Dynamic multi-resolution spatial models

Data from remote-sensing platforms play an important role in monitoring environmental processes, such as the distribution of stratospheric ozone. Remote-sense data are typically spatial, temporal, and massive. Existing prediction methods such as kriging are computationally infeasible. The multi-resolution spatial model (MRSM) captures nonstationary spatial dependence and produces fast optimal estimates using a change-of-resolution Kalman filter. However, past data can provide valuable information about the current status of the process being investigated. In this article, we incorporate the temporal dependence into the process by developing a dynamic MRSM. An application of the dynamic MRSM to a month of daily total column ozone data is presented, and on a given day the results of posterior inference are compared to those for the spatial-only MRSM. It is apparent that there are advantages to using the dynamic MRSM in regions where data are missing, such as when a whole swath of satellite data is missing.     

An application of Bayesian variable selection to spatial concurrent linear models

Spatial concurrent linear models, in which the model coefficients are spatial processes varying at a local level, are flexible and useful tools for analyzing spatial data. One approach places stationary Gaussian process priors on the spatial processes, but in applications the data may display strong nonstationary patterns. In this article, we propose a Bayesian variable selection approach based on wavelet tools to address this problem. The proposed approach does not involve any stationarity assumptions on the priors, and instead we impose a mixture prior directly on each wavelet coefficient. We introduce an option to control the priors such that high resolution coefficients are more likely to be zero. Computationally efficient MCMC procedures are provided to address posterior sampling, and uncertainty in the estimation is assessed through posterior means and standard deviations. Examples based on simulated data demonstrate the estimation accuracy and advantages of the proposed method. We also illustrate the performance of the proposed method for real data obtained through remote sensing.     

Hierarchical Bayesian Spatial Models for Multispecies Conservation Planning and Monitoring

Abstract: Biologists who develop and apply habitat models are often familiar with the statistical challenges posed by their data's spatial structure but are unsure of whether the use of complex spatial models will increase the utility of model results in planning. We compared the relative performance of nonspatial and hierarchical Bayesian spatial models for three vertebrate and invertebrate taxa of conservation concern (Church's sideband snails [Monadenia churchi], red tree voles [Arborimus longicaudus], and Pacific fishers [Martes pennanti pacifica]) that provide examples of a range of distributional extents and dispersal abilities. We used presence–absence data derived from regional monitoring programs to develop models with both landscape and site‐level environmental covariates. We used Markov chain Monte Carlo algorithms and a conditional autoregressive or intrinsic conditional autoregressive model framework to fit spatial models. The fit of Bayesian spatial models was between 35 and 55% better than the fit of nonspatial analogue models. Bayesian spatial models outperformed analogous models developed with maximum entropy (Maxent) methods. Although the best spatial and nonspatial models included similar environmental variables, spatial models provided estimates of residual spatial effects that suggested how ecological processes might structure distribution patterns. Spatial models built from presence–absence data improved fit most for localized endemic species with ranges constrained by poorly known biogeographic factors and for widely distributed species suspected to be strongly affected by unmeasured environmental variables or population processes. By treating spatial effects as a variable of interest rather than a nuisance, hierarchical Bayesian spatial models, especially when they are based on a common broad‐scale spatial lattice (here the national Forest Inventory and Analysis grid of 24 km² hexagons), can increase the relevance of habitat models to multispecies conservation planning.     

Optimal spatial sampling schemes for environmental surveys

A practical problem in spatial statistics is that of constructing spatial sampling designs for environmental monitoring network. This paper presents a fractal-based criterion for the construction of coverage designs to optimize the location of sampling points. The algorithm does not depend on the covariance structure of the process and provides desirable results for situations in which a poor prior knowledge is available. The statistical characteristics of the method are explored by a simulation study while a design exercise concerning the Pescara area monitoring network is used to demonstrate potential designs under realistic assumptions.     

Modeling species-habitat relationships with spatially autocorrelated observation data.

Spatial autocorrelation in wildlife observation data arises when extrinsic environmental processes and patterns that influence the spatial distribution of wildlife are themselves spatially structured, or when species are subject to intrinsic population processes, causing contagion or dispersion effects. Territoriality, Allee effects, dispersal limitations, and social clustering are examples of intrinsic processes. Both forms of autocorrelation can violate the assumptions of generalized linear regression models, resulting in biased estimation of model coefficients and diminished predictive performance. Such consequences may be avoided for extrinsic autocorrelation when autocorrelated environmental variables are available for use as model covariates, whereas intrinsic spatial autocorrelation requires an alternative modeling approach. The autologistic model provides an approach suited to the binary observations often obtained in wildlife surveys, but its performance has not been tested across widely varying sampling intensities or strengths of intrinsic spatial structure. Here we use simulated data to test the autologistic model under a range of sampling conditions. The autologistic model obtains better fits and substantially better predictive performance than the standard logistic regression model over the full range of sampling designs and intensities tested. We provide a simple Bayesian implementation of the autologistic model, which until now has not been achieved with standard statistical software alone. A step-by-step procedure is given for characterizing and modeling spatial autocorrelation in binary observation data, along with computer code for fitting autologistic models in WinBUGS, a freeware Bayesian analysis package. This approach avoids normal approximations to the pseudo-likelihood, in contrast to previous Bayesian applications of the autologistic model. We provide a sample application of the autologistic model, fitted to survey data for a gliding marsupial in southeastern Australia.     

