bluuebunny/crossref_metadata_2025 huggingface dataset:
Generalized Additive Models
Authors: Grego John M.
Published: January 2013

Generalized additive models replace the linear predictor in a linear model or generalized linear model framework with an additive predictor composed of nonparametric or semiparametric functions of the explanatory variables. Similarly to generalized linear models, the predictor is linear in the link function of the response mean, and the response variable can have a non normal distribution. The last decade has seen interesting new approaches to estimation of generalized additive models, and the development of a mixed effects framework for these models.
Generalized Estimating Equations
Authors: Darnell Ross
Published: January 2013

Interdependence is a characteristic feature of many environmental processes. However, the complexities for statistical analysis introduced by such interdependence have hampered the progress of environmental science. Why this is so can be understood by considering the workhorse of standard statistical analysis, thegeneralized linear model(GLM). A typical GLM divides variation in some measure into a systematic part and a random part. Typically substantive theory guides the construction of the model for the systematic part. For the random part, although some guidance may be obtained from knowledge of the distributional consequences of a simple and plausiblestochastic processthat might be responsible for this variation, and from experience gained with other comparable data, we rarely have complete confidence in our choice of distribution. In the case of spatial, longitudinal and multivariate outcomes the choice is among multivariate distributions since we need to describe the association across outcomes as well as within outcome variability. This becomes especially difficult for problems where the multivariate normal distribution is not a suitable choice for the random part of the model, since the available alternative distributions lack flexibility. Under these circumstances it is often helpful to use generalized estimating equations (GEEs). The GEE approach, while making weaker distributional assumptions than that required for a fully parametric linear model, maintains the properties of consistency and asymptotic normality of parameter estimates.
Global Environmental Epidemiology Network (
WHO
)
Authors: El‐shaarawi Abdel H.
Published: January 2013

GEENET aims to increase the national capacity of developing countries to secure environmental health by strengthening education, training, and applied research in environmental epidemiology.
Groundwater Monitoring and Assessment
Authors: Cai Zuansi , Thornton Steven F. , Lerner David N.
Published: January 2013

Groundwater is an important component of water supplies in most countries. It exists in aquifers under unsaturated and saturated conditions. The flow of groundwater is primarily controlled by the aquifer physical properties and hydraulic pressure gradients. The transport of solutes dissolved in groundwater is influenced by a combination of physical, chemical, and biological processes. Hydrodynamic dispersion is an important transport process, which influences the fate of contaminants in groundwater particularly the biodegradation of organic compounds. The quantitative analysis of groundwater resources can be completed using water balances and numerical modelling tools. Groundwater chemistry is controlled mainly by the aquifer composition but is vulnerable to contamination by many naturally occurring processes and human activities from point and diffuse sources. Modeling tools are generally used to simulate groundwater flow and solute transport in aquifers. Statistical analysis using Monte Carlo methods is often used to describe the uncertainty in parameters included in groundwater modeling studies. Groundwater quality assessment must be undertaken using monitoring well designs and sampling methods, which provide representative samples for analysis. This objective is important when using groundwater chemistry data to interpret the performance of in situ groundwater remediation concepts such as monitored natural attenuation.
Hansen‐Hurwitz Estimator
Authors: Christman Mary C.
Published: January 2013

The Hansen–Hurwitz estimator is a design‐based procedure for estimating population totals or means when sampling is with replacement. Its strength lies in its approach incorporating unequal sampling probabilities to provide an estimator that is more precise than many alternative estimators. It is commonly used for cluster sampling, stratified probability sampling, and adaptive sampling designs. A very common use of the estimator is for cluster sampling designs in which clusters are selected proportional to size.
Disease Mapping, Hierarchical Models For
Authors: Waller Lance A.
Published: January 2013

Hierarchical models for disease mapping.

