arXiv subjects

Geir-Arne Fuglstad

Publications and source records attributed to Geir-Arne Fuglstad.

28 records · Page 2Linked to original sources

arXiv2020

Bayesian Multiresolution Modeling Of Georeferenced Data

Current implementations of multiresolution methods are limited in terms of possible types of responses and approaches to inference. We provide a multiresolution approach for spatial analysis of non-Gaussian responses using latent Gaussian models and Bayesian inference via integrated nested Laplace approximation (INLA). The approach builds on `LatticeKrig', but uses a reparameterization of the model parameters that is intuitive and interpretable so that modeling and prior selection can be guided by expert knowledge about the different spatial scales at which dependence acts. The priors can be used to make inference robust and integration over model parameters allows for more accurate posterior estimates of uncertainty. The extended LatticeKrig (ELK) model is compared to a standard implementation of LatticeKrig (LK), and a standard Matérn model, and we find modest improvement in spatial oversmoothing and prediction for the ELK model for counts of secondary education completion for women in Kenya collected in the 2014 Kenya demographic health survey. Through a simulation study with Gaussian responses and a realistic mix of short and long scale dependencies, we demonstrate that the differences between the three approaches for prediction increases with distance to nearest observation.

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arXiv2019

Design- and Model-Based Approaches to Small-Area Estimation in a Low and Middle Income Country Context: Comparisons and Recommendations

The need for rigorous and timely health and demographic summaries has provided the impetus for an explosion in geographic studies, with a common approach being the production of pixel-level maps, particularly in low and middle income countries. In this context, household surveys are a major source of data, usually with a two-stage cluster design with stratification by region and urbanicity. Accurate estimates are of crucial interest for precision public health policy interventions, but many current studies take a cavalier approach to acknowledging the sampling design, while presenting results at a fine geographic scale. In this paper we investigate the extent to which accounting for sample design can affect predictions at the aggregate level, which is usually the target of inference. We describe a simulation study in which realistic sampling frames are created for Kenya, based on population and demographic information, with a survey design that mimics a Demographic Health Survey (DHS). We compare the predictive performance of various commonly-used models. We also describe a cluster level model with a discrete spatial smoothing prior that has not been previously used, but provides reliable inference. We find that including stratification and cluster level random effects can improve predictive performance. Spatially smoothed direct (weighted) estimates were robust to priors and survey design. Continuous spatial models performed well in the presence of fine scale variation; however, these models require the most "hand holding". Subsequently, we examine how the models perform on real data; specifically we model the prevalence of secondary education for women aged 20-29 using data from the 2014 Kenya DHS.

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arXiv2019

Intuitive joint priors for variance parameters

Variance parameters in additive models are typically assigned independent priors that do not account for model structure. We present a new framework for prior selection based on a hierarchical decomposition of the total variance along a tree structure to the individual model components. For each split in the tree, an analyst may be ignorant or have a sound intuition on how to attribute variance to the branches. In the former case a Dirichlet prior is appropriate to use, while in the latter case a penalised complexity (PC) prior provides robust shrinkage. A bottom-up combination of the conditional priors results in a proper joint prior. We suggest default values for the hyperparameters and offer intuitive statements for eliciting the hyperparameters based on expert knowledge. The prior framework is applicable for R packages for Bayesian inference such as INLA and RStan. Three simulation studies show that, in terms of the application-specific measures of interest, PC priors improve inference over Dirichlet priors when used to penalise different levels of complexity in splits. However, when expressing ignorance in a split, Dirichlet priors perform equally well and are preferred for their simplicity. We find that assigning current state-of-the-art default priors for each variance parameter individually is less transparent and does not perform better than using the proposed joint priors. We demonstrate practical use of the new framework by analysing spatial heterogeneity in neonatal mortality in Kenya in 2010-2014 based on complex survey data.

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arXiv2018

Spatial modelling with R-INLA: A review

Coming up with Bayesian models for spatial data is easy, but performing inference with them can be challenging. Writing fast inference code for a complex spatial model with realistically-sized datasets from scratch is time-consuming, and if changes are made to the model, there is little guarantee that the code performs well. The key advantages of R-INLA are the ease with which complex models can be created and modified, without the need to write complex code, and the speed at which inference can be done even for spatial problems with hundreds of thousands of observations. R-INLA handles latent Gaussian models, where fixed effects, structured and unstructured Gaussian random effects are combined linearly in a linear predictor, and the elements of the linear predictor are observed through one or more likelihoods. The structured random effects can be both standard areal model such as the Besag and the BYM models, and geostatistical models from a subset of the Matérn Gaussian random fields. In this review, we discuss the large success of spatial modelling with R-INLA and the types of spatial models that can be fitted, we give an overview of recent developments for areal models, and we give an overview of the stochastic partial differential equation (SPDE) approach and some of the ways it can be extended beyond the assumptions of isotropy and separability. In particular, we describe how slight changes to the SPDE approach leads to straight-forward approaches for non-stationary spatial models and non-separable space-time models.

