Spatial correlation structures for detections of individuals in spatial capture-recapture models.

Spatial capture-recapture (SCR) models are commonly used to estimate animal density from surveys on which detectors passively detect animals without physical capture, for example, using camera traps, hair snares, or microphones. An individual is more likely to be recorded by detectors close to its activity center, the centroid of its movement throughout the survey. Existing models to account for this spatial heterogeneity in detection probabilities rely on an assumption of independence between detection records at different detectors conditional on the animals' activity centers, which are treated as latent variables. In this paper, we show that this conditional independence assumption may be violated due to the way animals move around the survey region and encounter detectors, such that additional spatial correlation is almost inevitable. We highlight the links between the well-studied issue of unmodeled temporal heterogeneity in nonspatial capture-recapture and this variety of unmodeled spatial heterogeneity in SCR, showing that the latter causes predictable bias in the same way as the former. We address this by introducing a latent detection field into the model, and illustrate the resulting approach with a simulation study and an application to a camera-trap survey of snow leopards Panthera uncia. Our method is a unifying model for several existing SCR approaches, with special cases including standard SCR, models that account for nonspatial individual heterogeneity, and models with overdispersed detection counts.

Pointless spatial modeling.

The analysis of area-level aggregated summary data is common in many disciplines including epidemiology and the social sciences. Typically, Markov random field spatial models have been employed to acknowledge spatial dependence and allow data-driven smoothing. In the context of an irregular set of areas, these models always have an ad hoc element with respect to the definition of a neighborhood scheme. In this article, we exploit recent theoretical and computational advances to carry out modeling at the continuous spatial level, which induces a spatial model for the discrete areas. This approach also allows reconstruction of the continuous underlying surface, but the interpretation of such surfaces is delicate since it depends on the quality, extent and configuration of the observed data. We focus on models based on stochastic partial differential equations. We also consider the interesting case in which the aggregate data are supplemented with point data. We carry out Bayesian inference and, in the language of generalized linear mixed models, if the link is linear, an efficient implementation of the model is available via integrated nested Laplace approximations. For nonlinear links, we present two approaches: a fully Bayesian implementation using a Hamiltonian Monte Carlo algorithm and an empirical Bayes implementation, that is much faster and is based on Laplace approximations. We examine the properties of the approach using simulation, and then apply the model to the classic Scottish lip cancer data.

A geostatistical state-space model of animal densities for stream networks.

Population dynamics are often correlated in space and time due to correlations in environmental drivers as well as synchrony induced by individual dispersal. Many statistical analyses of populations ignore potential autocorrelations and assume that survey methods (distance and time between samples) eliminate these correlations, allowing samples to be treated independently. If these assumptions are incorrect, results and therefore inference may be biased and uncertainty underestimated. We developed a novel statistical method to account for spatiotemporal correlations within dendritic stream networks, while accounting for imperfect detection in the surveys. Through simulations, we found this model decreased predictive error relative to standard statistical methods when data were spatially correlated based on stream distance and performed similarly when data were not correlated. We found that increasing the number of years surveyed substantially improved the model accuracy when estimating spatial and temporal correlation coefficients, especially from 10 to 15 yr. Increasing the number of survey sites within the network improved the performance of the nonspatial model but only marginally improved the density estimates in the spatiotemporal model. We applied this model to brook trout data from the West Susquehanna Watershed in Pennsylvania collected over 34 yr from 1981 to 2014. We found the model including temporal and spatiotemporal autocorrelation best described young of the year (YOY) and adult density patterns. YOY densities were positively related to forest cover and negatively related to spring temperatures with low temporal autocorrelation and moderately high spatiotemporal correlation. Adult densities were less strongly affected by climatic conditions and less temporally variable than YOY but with similar spatiotemporal correlation and higher temporal autocorrelation.

Expected Number and Height Distribution of Critical Points of Smooth Isotropic Gaussian Random Fields.

We obtain formulae for the expected number and height distribution of critical points of smooth isotropic Gaussian random fields parameterized on Euclidean space or spheres of arbitrary dimension. The results hold in general in the sense that there are no restrictions on the covariance function of the field except for smoothness and isotropy. The results are based on a characterization of the distribution of the Hessian of the Gaussian field by means of the family of Gaussian orthogonally invariant (GOI) matrices, of which the Gaussian orthogonal ensemble (GOE) is a special case. The obtained formulae depend on the covariance function only through a single parameter (Euclidean space) or two parameters (spheres), and include the special boundary case of random Laplacian eigenfunctions.

Cluster-extent based thresholding in fMRI analyses: pitfalls and recommendations.

Cluster-extent based thresholding is currently the most popular method for multiple comparisons correction of statistical maps in neuroimaging studies, due to its high sensitivity to weak and diffuse signals. However, cluster-extent based thresholding provides low spatial specificity; researchers can only infer that there is signal somewhere within a significant cluster and cannot make inferences about the statistical significance of specific locations within the cluster. This poses a particular problem when one uses a liberal cluster-defining primary threshold (i.e., higher p-values), which often produces large clusters spanning multiple anatomical regions. In such cases, it is impossible to reliably infer which anatomical regions show true effects. From a survey of 814 functional magnetic resonance imaging (fMRI) studies published in 2010 and 2011, we show that the use of liberal primary thresholds (e.g., p<.01) is endemic, and that the largest determinant of the primary threshold level is the default option in the software used. We illustrate the problems with liberal primary thresholds using an fMRI dataset from our laboratory (N=33), and present simulations demonstrating the detrimental effects of liberal primary thresholds on false positives, localization, and interpretation of fMRI findings. To avoid these pitfalls, we recommend several analysis and reporting procedures, including 1) setting primary p<.001 as a default lower limit; 2) using more stringent primary thresholds or voxel-wise correction methods for highly powered studies; and 3) adopting reporting practices that make the level of spatial precision transparent to readers. We also suggest alternative and supplementary analysis methods.