Hierarchical models provide a convenient framework to combine information across multiple observational units. Such models are particularly convenient for small area estimation of disease rates to improve statistical precision of estimates associated with small local sample sizes. We review the basic framework of model‐based approaches for combining information across small administrative units through the use of random effects. Varying definitions of the random effects distribution allows one to combine information from all locations, neighboring locations, or a combination of both.
Hydrological Extremes
Authors: Katz Richard W.
Published: January 2013

An accurate estimation of the probability of occurrence of an extreme hydrological event is often required for the effective development and management of water resources. Examples include characterizing extreme rainfall event magnitudes to predict urban runoff, determining river flow magnitudes to design a culvert or bridge opening at a road crossing, and determining the likely severity of a drought event during the design life of a water supply system. In each of these examples, an understanding of the hydrological response of a watershed is essential in order to obtain a reliable estimate of the relationship between extreme hydrological event magnitudes and the probability of these events occurring. The role of the statistical theory of extreme values is emphasized.
Kronecker Product
Authors: Hallin Marc
Published: January 2013

The Kronecker product is a classical and an extremely convenient tool in multivariate analysis. We briefly define this product, and describe some of its main algebraic properties. We also briefly review the role of Kronecker products in the traditional assumption of separability of covariance functions in spatiotemporal models.
Conditional Entropy Profiles
Authors: Patil G.P.
Published: January 2013

When a landscape is represented by multiple landcover types, the challenge is to define a measurement of landscape fragmentation that can be applied to any defined geographic area. Such a measurement would ideally allow quantitative determination for when a landscape pattern has changed significantly, either within the same geographic extent over time, or among different locations within a similar ecoregion. Of interest is ecosystem identification, such as may be delineated by watershed boundaries close to a critical point of into a different, possibly degraded, ecosystem where the landscape matrix has become developed land. Such a measurement of landscape fragmentation can then be a primary component of an ecosystem risk assessment.
Line‐Transect Sampling, New Approaches
Authors: Melville Gavin , Cowling Ann
Published: January 2013

The widespread use of line‐transect surveys to estimate the abundance of ecological populations has seen a number of new developments in methodology. For example, nonparametric approaches have been introduced to estimate detection probabilities for objects in the target population. Also line‐transect data have been increasingly used to study a range of spatial models that may be of interest to ecologists. The treatment of measurement errors and recent sampling innovations such as sequential and adaptive sampling have increased the flexibility of the line‐transect approach and provided more robust estimates of abundance. Debate over an appropriate frame of inference, specifically design‐based versus model‐based, is a motivation for alternative estimation techniques such as mark–recapture and the use of Bayesian statistics. This article summarizes some of the recent developments in line‐transect sampling.
Markov Chain Monte Carlo (MCMC)
Authors: Barnes Katherine
Published: January 2013

Realistic statistical models often give rise to probability distributions that are computationally difficult to use for inference. Fortunately, we now have a collection of algorithms, known as Markov chain Monte Carlo (MCMC), that has brought many of these models within our computational reach. MCMC is a simulation technique that allows one to make (approximate) draws from complex, high dimensional probability distributions. Over the last 20 years a staggering amount of research has been done on both the theoretical and applied aspects of MCMC. This article does not intend to be a complete overview of MCMC but only hopes to get the reader started in the right direction. To this end, this article begins with a general description of the types of problems that necessitate the use of MCMC. It then introduces the fundamental algorithms and addresses some general implementation issues. Discussion of the Markov chain theory underpinning MCMC algorithms has intentionally been avoided.
Modeling, Environmental
Authors: Solow Andrew R.
Published: January 2013

In discussing environmental models, it is useful to distinguish between process‐based or mechanistic models and phenomenological or empirical models. Although the distinction is not always clear, mechanistic models are based on a scientific theory about the underlying environmental processes, whereas empirical models are based on observation alone. This article focuses on statistical analysis under mechanistic environmental models. This is not to imply that empirical environmental models are less interesting or less useful. Rather, it is because empirical environmental models are, from a statistical perspective, no different from empirical models in other fields. While the methods of statistical analysis under mechanistic environmental models are certainly not unique, such models tend to share certain characteristics that determine in part the kind of statistical issues that arise, and even the kind of statistical methods used to address these issues.
Morbidity and Mortality
Authors: Danaei Goodarz , Hernán Miguel A.
Published: January 2013