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arXiv2017

Constructing Priors that Penalize the Complexity of Gaussian Random Fields

Priors are important for achieving proper posteriors with physically meaningful covariance structures for Gaussian random fields (GRFs) since the likelihood typically only provides limited information about the covariance structure under in-fill asymptotics. We extend the recent Penalised Complexity prior framework and develop a principled joint prior for the range and the marginal variance of one-dimensional, two-dimensional and three-dimensional Matérn GRFs with fixed smoothness. The prior is weakly informative and penalises complexity by shrinking the range towards infinity and the marginal variance towards zero. We propose guidelines for selecting the hyperparameters, and a simulation study shows that the new prior provides a principled alternative to reference priors that can leverage prior knowledge to achieve shorter credible intervals while maintaining good coverage. We extend the prior to a non-stationary GRF parametrized through local ranges and marginal standard deviations, and introduce a scheme for selecting the hyperparameters based on the coverage of the parameters when fitting simulated stationary data. The approach is applied to a dataset of annual precipitation in southern Norway and the scheme for selecting the hyperparameters leads to concervative estimates of non-stationarity and improved predictive performance over the stationary model.

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arXiv2017

Estimating Under Five Mortality in Space and Time in a Developing World Context

Accurate estimates of the under-5 mortality rate (U5MR) in a developing world context are a key barometer of the health of a nation. This paper describes new models to analyze survey data on mortality in this context. We are interested in both spatial and temporal description, that is, wishing to estimate U5MR across regions and years, and to investigate the association between the U5MR and spatially-varying covariate surfaces. We illustrate the methodology by producing yearly estimates for subnational areas in Kenya over the period 1980 - 2014 using data from demographic health surveys (DHS). We use a binomial likelihood with fixed effects for the urban/rural stratification to account for the complex survey design. We carry out smoothing using Bayesian hierarchical models with continuous spatial and temporally discrete components. A key component of the model is an offset to adjust for bias due to the effects of HIV epidemics. Substantively, there has been a sharp decline in U5MR in the period 1980 - 2014, but large variability in estimated subnational rates remains. A priority for future research is understanding this variability. Temperature, precipitation and a measure of malaria infection prevalence were candidates for inclusion in the covariate model.

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arXiv2017

Modeling water supply networks and gastrointestinal disorder symptoms with CAR models

Background: The direct modeling of water networks is not a common practice in modern epidemiology. While space often serves as a proxy, it can be problematic. There are multiple ways to directly model water networks, but these methods are not straightforward and can be difficult to implement. This study suggests a simple approach for modeling water networks and diseases, and applies this method to a dataset of self-reported gastrointestinal conditions from a questionnaire-based population health survey in central Norway. Method: Our approach is based on a standard conditional autoregressive (CAR) model. An inverse matrix was constructed, with nodes weighted based on the distance to neighboring nodes within the networks. This matrix was then fitted as a generic model. To illustrate its possible use, we utilized data taken from a questionnaire-based population health survey, the HUNT Study, to measure self-reported gastrointestinal complaints. For hypothesis testing, we used the deviance information criterion (DIC) and included variables in a stepwise manner. Results: The full model converged after six hours. We found no relation between the water networks and the health conditions of people whose residences connected to different parts of the network in the geographical area studied. Conclusion: All water network models are simplifications of the real networks. Nevertheless, we suggest a valid approach for distinguishing between the general spatial effect and the water network using a generic model.

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arXiv2015

Does non-stationary spatial data always require non-stationary random fields?

A stationary spatial model is an idealization and we expect that the true dependence structures of physical phenomena are spatially varying, but how should we handle this non-stationarity in practice? We study the challenges involved in applying a flexible non-stationary model to a dataset of annual precipitation in the conterminous US, where exploratory data analysis shows strong evidence of a non-stationary covariance structure. The aim of this paper is to investigate the modelling pipeline once non-stationarity has been detected in spatial data. We show that there is a real danger of over-fitting the model and that careful modelling is necessary in order to properly account for varying second-order structure. In fact, the example shows that sometimes non-stationary Gaussian random fields are not necessary to model non-stationary spatial data.

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arXiv2014

Exploring a New Class of Non-stationary Spatial Gaussian Random Fields with Varying Local Anisotropy

Gaussian random fields (GRFs) constitute an important part of spatial modelling, but can be computationally infeasible for general covariance structures. An efficient approach is to specify GRFs via stochastic partial differential equations (SPDEs) and derive Gaussian Markov random field (GMRF) approximations of the solutions. We consider the construction of a class of non-stationary GRFs with varying local anisotropy, where the local anisotropy is introduced by allowing the coefficients in the SPDE to vary with position. This is done by using a form of diffusion equation driven by Gaussian white noise with a spatially varying diffusion matrix. This allows for the introduction of parameters that control the GRF by parametrizing the diffusion matrix. These parameters and the GRF may be considered to be part of a hierarchical model and the parameters estimated in a Bayesian framework. The results show that the use of an SPDE with non-constant coefficients is a promising way of creating non-stationary spatial GMRFs that allow for physical interpretability of the parameters, although there are several remaining challenges that would need to be solved before these models can be put to general practical use.

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arXiv2013

Non-stationary Spatial Modelling with Applications to Spatial Prediction of Precipitation

A non-stationary spatial Gaussian random field (GRF) is described as the solution of an inhomogeneous stochastic partial differential equation (SPDE), where the covariance structure of the GRF is controlled by the coefficients in the SPDE. This allows for a flexible way to vary the covariance structure, where intuition about the resulting structure can be gained from the local behaviour of the differential equation. Additionally, computations can be done with computationally convenient Gaussian Markov random fields which approximate the true GRFs. The model is applied to a dataset of annual precipitation in the conterminous US. The non-stationary model performs better than a stationary model measured with both CRPS and the logarithmic scoring rule.

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