Estimation of parameterized spatio-temporal dynamic models

Spatio-temporal processes are often high-dimensional, exhibiting complicated variability across space and time. Traditional state-space model approaches to such processes in the presence of uncertain data have been shown to be useful. However, estimation of state-space models in this context is ofte...

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Bibliographic Details
Published inJournal of statistical planning and inference Vol. 137; no. 2; pp. 567 - 588
Main Authors Xu, Ke, Wikle, Christopher K.
Format Journal Article
LanguageEnglish
Published Lausanne Elsevier B.V 01.02.2007
New York,NY Elsevier Science
Amsterdam
Subjects
Dynamic
EM algorithm
Exact sciences and technology
General EM
General topics
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Parametric inference
Partial differential equations, boundary value problems
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Probability and statistics
Sciences and techniques of general use
Spatial
Spatio-temporal
State-space
Statistics
Time series
Spatio-temporal
Dynamic
General EM
Spatial
State-space
Time series
EM algorithm
OR algorithm
Differential equation
Advection diffusion equation
State space
Parameterization
Statistical simulation
Partial differential equation
Diffusion equation
Dynamic model
Drought
State estimation
Maximization
Prior distribution
Space time
Statistical decision
State space method
Statistical method
Expectation
Online AccessGet full text
ISSN0378-3758
1873-1171
DOI10.1016/j.jspi.2005.12.005

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Summary:Spatio-temporal processes are often high-dimensional, exhibiting complicated variability across space and time. Traditional state-space model approaches to such processes in the presence of uncertain data have been shown to be useful. However, estimation of state-space models in this context is often problematic since parameter vectors and matrices are of high dimension and can have complicated dependence structures. We propose a spatio-temporal dynamic model formulation with parameter matrices restricted based on prior scientific knowledge and/or common spatial models. Estimation is carried out via the expectation–maximization (EM) algorithm or general EM algorithm. Several parameterization strategies are proposed and analytical or computational closed form EM update equations are derived for each. We apply the methodology to a model based on an advection–diffusion partial differential equation in a simulation study and also to a dimension-reduced model for a Palmer Drought Severity Index (PDSI) data set.
ISSN:0378-3758
1873-1171
DOI:10.1016/j.jspi.2005.12.005