The frequency of overall or cause‐specific morbidity and mortality is used in national and global statistics to characterize the health status of a population. Summary measures of population health combine the frequency of morbidity and mortality into one measure of burden of disease using disability weights or quality of life measures.
M
ultistage
D
esign
Authors: Christman Mary C.
Published: January 2013

Multistage sampling designs are probability based sampling strategies for obtaining more information about a population with less cost than would be possible under a single stage design. Examples of such approaches include ranked set sampling, double sampling for stratification, and multistage cluster sampling. In all cases a first stage sample is selected, e.g. a set of randomly selected transects through a habitat, and subsequently a subset of observations from this initial sample, e.g. observations at randomly selected locations along the transects, are selected for data collection.
Nearest Neighbor Methods
Authors: Dixon Philip M.
Published: January 2013

This article discusses nearest neighbor (NN) methods for the analysis of spatial point patterns and the analysis of field experiments. The distance from a point to its NN, or quantities derived from that distance, can be used to test whether the observed locations are a realization of a specific spatial point process. Edge effects, caused by recording data only within a bounded study area, can be important. When locations are marked (e.g.,by the species of plant), NN methods provide information on the relationship between the marks. NN methods for field experiments can be used to model local spatial variability.
Network Ecology
Authors: Borrett Stuart R. , Christian Robert R. , Ulanowicz Robert E.
Published: January 2013

Network ecology is the investigation of complex ecological systems (e.g., metapopulations, communities, ecosystems, landscapes) by modeling them as networks of interactions and applying network analyses. It is a subdiscipline of both ecosystem ecology and network science. A network model is composed of set of nodes and one of edges that map a relationship between these nodes. For example in ecosystems, nodes might represent species, functional groups, or nonliving resource pools (e.g., detritus), and weighted, directed edges show the flow of energy‐matter from one node to another. Many algorithms exist for analyzing network organization, functioning, and in some cases dynamics. These algorithms can be found in a limited number of readily available software packages. This article is an introduction to network ecology through the lens of ecosystems. It traces the origins of ecological network analysis, reviews a family of algorithms and software to analyze such networks, and then delves into more detail about selected methods. We conclude by highlighting recent advances in ecological science due to the application of network ecology.
Nonparametric Regression Model
Authors: Opsomer Jean D.
Published: January 2013

Nonparametric regression is a rapidly growing and exciting branch of statistics, both because of recent theoretical developments and because of more widespread use of fast and inexpensive computers. Many methods are currently available, including kernel‐based methods, regression splines, smoothing splines and wavelet and Fourier series expansions. This article introduces the main types of smoothing methods and discusses the usefulness of nonparametric regression for analyzing datasets, particularly of the types encountered in environmental statistics.
S
patial
D
esign,
O
ptimal
Authors: Zimmerman Dale L.
Published: January 2013

Statistical inferences from spatial data are affected substantially by the spatial configuration of the sites where those data are observed. Thus, it is natural to try to select a configuration that optimizes, in some sense, the quality of the desired inference(s). This article lays out the classical framework for optimal model‐based spatial sampling design. Prediction error variance design criteria are featured, but optimality criteria for estimating model parameters are also mentioned. Optimal designs may be built “from scratch” or by expanding or contracting an existing design.
Pelagic Ecology
Authors: Reynolds Colin S.
Published: January 2013

The term ‘pelagic zone’ refers essentially to the open ocean, beyond the continental shelves. However, ‘the pelagic’ is understood by freshwater ecologists to mean simply ‘the open water’ of large lakes and reservoirs. In either instance, the notion of a liquid environment, remote from the shores and bottom of the containing basin, is clear. In extent, the marine pelagic is, by far, the greatest of the world's major ecosystems, covering some 361 × 10
6
km
2
(or 71% of the planet's surface) and accommodating an estimated volume of 1.35 × 10
9
km
3
. In contrast, the aggregate volume of the world's lakes and rivers is a relatively modest 225 × 10
3
 km
3
.
Permutation Tests
Authors: Hallin Marc , Ley Christophe
Published: January 2013

