A general science-based framework for dynamical spatio-temporal models

Wikle, Christopher K.; Hooten, Mevin B.

doi:10.1007/s11749-010-0209-z

Cited by 180 publications

(215 citation statements)

References 99 publications

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“…The development of analytical covariance functions for the governing SPDEs of such processes are typically intractable, yet the motivating Markovian models suggested by the discretization (either in physical or spectral space) are quite tractable and flexible (for example, see Hooten and Wikle (2007)). Wikle and Hooten (2010) discussed a general form for 'quadratic interaction models' and showed the connection to various classes of spatiotemporal PDEs. Wikle and Holan (2011) extend this to higher order interactions.…”

Section: Alfred Stein (Twente University Enschede)mentioning

confidence: 99%

An Explicit Link between Gaussian Fields and Gaussian Markov Random Fields: The Stochastic Partial Differential Equation Approach

Lindgren

Rue

Lindström

2011

Journal of the Royal Statistical Society Series B: Statistical Methodology

2,248

2,892

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Summary.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 R 2 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 R d , 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.

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Section: Alfred Stein (Twente University Enschede)mentioning

confidence: 99%

An Explicit Link between Gaussian Fields and Gaussian Markov Random Fields: The Stochastic Partial Differential Equation Approach

Lindgren

Rue

Lindström

2011

Journal of the Royal Statistical Society Series B: Statistical Methodology

2,248

2,892

View full text Add to dashboard Cite

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“…Other reduced rank approaches could also be used (e.g. [48]), or indeed the inverse covariance matrix could be modelled directly (e.g. ; Lindgren et al [29]).…”

Section: Discussionmentioning

confidence: 99%

Two-scale spatial models for binary data

Hardouin¹,

Cressie²

2017

Stat Methods Appl

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A spatial lattice model for binary data is constructed from two spatial scales linked through conditional probabilities. A coarse grid of lattice locations is specified and all remaining locations (which we call the background) capture fine-scale spatial dependence. Binary data on the coarse grid are modelled with an autologistic distribution, conditional on the binary process on the back-ground. The background behaviour is captured through a hidden Gaussian process after a logit transformation on its Bernoulli success probabilities. The likelihood is then the product of the (conditional) autologistic probability distribution and the hidden Gaussian-Bernoulli process. The parameters of the new model come from both spatial scales. A series of simulations illustrates the spatial-dependence properties of the model and likelihood-based methods are used to estimate its parameters. Presence-absence data of corn borers in the roots of corn plants are used to illustrate how the model is fitted. Abstract A spatial lattice model for binary data is constructed from two spatial scales linked through conditional probabilities. A coarse grid of lattice locations is specified and all remaining locations (which we call the background) capture fine-scale spatial dependence. Binary data on the coarse grid are modelled with an autologistic distribution, conditional on the binary process on the background. The background behaviour is captured through a hidden Gaussian process after a logit transformation on its Bernoulli success probabilities. The likelihood is then the product of the (conditional) autologistic probability distribution and the hidden Gaussian-Bernoulli process. The parameters of the new model come from both spatial scales. A series of simulations illustrates the spatial-dependence properties of the model and likelihood-based methods are used to estimate its parameters. Presence-absence data of corn borers in the roots of corn plants are used to illustrate how the model is fitted.

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“…Note that (5) and (6) combine to form a state-space model that fits within the general spatio-temporal modeling framework proposed by Wikle and Hooten [51].…”

Section: Modeling Movementmentioning

confidence: 99%

Temporal variation and scale in movement-based resource selection functions

Hooten

Hanks

Johnson

et al. 2014

Statistical Methodology

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a b s t r a c tA common population characteristic of interest in animal ecology studies pertains to the selection of resources. That is, given the resources available to animals, what do they ultimately choose to use? A variety of statistical approaches have been employed to examine this question and each has advantages and disadvantages with respect to the form of available data and the properties of estimators given model assumptions. A wealth of high resolution telemetry data are now being collected to study animal population movement and space use and these data present both challenges and opportunities for statistical inference. We summarize traditional methods for resource selection and then describe several extensions to deal with measurement uncertainty and an explicit movement process that exists in studies involving high-resolution telemetry data. Our approach uses a correlated random walk movement model to obtain temporally varying use and availability distributions that are employed in a weighted distribution context to estimate selection coefficients. The temporally varying coefficients are then weighted by their contribution to selection and combined to provide inference at the population level. The result is an intuitive and accessible statistical procedure that uses readily available software and is computationally feasible for large datasets. These methods are *

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A general science-based framework for dynamical spatio-temporal models

Cited by 180 publications

References 99 publications

An Explicit Link between Gaussian Fields and Gaussian Markov Random Fields: The Stochastic Partial Differential Equation Approach

An Explicit Link between Gaussian Fields and Gaussian Markov Random Fields: The Stochastic Partial Differential Equation Approach

Two-scale spatial models for binary data

Temporal variation and scale in movement-based resource selection functions

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