Hierarchical Bayesian space-time models

Space-time data are ubiquitous in the environmental sciences. Often, as is the case with atmo- spheric and oceanographic processes, these data contain many different scales of spatial and temporal variability. Such data are often non-stationary in space and time and may involve many observation/prediction locations. These factors can limit the effectiveness of traditional space- time statistical models and methods. In this article, we propose the use of hierarchical space-time models to achieve more flexible models and methods for the analysis of environmental data distributed in space and time. The first stage of the hierarchical model specifies a measurement- error process for the observational data in terms of some 'state' process. The second stage allows for site-specific time series models for this state variable. This stage includes large-scale (e.g. seasonal) variability plus a space-time dynamic process for the anomalies'. Much of our interest is with this anomaly proc ess. In the third stage, the parameters of these time series models, which are distributed in space, are themselves given a joint distribution with spatial dependence (Markov random fields). The Bayesian formulation is completed in the last two stages by speci- fying priors on parameters. We implement the model in a Markov chain Monte Carlo framework and apply it to an atmospheric data set of monthly maximum temperature.     

Model-based combination of spatial information for stream networks

Evolutionary improvements in Geographic Information Systems (GIS) now routinely allow the management and mapping of spatial-temporal information. In response, the development of statistical models to combine information of different types and spatial support is of vital importance to environmental science. In this paper we develop a hierarchical spatial statistical model for environmental indicators of stream and river systems in the United States Mid-Atlantic Region by combining information from separate monitoring surveys, available contextual information on hydrologic units and remote sensing information. These models are used to estimate the indicators throughout the riverine system based on information from multiple sources and aggregate scales. The analysis is based on information underlying the Landscape Atlas of the mid-Atlantic region produced by the US Environmental Monitoring and Assessment Program (EMAP). We also combine information from two overlapping separate monitoring surveys, the EMAP Stream and River Survey and the Maryland Biological Streams Survey. We present a general framework for comparative distributional analysis based on the concept of a relative spatial distribution. As an application, the spatial model is used to predict spatial distributions and relative spatial distributions for a watershed.     

The Use of Bayesian Model Averaging to Better Represent Uncertainty in Ecological Models

Abstract:   In conservation biology, uncertainty about the choice of a statistical model is rarely considered. Model-selection uncertainty occurs whenever one model is chosen over plausible alternative models to represent understanding about a process and to make predictions about future observations. The standard approach to representing prediction uncertainty involves the calculation of prediction (or confidence) intervals that incorporate uncertainty about parameter estimates contingent on the choice of a "best" model chosen to represent truth. However, this approach to prediction based on statistical models tends to ignore model-selection uncertainty, resulting in overconfident predictions. Bayesian model averaging (BMA) has been promoted in a range of disciplines as a simple means of incorporating model-selection uncertainty into statistical inference and prediction. Bayesian model averaging also provides a formal framework for incorporating prior knowledge about the process being modeled. We provide an example of the application of BMA in modeling and predicting the spatial distribution of an arboreal marsupial in the Eden region of southeastern Australia. Other approaches to estimating prediction uncertainty are discussed.     

Space-time statistics for environmental and agricultural related phenomena

This paper presents an overview of space-time statistical procedures to analyse agricultural and environmental related phenomena. It starts with an application on root-rot development in cotton. Dependence modelling in space and time is done with the space-time variogram. Various kriging interpolators are presented for making predictions in space and time. Simulated annealing is used to design an optimal monitoring network for estimation of space-time variograms. In the application no clear indication was found for anisotropy, although strong evidence exists that the disease not only proceeds within rows but also jumps between rows. The optimal sampling scheme showed a spatial clustering of observations at the first and the last monitoring day and less observations at intermediate times.     

Delimiting synchronous populations from monitoring data

We propose to investigate spatial synchrony in population dynamics from monitoring data. We develop a statistical procedure to delineate populations of sites with synchronous dynamics from short time series. The procedure relies on a new norm, the synchronous total variation norm, which promotes synchrony in the estimation of the sites dynamics. The method is tested on some synthetic data sets and is applied on data from the French breeding bird monitoring program.     

