Geir-Arne Fuglstad

Constructing Priors that Penalize the Complexity of Gaussian Random Fields

ABSTRACT 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 penalized 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 penalizes complexity by shrinking the range toward infinity and the marginal variance toward 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 nonstationary GRF parameterized 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 conservative estimates of nonstationarity and improved predictive performance over the stationary model. Supplementary materials for this article are available online.

Assessing comorbidity and correlates of wasting and stunting among children in Somalia using cross-sectional household surveys: 2007 to 2010.

Objective Wasting and stunting may occur together at the individual child level; however, their shared geographic distribution and correlates remain unexplored. Understanding shared and separate correlates may inform interventions. We aimed to assess the spatial codistribution of wasting, stunting and underweight and investigate their shared correlates among children aged 6–59 months in Somalia. Setting Cross-sectional nutritional assessments surveys were conducted using structured interviews among communities in Somalia biannually from 2007 to 2010. A two-stage cluster sampling methodology was used to select children aged 6–59 months from households across three livelihood zones (pastoral, agropastoral and riverine). Using these data and environmental covariates, we implemented a multivariate spatial technique to estimate the codistribution and divergence of the risks and correlates of wasting and stunting at the 1×1 km spatial resolution. Participants 73 778 children aged 6–59 months from 1066 survey clusters in Somalia. Results Observed pairwise child level empirical correlations were 0.30, 0.70 and 0.73 between weight-for-height and height-for-age; height-for-age and weight-for-age, and weight-for-height and weight-for-age, respectively. Access to foods with high protein content and vegetation cover, a proxy of rainfall or drought, were associated with lower risk of wasting and stunting. Age, gender, illness, access to carbohydrates and temperature were correlates of all three indicators. The spatial codistribution was highest between stunting and underweight with relative risk values ranging between 0.15 and 6.20, followed by wasting and underweight (range: 0.18–5.18) and lowest between wasting and stunting (range: 0.26–4.32). Conclusions The determinants of wasting and stunting are largely shared, but their correlation is relatively variable in space. Significant hotspots of different forms of malnutrition occurred in the South Central regions of the country. Although nutrition response in Somalia has traditionally focused on wasting rather than stunting, integrated programming and interventions can effectively target both conditions to alleviate common risk factors.

Landscape relatedness : detecting contemporary fine-scale spatial structure in wild populations

ContextMethods for detecting contemporary, fine-scale population genetic structure in continuous populations are scarce. Yet such methods are vital for ecological and conservation studies, particularly under a changing landscape.ObjectivesHere we present a novel, spatially explicit method that we call landscape relatedness (LandRel). With this method, we aim to detect contemporary, fine-scale population structure that is sensitive to spatial and temporal changes in the landscape.MethodsWe interpolate spatially determined relatedness values based on SNP genotypes across the landscape. Interpolations are calculated using the Bayesian inference approach integrated nested Laplace approximation. We empirically tested this method on a continuous population of brown bears (Ursus arctos) spanning two counties in Sweden.ResultsTwo areas were identified as differentiated from the remaining population. Further analysis suggests that inbreeding has occurred in at least one of these areas.ConclusionsLandRel enabled us to identify previously unknown fine-scale structuring in the population. These results will help direct future research efforts, conservation action and aid in the management of the Scandinavian brown bear population. LandRel thus offers an approach for detecting subtle population structure with a focus on contemporary, fine-scale analysis of continuous populations.

Estimating under-five mortality in space and time in a developing world context

Accurate estimates of the under-five mortality rate in a developing world context are a key barometer of the health of a nation. This paper describes a new model to analyze survey data on mortality in this context. We are interested in both spatial and temporal description, that is wishing to estimate under-five mortality rate across regions and years and to investigate the association between the under-five mortality rate 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 the Demographic and Health Surveys, which use stratified cluster sampling. We use a binomial likelihood with fixed effects for the urban/rural strata and random effects for the clustering to account for the complex survey design. Smoothing is carried out 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 Kenya in the under-five mortality rate in the period 1980–2014, but large variability in estimated subnational rates remains. A priority for future research is understanding this variability. In exploratory work, we examine whether a variety of spatial covariate surfaces can explain the variability in under-five mortality rate. Temperature, precipitation, a measure of malaria infection prevalence, and a measure of nearness to cities were candidates for inclusion in the covariate model, but the interplay between space, time, and covariates is complex.