Geology topics

Jay M. Ver Hoef

Publications and source records attributed to Jay M. Ver Hoef.

8 recordsLinked to original sources

USGS2019

Simultaneous autoregressive (SAR) model

Simultaneous autoregressive (SAR) models are useful for accommodating various forms of dependence among data that have discrete support in a space of interest. These models are often specified hierarchically as mixed-effects regression models with first-moment structure controlled by a conventional linear regression term and second-moment structure induced by correlated random effects. In their general form, SAR models resemble conditional autoregressive (CAR) models, and can be made equivalent but are often parameterized differently. Importantly, SAR models can be specified by simultaneously regressing a discrete spatial process on itself. Thus, they allow one to construct statistical models for processes with directional graphical properties that pertain to data generating mechanisms. Most commonly SAR models have been used to account for structure among data with areal spatial support in applications involving ecology, epidemiology, sociology, and environmental science.

Book chapter↗

USGS2019

On the relationship between conditional (CAR) and simultaneous (SAR) autoregressive models

We clarify relationships between conditional (CAR) and simultaneous (SAR) autoregressive models. We review the literature on this topic and find that it is mostly incomplete. Our main result is that a SAR model can be written as a unique CAR model, and while a CAR model can be written as a SAR model, it is not unique. In fact, we show how any multivariate Gaussian distribution on a finite set of points with a positive-definite covariance matrix can be written as either a CAR or a SAR model. We illustrate how to obtain any number of SAR covariance matrices from a single CAR covariance matrix by using Givens rotation matrices on a simulated example. We also discuss sparseness in the original CAR construction, and for the resulting SAR weights matrix. For a real example, we use crime data in 49 neighborhoods from Columbus, Ohio, and show that a geostatistical model optimizes the likelihood much better than typical first-order CAR models. We then use the implied weights from the geostatistical model to estimate CAR model parameters that provides the best overall optimization.

Spatial Statistics↗

USGS2018

Spatial autoregressive models for statistical inference from ecological data

Ecological data often exhibit spatial pattern, which can be modeled as autocorrelation. Conditional autoregressive (CAR) and simultaneous autoregressive (SAR) models are network‐based models (also known as graphical models) specifically designed to model spatially autocorrelated data based on neighborhood relationships. We identify and discuss six different types of practical ecological inference using CAR and SAR models, including: (1) model selection, (2) spatial regression, (3) estimation of autocorrelation, (4) estimation of other connectivity parameters, (5) spatial prediction, and (6) spatial smoothing. We compare CAR and SAR models, showing their development and connection to partial correlations. Special cases, such as the intrinsic autoregressive model (IAR), are described. Conditional autoregressive and SAR models depend on weight matrices, whose practical development uses neighborhood definition and row‐standardization. Weight matrices can also include ecological covariates and connectivity structures, which we emphasize, but have been rarely used. Trends in harbor seals ( Phoca vitulina ) in southeastern Alaska from 463 polygons, some with missing data, are used to illustrate the six inference types. We develop a variety of weight matrices and CAR and SAR spatial regression models are fit using maximum likelihood and Bayesian methods. Profile likelihood graphs illustrate inference for covariance parameters. The same data set is used for both prediction and smoothing, and the relative merits of each are discussed. We show the nonstationary variances and correlations of a CAR model and demonstrate the effect of row‐standardization. We include several take‐home messages for CAR and SAR models, including (1) choosing between CAR and IAR models, (2) modeling ecological effects in the covariance matrix, (3) the appeal of spatial smoothing, and (4) how to handle isolated neighbors. We highlight several reasons why ecologists will want to make use of autoregressive models, both directly and in hierarchical models, and not only in explicit spatial settings, but also for more general connectivity models.

Ecological Monographs↗

USGS2015

Using spatiotemporal statistical models to estimate animal abundance and infer ecological dynamics from survey counts

Ecologists often fit models to survey data to estimate and explain variation in animal abundance. Such models typically require that animal density remains constant across the landscape where sampling is being conducted, a potentially problematic assumption for animals inhabiting dynamic landscapes or otherwise exhibiting considerable spatiotemporal variation in density. We review several concepts from the burgeoning literature on spatiotemporal statistical models, including the nature of the temporal structure (i.e., descriptive or dynamical) and strategies for dimension reduction to promote computational tractability. We also review several features as they specifically relate to abundance estimation, including boundary conditions, population closure, choice of link function, and extrapolation of predicted relationships to unsampled areas. We then compare a suite of novel and existing spatiotemporal hierarchical models for animal count data that permit animal density to vary over space and time, including formulations motivated by resource selection and allowing for closed populations. We gauge the relative performance (bias, precision, computational demands) of alternative spatiotemporal models when confronted with simulated and real data sets from dynamic animal populations. For the latter, we analyze spotted seal ( Phoca largha ) counts from an aerial survey of the Bering Sea where the quantity and quality of suitable habitat (sea ice) changed dramatically while surveys were being conducted. Simulation analyses suggested that multiple types of spatiotemporal models provide reasonable inference (low positive bias, high precision) about animal abundance, but have potential for overestimating precision. Analysis of spotted seal data indicated that several model formulations, including those based on a log-Gaussian Cox process, had a tendency to overestimate abundance. By contrast, a model that included a population closure assumption and a scale prior on total abundance produced estimates that largely conformed to our a priori expectation. Although care must be taken to tailor models to match the study population and survey data available, we argue that hierarchical spatiotemporal statistical models represent a powerful way forward for estimating abundance and explaining variation in the distribution of dynamical populations.

