GEOSTATISTICAL INFERENCE UNDER PREFERENTIAL SAMPLING

Geostatistics involves the fitting of spatially continuous models to spatially discrete data (Chil`es and Delfiner, 1999). Preferential sampling arises when the process that determines the data-locations and the process being modelled are stochastically dependent. Conventional geostatistical methods assume, if only implicitly, that sampling is non-preferential. However, these methods are often used in situations where sampling is likely to be preferential. For example, in mineral exploration samples may be concentrated in areas thought likely to yield high-grade ore. We give a general expression for the likelihood function of preferentially sampled geostatistical data and describe how this can be evaluated approximately using Monte Carlo methods. We present a model for preferential sampling, and demonstrate through simulated examples that ignoring preferential sampling can lead to seriously misleading inferences. We describe an application of the model to a set of bio-monitoring data from Galicia, northern Spain, in which making allowance for preferential sampling materially changes the inferences.

Spatial heterogeneity of soil nutrients and plant species in herb-dominated communities of contrasting land use

Recent interest in spatial pattern in terrestrial ecosystems has come from an awareness of theintimate relationship between spatial heterogeneity of soil resources and maintenance of plant species diversity. Soil and vegetation can vary spatially inresponse to several state factors of the system. In this study, we examined fine-scale spatial variability of soil nutrients and vascular plant species in contrasting herb-dominated communities (a pasture and an oldfield) to determine degree of spatial dependenceamong soil variables and plant community characteristics within these communities by sampling at 1-m intervals. Each site was divided into 25 1-m 2 plots. Mineral soil was sampled (2-cm diameter, 5-cm depth) from each of four 0.25-m2 quarters and combined into a single composite sample per plot. Soil organic matter was measured as loss-on-ignition. Extractable NH4 and NO3 were determined before and after laboratory incubation to determine potential net N mineralization and nitrification. Cations were analyzed using inductively coupled plasma emission spectrometry. Vegetation was assessed using estimated percent cover. Most soiland plant variables exhibited sharp contrasts betweenpasture and old-field sites, with the old field having significantly higher net N mineralization/nitrification, pH, Ca, Mg, Al, plant cover, and species diversity, richness, and evenness. Multiple regressions revealedthat all plant variables (species diversity, richness,evenness, and cover) were significantly related to soil characteristics (available nitrogen, organic matter,moisture, pH, Ca, and Mg) in the pasture; in the old field only cover was significantly related to soil characteristics (organic matter and moisture). Both sites contrasted sharply with respect to spatial pattern of soil variables, with the old field exhibiting a higher degree of spatial dependence. These results demonstrate that land-use practices can exert profound influence on spatial heterogeneity of both soil properties and vegetation in herb-dominated communities.

A BAYESIAN HIERARCHICAL FRAMEWORK FOR SPATIAL MODELING OF fMRI DATA

Functional neuroimaging techniques enable investigations into the neural basis of human cognition, emotions, and behaviors. In practice, applications of functional magnetic resonance imaging (fMRI) have provided novel insights into the neuropathophysiology of major psychiatric,neurological, and substance abuse disorders, as well as into the neural responses to their treatments. Modern activation studies often compare localized task-induced changes in brain activity between experimental groups. One may also extend voxel-level analyses by simultaneously considering the ensemble of voxels constituting an anatomically defined region of interest (ROI) or by considering means or quantiles of the ROI. In this work we present a Bayesian extension of voxel-level analyses that offers several notable benefits. First, it combines whole-brain voxel-by-voxel modeling and ROI analyses within a unified framework. Secondly, an unstructured variance/covariance for regional mean parameters allows for the study of inter-regional functional connectivity, provided enough subjects are available to allow for accurate estimation. Finally, an exchangeable correlation structure within regions allows for the consideration of intra-regional functional connectivity. We perform estimation for our model using Markov Chain Monte Carlo (MCMC) techniques implemented via Gibbs sampling which, despite the high throughput nature of the data, can be executed quickly (less than 30 minutes). We apply our Bayesian hierarchical model to two novel fMRI data sets: one considering inhibitory control in cocaine-dependent men and the second considering verbal memory in subjects at high risk for Alzheimer’s disease. The unifying hierarchical model presented in this manuscript is shown to enhance the interpretation content of these data sets.