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111
Implementing approximate Bayesian inference for latent Gaussian models using integrated nested Laplace approximations: A manual for the inlaprogram
, 2008
"... Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalised) linear models, (generalised) additive models, smoothingspline models, statespace models, semiparametric regression, spatial and spatiotemp ..."
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Cited by 294 (20 self)
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Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalised) linear models, (generalised) additive models, smoothingspline models, statespace models, semiparametric regression, spatial and spatiotemporal models, logGaussian Coxprocesses, geostatistical and geoadditive models. In this paper we consider approximate Bayesian inference in a popular subset of structured additive regression models, latent Gaussian models, where the latent field is Gaussian, controlled by a few hyperparameters and with nonGaussian response variables. The posterior marginals are not available in closed form due to the nonGaussian response variables. For such models, Markov chain Monte Carlo methods can be implemented, but they are not without problems, both in terms of convergence and computational time. In some practical applications, the extent of these problems is such that Markov chain Monte Carlo is simply not an appropriate tool for routine analysis. We show that, by using an integrated nested Laplace approximation and its simplified version, we can directly compute very accurate approximations to the posterior marginals. The main benefit of these approximations
An Explicit Link between Gaussian Fields and Gaussian Markov random fields: the SPDE approach
 PREPRINTS IN MATHEMATICAL SCIENCES
, 2010
"... Continuously indexed Gaussian fields (GFs) is the most important ingredient in spatial statistical modelling and geostatistics. The specification through the covariance function gives an intuitive interpretation of its properties. On the computational side, GFs are hampered with the bign problem, ..."
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Cited by 115 (17 self)
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Continuously indexed Gaussian fields (GFs) is the most important ingredient in spatial statistical modelling and geostatistics. The specification through the covariance function gives an intuitive interpretation of its properties. On the computational side, GFs are hampered with the bign problem, since the cost of factorising dense matrices is cubic in the dimension. Although the computational power today is alltimehigh, this fact seems still to be a computational bottleneck in applications. Along with GFs, there is the class of Gaussian Markov random fields (GMRFs) which are discretely indexed. The Markov property makes the involved precision matrix sparse which enables the use of numerical algorithms for sparse matrices, that for fields in R 2 only use the squareroot 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 parametrisation. In this paper, we show that using an approximate stochastic weak solution to (linear) stochastic partial differential equations (SPDEs), we can, for some GFs in the Matérn class, provide an explicit link, for any triangulation of R d, between GFs and GMRFs. The consequence is that we can take the best from the two worlds and do the modelling using GFs but do the computations using GMRFs. Perhaps more importantly,
Dimension reduction and alleviation of confounding for spatial generalized linear mixed models
 Journal of the Royal Statistical Society: Series B (Statistical Methodology
, 2013
"... Abstract. Nongaussian spatial data are very common in many disciplines. For instance, count data are common in disease mapping, and binary data are common in ecology. When fitting spatial regressions for such data, one needs to account for dependence to ensure reliable inference for the regression ..."
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Cited by 14 (1 self)
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Abstract. Nongaussian spatial data are very common in many disciplines. For instance, count data are common in disease mapping, and binary data are common in ecology. When fitting spatial regressions for such data, one needs to account for dependence to ensure reliable inference for the regression coefficients. The spatial generalized linear mixed model (SGLMM) offers a very popular and flexible approach to modeling such data, but the SGLMM suffers from three major shortcomings: (1) uninterpretability of parameters due to spatial confounding, (2) variance inflation due to spatial confounding, and (3) highdimensional spatial random effects that make fully Bayesian inference for such models computationally challenging. We propose a new parameterization of the SGLMM that alleviates spatial confounding and speeds computation by greatly reducing the dimension of the spatial random effects. We illustrate the application of our approach to simulated binary, count, and Gaussian spatial datasets, and to a large infant mortality dataset.
Monitoring global forest cover using data mining
 ACM Transactions on Intelligent Systems and Technology
, 2011
"... Forests are a critical component of the planet’s ecosystem. Unfortunately, there has been significant degradation in forest cover over recent decades as a result of logging, conversion to crop, plantation, and pasture land, or disasters (natural or man made) such as forest fires, floods, and hurrica ..."