Ecological Monographs↗

USGS2014

When to be discrete: The importance of time formulation in understanding animal movement

Animal movement is essential to our understanding of population dynamics, animal behavior, and the impacts of global change. Coupled with high-resolution biotelemetry data, exciting new inferences about animal movement have been facilitated by various specifications of contemporary models. These approaches differ, but most share common themes. One key distinction is whether the underlying movement process is conceptualized in discrete or continuous time. This is perhaps the greatest source of confusion among practitioners, both in terms of implementation and biological interpretation. In general, animal movement occurs in continuous time but we observe it at fixed discrete-time intervals. Thus, continuous time is conceptually and theoretically appealing, but in practice it is perhaps more intuitive to interpret movement in discrete intervals. With an emphasis on state-space models, we explore the differences and similarities between continuous and discrete versions of mechanistic movement models, establish some common terminology, and indicate under which circumstances one form might be preferred over another. Counter to the overly simplistic view that discrete- and continuous-time conceptualizations are merely different means to the same end, we present novel mathematical results revealing hitherto unappreciated consequences of model formulation on inferences about animal movement. Notably, the speed and direction of movement are intrinsically linked in current continuous-time random walk formulations, and this can have important implications when interpreting animal behavior. We illustrate these concepts in the context of state-space models with multiple movement behavior states using northern fur seal ( Callorhinus ursinus ) biotelemetry data.

Movement Ecology↗

USGS2014

Applications of spatial statistical network models to stream data

Streams and rivers host a significant portion of Earth's biodiversity and provide important ecosystem services for human populations. Accurate information regarding the status and trends of stream resources is vital for their effective conservation and management. Most statistical techniques applied to data measured on stream networks were developed for terrestrial applications and are not optimized for streams. A new class of spatial statistical model, based on valid covariance structures for stream networks, can be used with many common types of stream data (e.g., water quality attributes, habitat conditions, biological surveys) through application of appropriate distributions (e.g., Gaussian, binomial, Poisson). The spatial statistical network models account for spatial autocorrelation (i.e., nonindependence) among measurements, which allows their application to databases with clustered measurement locations. Large amounts of stream data exist in many areas where spatial statistical analyses could be used to develop novel insights, improve predictions at unsampled sites, and aid in the design of efficient monitoring strategies at relatively low cost. We review the topic of spatial autocorrelation and its effects on statistical inference, demonstrate the use of spatial statistics with stream datasets relevant to common research and management questions, and discuss additional applications and development potential for spatial statistics on stream networks. Free software for implementing the spatial statistical network models has been developed that enables custom applications with many stream databases.

WIREs Water↗

USGS2013

Modelling dendritic ecological networks in space: anintegrated network perspective

Dendritic ecological networks (DENs) are a unique form of ecological networks that exhibit a dendritic network topology (e.g. stream and cave networks or plant architecture). DENs have a dual spatial representation; as points within the network and as points in geographical space. Consequently, some analytical methods used to quantify relationships in other types of ecological networks, or in 2-D space, may be inadequate for studying the influence of structure and connectivity on ecological processes within DENs. We propose a conceptual taxonomy of network analysis methods that account for DEN characteristics to varying degrees and provide a synthesis of the different approaches within the context of stream ecology. Within this context, we summarise the key innovations of a new family of spatial statistical models that describe spatial relationships in DENs. Finally, we discuss how different network analyses may be combined to address more complex and novel research questions. While our main focus is streams, the taxonomy of network analyses is also relevant anywhere spatial patterns in both network and 2-D space can be used to explore the influence of multi-scale processes on biota and their habitat (e.g. plant morphology and pest infestation, or preferential migration along stream or road corridors).

Ecology Letters↗

USGS2001

Serologic survey for canine coronavirus in wolves from Alaska

Wolves ( Canis lupus ) were captured in three areas of Interior Alaska (USA). Four hundred twenty-five sera were tested for evidence of exposure to canine coronavirus by means of an indirect fluorescent antibody procedure. Serum antibody prevalence averaged 70% (167/240) during the spring collection period and 25% (46/185) during the autumn collection period. Prevalence was 0% (0/42) in the autumn pup cohort (age 4-5 mo), and 60% (58/97) in the spring pup cohort (age 9-10 mo). Prevalence was lowest in the Eastern Interior study area. A statistical model indicates that prevalence increased slightly each year in all three study areas. These results indicate that transmission occurs primarily during the winter months, antibody decay is quite rapid, and reexposure during the summer is rare.

Alaska↗