Sampling variability and estimates of density dependence: a composite-likelihood approach

It is well known that sampling variability, if not properly taken into account, affects various ecologically important analyses. Statistical inference for stochastic population dynamics models is difficult when, in addition to the process error, there is also sampling error. The standard maximum-likelihood approach suffers from large computational burden. In this paper, I discuss an application of the composite-likelihood method for estimation of the parameters of the Gompertz model in the presence of sampling variability. The main advantage of the method of composite likelihood is that it reduces the computational burden substantially with little loss of statistical efficiency. Missing observations are a common problem with many ecological time series. The method of composite likelihood can accommodate missing observations in a straightforward fashion. Environmental conditions also affect the parameters of stochastic population dynamics models. This method is shown to handle such nonstationary population dynamics processes as well. Many ecological time series are short, and statistical inferences based on such short time series tend to be less precise. However, spatial replications of short time series provide an opportunity to increase the effective sample size. Application of likelihood-based methods for spatial time-series data for population dynamics models is computationally prohibitive. The method of composite likelihood is shown to have significantly less computational burden, making it possible to analyze large spatial time-series data. After discussing the methodology in general terms, I illustrate its use by analyzing a time series of counts of American Redstart (Setophaga ruticilla) from the Breeding Bird Survey data, San Joaquin kit fox (Vulpes macrotis mutica) population abundance data, and spatial time series of Bull trout (Salvelinus confluentus) redds count data.     

Multimethod,multistate Bayesian hierarchical modeling approach for use in regional monitoring of wolves

In many cases, the first step in large‐carnivore management is to obtain objective, reliable, and cost‐effective estimates of population parameters through procedures that are reproducible over time. However, monitoring predators over large areas is difficult, and the data have a high level of uncertainty. We devised a practical multimethod and multistate modeling approach based on Bayesian hierarchical‐site‐occupancy models that combined multiple survey methods to estimate different population states for use in monitoring large predators at a regional scale. We used wolves (Canis lupus) as our model species and generated reliable estimates of the number of sites with wolf reproduction (presence of pups). We used 2 wolf data sets from Spain (Western Galicia in 2013 and Asturias in 2004) to test the approach. Based on howling surveys, the naïve estimation (i.e., estimate based only on observations) of the number of sites with reproduction was 9 and 25 sites in Western Galicia and Asturias, respectively. Our model showed 33.4 (SD 9.6) and 34.4 (3.9) sites with wolf reproduction, respectively. The number of occupied sites with wolf reproduction was 0.67 (SD 0.19) and 0.76 (0.11), respectively. This approach can be used to design more cost‐effective monitoring programs (i.e., to define the sampling effort needed per site). Our approach should inspire well‐coordinated surveys across multiple administrative borders and populations and lead to improved decision making for management of large carnivores on a landscape level. The use of this Bayesian framework provides a simple way to visualize the degree of uncertainty around population‐parameter estimates and thus provides managers and stakeholders an intuitive approach to interpreting monitoring results. Our approach can be widely applied to large spatial scales in wildlife monitoring where detection probabilities differ between population states and where several methods are being used to estimate different population parameters.     

Efficient species-level monitoring at the landscape scale

Monitoring the population trends of multiple animal species at a landscape scale is prohibitively expensive. However, advances in survey design, statistical methods, and the ability to estimate species presence on the basis of detection-nondetection data have greatly increased the feasibility of species-level monitoring. For example, recent advances in monitoring make use of detection-nondetection data that are relatively inexpensive to acquire, historical survey data, and new techniques in genetic evaluation. The ability to use indirect measures of presence for some species greatly increases monitoring efficiency and reduces survey costs. After adjusting for false absences, the proportion of sample units in a landscape where a species is detected (occupancy) is a logical state variable to monitor. Occupancy monitoring can be based on real-time observation of a species at a survey site or on evidence that the species was at the survey location sometime in the recent past. Temporal and spatial patterns in occupancy data are related to changes in animal abundance and provide insights into the probability of a species' persistence. However, even with the efficiencies gained when occupancy is the monitored state variable, the task of species-level monitoring remains daunting due to the large number of species. We propose that a small number of species be monitored on the basis of specific management objectives, their functional role in an ecosystem, their sensitivity to environmental changes likely to occur in the area, or their conservation importance.     