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Cited by 13 (9 self)
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Forests are a critical component of the planet’s ecosystem. Unfortunately, there has been significant degradation in forest cover over recent decades as a result of logging, conversion to crop, plantation, and pasture land, or disasters (natural or man made) such as forest fires, floods, and hurricanes. As a result, significant attention is being given to the sustainable use of forests. A key to effective forest management is quantifiable knowledge about changes in forest cover. This requires identification and characterization of changes and the discovery of the relationship between these changes and natural and anthropogenic variables. In this article, we present our preliminary efforts and achievements in addressing some of these tasks along with the challenges and opportunities that need to be addressed in the future. At a higher level, our goal is to provide an overview of the exciting opportunities and challenges in developing and applying data mining approaches to provide critical information for forest and land use management.
Bayesian Modeling with Gaussian Processes using the GPstuff Toolbox
, 2014
"... Gaussian processes (GP) are powerful tools for probabilistic modeling purposes. They can be used to define prior distributions over latent functions in hierarchical Bayesian models. The prior over functions is defined implicitly by the mean and covariance function, which determine the smoothness and ..."
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Cited by 12 (1 self)
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Gaussian processes (GP) are powerful tools for probabilistic modeling purposes. They can be used to define prior distributions over latent functions in hierarchical Bayesian models. The prior over functions is defined implicitly by the mean and covariance function, which determine the smoothness and variability of the function. The inference can then be conducted directly in the function space by evaluating or approximating the posterior process. Despite their attractive theoretical properties GPs provide practical challenges in their implementation. GPstuff is a versatile collection of computational tools for GP models compatible with Linux and Windows MATLAB and Octave. It includes, among others, various inference methods, sparse approximations and tools for model assessment. In this work, we review these tools and demonstrate the use of GPstuff in several models.
Estimation and prediction in spatial models with block composite likelihoods
 Journal of Computational and Graphical Statistics (To Appear
, 2013
"... 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 s ..."
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Cited by 11 (2 self)
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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 realdata examples
A hierarchical maxstable spatial model for extreme precipitation
 Ann. of Appl. Stat
, 2012
"... Extreme environmental phenomena such as major precipitation events manifestly exhibit spatial dependence. Maxstable processes are a class of asymptoticallyjustified models that are capable of representing spatial dependence among extreme values. While these models satisfy modeling requirements, ..."
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Cited by 11 (1 self)
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Extreme environmental phenomena such as major precipitation events manifestly exhibit spatial dependence. Maxstable processes are a class of asymptoticallyjustified models that are capable of representing spatial dependence among extreme values. While these models satisfy modeling requirements, they are limited in their utility because their corresponding joint likelihoods are unknown for more than a trivial number of spatial locations, preventing, in particular, Bayesian analyses. In this paper, we propose a new random effects model to account for spatial dependence. We show that our specification of the random effect distribution leads to a maxstable process that has the popular Gaussian extreme value process (GEVP) as a limiting case. The proposed model is used to analyze the yearly maximum precipitation from a regional climate model. 1. Introduction. Spatial
Approximate Bayesian Inference for Large Spatial Datasets Using Predictive Process Models
, 2010
"... This article addresses the challenges of estimating hierarchical spatial models to large datasets. With the increasing availability of geocoded scientific data, hierarchical models involving spatial processes have become a popular method for carrying out spatial inference. Such models are customar ..."
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Cited by 10 (0 self)
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This article addresses the challenges of estimating hierarchical spatial models to large datasets. With the increasing availability of geocoded scientific data, hierarchical models involving spatial processes have become a popular method for carrying out spatial inference. Such models are customarily estimated using Markov chain Monte Carlo algorithms that, while immensely flexible, can become prohibitively expensive. In particular, fitting hierarchical spatial models often involves expensive decompositions of dense matrices whose computational complexity increases in cubic order with the number of spatial locations. Such matrix computations are required in each iteration of the Markov chain Monte Carlo algorithm, rendering them infeasible for large spatial data sets. This article proposes to address the computational challenges in modeling large spatial datasets by merging two recent developments. First, we use the predictive process model as a reducedrank spatial process, to diminish the dimensionality of the model. Then we proceed to develop a computational framework for estimating predictive process models using the integrated nested Laplace approximation. We discuss settings where the first stage likelihood