Permutation tests are an interesting and conceptually simple alternative to traditional tests when the required distributional assumptions (typically, Gaussian assumptions) are likely to be violated. We start with three motivational examples explaining how to construct permutation and sampled permutation tests, and provide empirical evidence of the way they outperform their traditional competitors onseveral counts: validity, unbiasedness, and power. We then show how permutation tests follow from more traditional Neyman alpha‐structure arguments, and discuss some asymptotic results establishing that extended validity, in this context, does not imply any loss of asymptotic efficiency.
Air Quality Index, Facilitating Communication With
Authors: Hunt Jr William F.
Published: January 2013

Air quality indicators can take many different forms. Why are they needed? We live in a technical society that collects vast quantities of environmental data. Indicators translate this environmental data into a form that is readily understood. Those asking questions seek answers in the simplest form. Is the environmental problem becoming better or worse? Often the questioner is told the problem is “too complex.” The governmental official or scientist may prefer to give no answer at all than give an imperfect answer that could lead to a misunderstanding. The layman prefers an imperfect answer to no answer at all. An indicator must be able to translate complex information into a form that is readily understood by decision makers as well as laymen. Indicators may have many uses: daily reporting to the general public (for those pollutants with short‐term health effects), for trends, and for evaluating the overall effectiveness of environmental policies/regulations across multiple pollutants. This article discusses the development of the Pollutant Standards Index (1976), which was promulgated as the index used for public reporting in 1979 and was later updated to become the USEPA's Air Quality Index (1999).
Population Ecology
Authors: Dixon Philip M.
Published: January 2013

An ecological population is the collection of individuals of a particular species in a specific geographic area. Population ecology is the study of the numbers of individuals in a population and how and why that number changes. This article describes commonly used quantitative models for change in population size.
Random Effects
Authors: Piegorsch Walter W.
Published: January 2013

A brief introduction is given on incorporation of random‐effect components for the factors in an analysis of variance calculation. Extensions to mixed‐effects models and generalized linear mixed models are also noted.
Record Linkage
Authors: Winkler William E.
Published: January 2013

This article describes methods from statistics and machine learning that are used in identifying duplicates within and across files.
Repeated Measures
Authors: Kenward Michael G.
Published: January 2013

A repeated measures study is distinguished by the collection of a sequence of measurements from each unit over a period of time. Repeated measures can be collected in both experimental and observational settings; examples of the latter are often referred to as longitudinal studies. The sequence of measurements from one unit is sometimes called the unit's
profile
. These profiles form a collection of short time series, and one should expect the measurements from the same unit to be mutually correlated.
Resampling Methods
Authors: Tu Wanzhu
Published: January 2013

This article presents an overview of existing resampling methods and their applications in parameter estimations and statistical inference. It describes the essential concepts and basic operating procedures of the most frequently used resampling methods, including the jackknife, bootstrap, permutation test, and cross‐validation. This article also discusses the interconnections among these methods. Finally, it briefly reviews the currently available software for implementation of the most commonly used resampling procedures.
Resource Selection
Authors: Nielson Ryan M. , Thomas Dana L. , Mcdonald Lyman L.
Published: January 2013

Field studies designed to compare resource (e.g., food or habitat) use and availability are commonly called resource selection studies. The motivation for conducting selection studies and the factors influencing resource selection are briefly described. Common study designs and statistical methods for assessing resource selection are presented.
Royal Statistical Society, Environmental Statistics Section (Formerly Study Group)
Authors: El‐shaarawi Abdel H.
Published: January 2013

The group was formed in 1996 and then became a full section, the Environmental Statistics Section, of the Royal Statistical Society in the United Kingdom. Its objectives are to act as a national focus for statisticians in the United Kingdom involved in environmental work and to provide a cadre of experts who can be called upon for professional advice.
Sample Support
Authors: Goovaerts Pierre
Published: January 2013

Sample support generally refers to the length, area, or volume associated with a measurement or observation. The term originates in the field of geostatistics, primarily from mining applications. To appreciate the issues associated with this term, this entry provides (i) a more complete definition of sample support as used in geostatistics; (ii) a description of the problems that arise in working with data of differing supports; (iii) a brief overview of the solutions to change of support problems.
Sediment Transport
Authors: Rodrigues Stéphane , Moatar Florentina , Claude Nicolas
Published: January 2013

