Joint Composite Estimating Functions in Spatiotemporal Models

Bai, Yun; Song, Peter X.‐K.; Raghunathan, T. E.

doi:10.1111/j.1467-9868.2012.01035.x

Cited by 39 publications

(49 citation statements)

References 60 publications

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“…Bai et al (2012) studied composite models for parameter estimation in spatio-temporal models and Bevilacqua et al (2012) propose weighted composite likelihood models for pairwise interactions of space-time variables.…”

Section: Closing Remarksmentioning

confidence: 99%

Estimation and Prediction in Spatial Models With Block Composite Likelihoods

Eidsvik

Shaby²,

Reich

et al. 2014

Journal of Computational and Graphical Statistics

117

101

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A block composite likelihood is developed for estimation and prediction in large spatial datasets.The composite likelihood is constructed from the joint densities of pairs of adjacent spatial blocks.This allows large datasets to be split into many smaller datasets, each of which can be evaluated separately, and combined through a simple summation. Estimates for unknown parameters are obtained by maximizing the block composite likelihood function. In addition, a new method for optimal spatial prediction under the block composite likelihood is presented. Asymptotic variances for both parameter estimates and predictions are computed using Godambe sandwich matrices. The approach gives considerable improvements in computational efficiency, and the composite structure obviates the need to load entire datasets into memory at once, completely avoiding memory limitations imposed by massive datasets. Moreover, computing time can be reduced even further by distributing the operations using parallel computing. A simulation study shows that composite likelihood estimates and predictions, as well as their corresponding asymptotic confidence intervals, are competitive with those based on the full likelihood. The procedure is demonstrated on one dataset from the mining industry and one dataset of satellite retrievals. The real-data examples show that the block composite results tend to outperform two competitors; the predictive process model and fixed rank Kriging. Supplemental material for this article is available online.

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Section: Closing Remarksmentioning

confidence: 99%

Estimation and Prediction in Spatial Models With Block Composite Likelihoods

Eidsvik

Shaby²,

Reich

et al. 2014

Journal of Computational and Graphical Statistics

117

101

View full text Add to dashboard Cite

show abstract

“…A way to solve the computational problem is to reduce the complexity of the spatial correlation matrix (Cressie and Johannesson, ). Alternatively, the full likelihood can be approximated by a composite likelihood (Lindsay, ), which is formed by a product of lower dimensional conditional or marginal component likelihoods (Yasui and Lele, ; Heagerty and Lele, ; Curriero and Lele, ; Bai et al ., ). In this approach, the component likelihoods are based on data from a small number (usually pairs) of locations so the resulting estimating equations can be evaluated without the need for inversion of high dimensional correlation matrices.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Spatial Data with a Nested Correlation Structure

Adegboye

Leung

Wang

2017

Journal of the Royal Statistical Society Series C: Applied Statistics

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Summary Spatial statistical analyses are often used to study the link between environmental factors and the incidence of diseases. In modelling spatial data, the existence of spatial correlation between observations must be considered. However, in many situations, the exact form of the spatial correlation is unknown. This paper studies environmental factors that might influence the incidence of malaria in Afghanistan. We assume that spatial correlation may be induced by multiple latent sources. Our method is based on a generalized estimating equation of the marginal mean of disease incidence, as a function of the geographical factors and the spatial correlation. Instead of using one set of generalized estimating equations, we embed a series of generalized estimating equations, each reflecting a particular source of spatial correlation, into a larger system of estimating equations. To estimate the spatial correlation parameters, we set up a supplementary set of estimating equations based on the correlation structures that are induced from the various sources. Simultaneous estimation of the mean and correlation parameters is performed by alternating between the two systems of equations.

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“…They showed that the estimators of their methods are consistent and asymptotic normal under increasing domain asymptotics (Cressie (1993)). Bai, Song, and Raghunathan (2012) also developed a CL method based on pairwise differences, forming a joint estimation function based on spatial, temporal and spatio-temporal group-based estimation functions. A second approach seeks to simplify model specifications of covariance structures to achieve computational efficiency.…”

Section: Introductionmentioning

confidence: 99%

Full-Scale Approximations of Spatio-Temporal Covariance Models for Large Datasets

Zhang¹,

Sang²,

Huang³

2014

STAT SINICA

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. (2015). Full-scale approximations of spatio-temporal covariance models for large datasets. Statistica Sinica, 25 99-114. Full-scale approximations of spatio-temporal covariance models for large datasets AbstractVarious continuously-indexed spatio-temporal process models have been constructed to characterize spatiotemporal dependence structures, but the computational complexity for model fitting and predictions grows in a cubic order with the size of dataset and application of such models is not feasible for large datasets. This article extends the full-scale approximation (FSA) approach by Sang and Huang (2012) to the spatiotemporal context to reduce computational complexity. A reversible jump Markov chain Monte Carlo (RJMCMC) algorithm is proposed to select knots automatically from a discrete set of spatio-temporal points. Our approach is applicable to nonseparable and nonstationary spatio-temporal covariance models. We illustrate the effectiveness of our method through simulation experiments and application to an ozone measurement dataset. Disciplines Engineering | Science and Technology Studies FULL-SCALE APPROXIMATIONS OF SPATIO-TEMPORAL COVARIANCE MODELS FOR LARGE DATASETSBohai Zhang, Huiyan Sang and Jianhua Z. Huang Texas A&M UniversityAbstract: Various continuously-indexed spatio-temporal process models have been constructed to characterize spatio-temporal dependence structures, but the computational complexity for model fitting and predictions grows in a cubic order with the size of dataset and application of such models is not feasible for large datasets. This article extends the full-scale approximation (FSA) approach by Sang and Huang (2012) to the spatio-temporal context to reduce computational complexity. A reversible jump Markov chain Monte Carlo (RJMCMC) algorithm is proposed to select knots automatically from a discrete set of spatio-temporal points. Our approach is applicable to nonseparable and nonstationary spatio-temporal covariance models. We illustrate the effectiveness of our method through simulation experiments and application to an ozone measurement dataset.

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Joint Composite Estimating Functions in Spatiotemporal Models

Cited by 39 publications

References 60 publications

Estimation and Prediction in Spatial Models With Block Composite Likelihoods

Estimation and Prediction in Spatial Models With Block Composite Likelihoods

Analysis of Spatial Data with a Nested Correlation Structure

Full-Scale Approximations of Spatio-Temporal Covariance Models for Large Datasets

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