Model based grouping of species across environmental gradients

We present a novel approach to the statistical analysis and prediction of multispecies data. The approach allows the simultaneous grouping and quantification of multiple species’ responses to environmental gradients. The underlying statistical model is a finite mixture model, where mixing is performed over the individual species’ responses to environmental gradients. Species with similar responses are grouped with minimal information loss. We term these groups species archetypes. Each species archetype has an associated GLM that can be used to predict distributions with appropriate measures of uncertainty. Initially, we illustrate the concept and method using artificial data and then with application to real data comprising 200 species from the Great Barrier Reef (GBR) lagoon on 13 oceanographic and geological gradients from 12°S to 24°S. The 200 species from the GBR are well represented by 15 species archetypes. The model is interpreted through maps of the probability of presence for a fine scale set of locations throughout the study area. Maps of uncertainty are also produced to provide statistical context. The presence of each species archetype was strongly influenced by oceanographic gradients, principally temperature, oxygen and salinity. The number of species in each group ranged from 4 to 34. The method has potential application to the analysis of multispecies distribution patterns and for multispecies management.     

External drift kriging of NOx concentrations with dispersion model output in a reduced air quality monitoring network

In the mid nineteen eighties the Dutch NO_x air quality monitoring network was reduced from 73 to 32 rural and city background stations, leading to higher spatial uncertainties. In this study, several other sources of information are being used to help reduce uncertainties in parameter estimation and spatial mapping. For parameter estimation, we used Bayesian inference. For mapping, we used kriging with external drift (KED) including secondary information from a dispersion model. The methods were applied to atmospheric NO_x concentrations on rural and urban scales. We compared Bayesian estimation with restricted maximum likelihood estimation and KED with universal kriging. As a reference we also included ordinary least squares (OLS). Comparison of several parameter estimation and spatial interpolation methods was done by cross-validation. Bayesian analysis resulted in an error reduction of 10 to 20% as compared to restricted maximum likelihood, whereas KED resulted in an error reduction of 50% as compared to universal kriging. Where observations were sparse, the predictions were substantially improved by inclusion of the dispersion model output and by using available prior information. No major improvement was observed as compared to OLS, the cause presumably being that much good information is contained in the dispersion model output, so that no additional spatial residual random field is required to explain the data. In all, we conclude that reduction in the monitoring network could be compensated by modern geostatistical methods, and that a traditional simple statistical model is of an almost equal quality.

Abfallwirtschaftskonzept im Rahmen eines Integrierten Umweltmanagementsystems

Economic regulations on recycling and respective waste disposal legislation will increasingly demand the realization of new waste management concepts. They do not stem from a ministerial goal in itself, but instead offen the enterprizes a chance to develop their own waste disposal strategies with a goal toward the future. In the course of an Intra-company analysis, this waste disposal concept must take the operative organization, the relevant processes and manufacturing techniques, the accumulation of waste in the cost centers as well as the waste disposal and utilization into consideration. Fundamental principles include the environmental regulations applicable to the enterprize in the form of both federal decress and injunctions. An environmental examination report demonstrates the methodical possiblities for stock-taking and makes it possible to identify the measures necessary for improving the operational waste disposal situation. The mandatory data acquisition and a feasible waste monitoring network can be used in the course of environmental management system for making an expert opinion by an independent, reputable environmental verifier.     

Detecting and Modeling Spatial and Temporal Dependence in Conservation Biology

Abstract: Due to the structuring forces and large-scale physical processes that shape our biosphere, we often find that environmental and ecological data are either spatially or temporally—or both spatially and temporally—dependent. When these data are analyzed, statistical techniques and models are frequently applied that were developed for independent data. We describe some of the detrimental consequences, such as inefficient parameter estimators, biased hypothesis test results, and inaccurate predictions, of ignoring spatial and temporal data dependencies, and we cite an example of adverse statistical results occurring when spatial dependencies were disregarded. We also discuss and recommend available techniques used to detect and model spatial and temporal dependence, including variograms, covariograms, autocorrelation and partial autocorrelation plots, geostatistical techniques, Gaussian autoregressive models, K functions, and ARIMA models, in environmental and ecological research to avoid the aforementioned difficulties.     

A multivariate prediction of spatial process with non-stationary covariance for Kuwait non-methane hydrocarbons levels

Predicting unmeasured realizations of multivariate spatial process responses is a fundamental problem in environmetrics. The study of levels of air pollutants is important for understanding and improving air quality in major urban areas. This research aims to handle the prediction in a Bayesian framework for non-methane hydrocarbons NMHC pollutant for the State of Kuwait where records of six monitor stations located in different sites are observed at successive time points. Our objective is to study the distribution level of NMHC with respect to time and metreological parameters and space and use this distribution to predict the concentration of NMHC in other sites of Kuwait using the minimum amount of data (reducing the cost). We will implement a hierarchical Bayesian approach assuming Gaussian random field technique that allows us to pool the data from different sites in predicting the exposure of the non-methane hydrocarbons in different regions of Kuwait.