Shape-constrained Gaussian process regression for surface reconstruction and multimodal, non-rigid image registration.

We present a new statistical framework for landmark ?>curve-based image registration and surface reconstruction. The proposed method first elastically aligns geometric features (continuous, parameterized curves) to compute local deformations, and then uses a Gaussian random field model to estimate the full deformation vector field as a spatial stochastic process on the entire surface or image domain. The statistical estimation is performed using two different methods: maximum likelihood and Bayesian inference via Markov Chain Monte Carlo sampling. The resulting deformations accurately match corresponding curve regions while also being sufficiently smooth over the entire domain. We present several qualitative and quantitative evaluations of the proposed method on both synthetic and real data. We apply our approach to two different tasks on real data: (1) multimodal medical image registration, and (2) anatomical and pottery surface reconstruction.

A Clipped Gaussian Geo-Classification model for poverty mapping.

The importance of discrete spatial models cannot be overemphasized, especially when measuring living standards. The battery of measurements is generally categorical with nearer geo-referenced observations featuring stronger dependencies. This study presents a Clipped Gaussian Geo-Classification (CGG-C) model for spatially-dependent ordered data, and compares its performance with existing methods to classify household poverty using Ghana living standards survey (GLSS 6) data. Bayesian inference was performed on data sampled by MCMC. Model evaluation was based on measures of classification and prediction accuracy. Spatial associations, given some household features, were quantified, and a poverty classification map for Ghana was developed. Overall, the results of estimation showed that many of the statistically significant covariates were generally strongly related with the ordered response variable. Households at specific locations tended to uniformly experience specific levels of poverty, thus, providing an empirical spatial character of poverty in Ghana. A comparative analysis of validation results showed that the CGG-C model (with 14.2% misclassification rate) outperformed the Cumulative Probit (CP) model with misclassification rate of 17.4%. This approach to poverty analysis is relevant for policy design and the implementation of cost-effective programmes to reduce category and site-specific poverty incidence, and monitor changes in both category and geographical trends thereof.

Assessment of internal refractive index profile of stochastically inhomogeneous nuclear models via analysis of two-dimensional optical scattering patterns.

SIGNIFICANCE: Optical scattering signals obtained from tissue constituents contain a wealth of structural information. Conventional intensity features, however, are mostly dictated by the overall morphology and mean refractive index of these constituents, making it very difficult to exclusively sense internal refractive index fluctuations. AIM: We perform a systematic analysis to elucidate how changes in internal refractive index profile of cell nuclei can best be detected via optical scattering. APPROACH: We construct stochastically inhomogeneous nuclear models and numerically simulate their azimuth-resolved scattering patterns. We then process these two-dimensional patterns with the goal of identifying features that directly point to subnuclear structure. RESULTS: Azimuth-dependent intensity variations over the side scattering range provide significant insights into subnuclear refractive index profile. A particular feature we refer to as contrast ratio is observed to be highly sensitive to the length scale and extent of refractive index fluctuations; further, this feature is not susceptible to changes in the overall size and mean refractive index of nuclei, thereby allowing for selective tracking of subnuclear structure that can be linked to chromatin distribution. CONCLUSIONS: Our analysis will potentially pave the way for scattering-based assessment of chromatin reorganization that is considered to be a key hallmark of precancer progression.

Sharp Convergence of Nonlinear Functionals of a Class of Gaussian Random Fields.

We present a self-contained proof of a uniform bound on multi-point correlations of trigonometric functions of a class of Gaussian random fields. It corresponds to a special case of the general situation considered in Hairer and Xu (large-scale limit of interface fluctuation models. ArXiv e-prints arXiv:1802.08192, 2018), but with improved estimates. As a consequence, we establish convergence of a class of Gaussian fields composite with more general functions. These bounds and convergences are useful ingredients to establish weak universalities of several singular stochastic PDEs.

Monochromaticity of orientation maps in v1 implies minimum variance for hypercolumn size.

In the primary visual cortex of many mammals, the processing of sensory information involves recognizing stimuli orientations. The repartition of preferred orientations of neurons in some areas is remarkable: a repetitive, non-periodic, layout. This repetitive pattern is understood to be fundamental for basic non-local aspects of vision, like the perception of contours, but important questions remain about its development and function. We focus here on Gaussian Random Fields, which provide a good description of the initial stage of orientation map development and, in spite of shortcomings we will recall, a computable framework for discussing general principles underlying the geometry of mature maps. We discuss the relationship between the notion of column spacing and the structure of correlation spectra; we prove formulas for the mean value and variance of column spacing, and we use numerical analysis of exact analytic formulae to study the variance. Referring to studies by Wolf, Geisel, Kaschube, Schnabel, and coworkers, we also show that spectral thinness is not an essential ingredient to obtain a pinwheel density of π, whereas it appears as a signature of Euclidean symmetry. The minimum variance property associated to thin spectra could be useful for information processing, provide optimal modularity for V1 hypercolumns, and be a first step toward a mathematical definition of hypercolumns. A measurement of this property in real maps is in principle possible, and comparison with the results in our paper could help establish the role of our minimum variance hypothesis in the development process.