http://dx.doi.org/10.1111/j.1467-9868.2011.00777.x
ArticleID:RSSB777
istex:63C771D23AA72790294C83646AA2C52E316D6D5A
ark:/67375/WNG-H3DD1B8S-4
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ObjectType-Article-2
ObjectType-Feature-1
Descrição: Continuously indexed Gaussian fields (GFs) are the most important ingredient in spatial statistical modelling and geostatistics. The specification through the covariance function gives an intuitive interpretation of the field properties. On the computational side, GFs are hampered with the big n problem, since the cost of factorizing dense matrices is cubic in the dimension. Although computational power today is at an all time high, this fact seems still to be a computational bottleneck in many applications. Along with GFs, there is the class of Gaussian Markov random fields (GMRFs) which are discretely indexed. The Markov property makes the precision matrix involved sparse, which enables the use of numerical algorithms for sparse matrices, that for fields in only use the square root of the time required by general algorithms. The specification of a GMRF is through its full conditional distributions but its marginal properties are not transparent in such a parameterization. We show that, using an approximate stochastic weak solution to (linear) stochastic partial differential equations, we can, for some GFs in the Matérn class, provide an explicit link, for any triangulation of , between GFs and GMRFs, formulated as a basis function representation. The consequence is that we can take the best from the two worlds and do the modelling by using GFs but do the computations by using GMRFs. Perhaps more importantly, our approach generalizes to other covariance functions generated by SPDEs, including oscillating and non-stationary GFs, as well as GFs on manifolds. We illustrate our approach by analysing global temperature data with a non-stationary model defined on a sphere.
Editor: Oxford, UK: Blackwell Publishing Ltd
Idioma: Inglês

Links

Voltar para lista de resultados

Resultado 1 Avançar Ir para próxima página

Realização: Logos de Redes Sociais:

explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach

Lindgren, Finn ; Rue, Håvard ; Lindström, Johan

Oxford, UK: Blackwell Publishing Ltd

Buscando em bases de dados remotas. Favor aguardar.