Sediment transport is a geological process involved in the morphological evolution of the surface of the earth. Fundamental and applied aspects concerning this process are of interest for human societies. Sediment transport can be triggered by a moving fluid on cohesive or noncohesive sediments produced by the weathering of landmasses. The transport of sediments is influenced by complex interactions between physical features of particles and properties of flow. For instance, the mechanics of flow close to the bed of a river or a sea is implied in the threshold of motion of sediments and in their migration downstream. Processes involved in sediment transport and the estimation of transport rates in rivers and coastal environments constitute major scientific issues. The development of new analytical devices in the recent years offers new perspectives for the evaluation of sediment transport rates by combining direct or indirect measurements performed on the field and semiempirical equations. These tools are promising for understanding of the physical processes involved in sediment transport.
Risk Assessment, Seismological
Authors: Özel Gamze
Published: January 2013

Seismic risk is usually defined as the probability of exceeding a specified level of loss due to earthquakes for a set of goods within a reference period of time. Usually it is measured by considering the convolution of three main factors: hazard (probability of earthquakes), vulnerability (probability of damage, given the earthquake), and exposure (probability of loss given the damage). Thus, the seismic risk in a geographical region depends on many uncertain variables pertaining to the three main factors listed above. Some of the uncertainties are reducible through deeper investigation, while others reflect intrinsic randomness and are therefore unavoidable. Seismic risk assessment (SRA) is very important for public safety and hazards mitigation. It is also important for the correct determination of earthquake insurance premiums, and for understanding the social and psychological effects of earthquakes. This study represents an extensive review and evaluation of SRA methodology. SRA strategy, source parameters, attenuation, and local site effects are explained in detail. Global and national seismic hazard maps relating to seismic risk are presented. A variety of references concerned with the problem SRA are given.
Seismological Modeling
Authors: Rathbun Stephen L.
Published: January 2013

Temporal point process models for seismological applications are described including Poisson point process, Hawkes' self‐exciting point process for clustered events, and the stress‐release point process for regularly‐spaced events. Earthquake magnitudes may be included in marked versions of the point process models. In seismology, the self‐exciting point process model is often referred to as the epidemic‐type aftershock sequences (ETAS) model and is suitable for modeling aftershock sequences. Dependencies among seismological events may be described using Laguerre polynomials or the modified Omori function and versions of the model can be constructed under which high‐magnitude shocks produce a higher mean number of aftershocks. The ETAS model can also accommodate long‐term trends and periodic behavior. Under the stress‐release model describes the release of tectonic stress following each earthquake. Maximum likelihood estimation of model parameters and its statistical inference are briefly described. Methods are applied to a sequence of 432 California earthquakes.
Smoothing in environmental epidemiology
Authors: Ryan Louise
Published: January 2013

Smoothing is a branch of regression analysis that allows for a predictor to impact the response as an arbitrary smooth function. It is also known as nonparametric regression. The purpose of this article is to alleviate the restrictiveness of parametric functional relationships, such as that imposed by linearity.
Spatial Analysis in Ecology
Authors: Fortin Marie‐josée , Dale Mark R.T. , Ver Hoef Jay M.
Published: January 2013

The first step in understanding ecological processes is to identify patterns. Ecological data are usually characterized by spatial structures due to spatial autocorrelation.Spatial autocorrelationrefers to the pattern in which observations from nearby locations are more likely to have similar magnitude than by chance alone. The magnitude, intensity, as well as extent of spatial autocorrelation can be quantified using spatial statistics. Most ecological data exhibit some degree of spatial autocorrelation, depending on the scale at which the data were recorded and then analyzed. Ecological phenomena are also characterized by the multiple ecological processes that act upon them; these processes often operate at more than one spatial scale. Ecological data are a composite of several spatial scales: trends at macroscales; patches, gradients and patterns at meso‐ and local scales; and random patterns at local and microscales. The different processes and patterns at different scales are not necessarily linear or additive, and this contributes to the degree of spatial dependence in the data.
Spatial Distribution
Authors: Waller Lance A.
Published: January 2013

We review the role of the distribution of random quantities across space in inference. Different data structures often define different questions of interest and we review these for geostatistical, point process, and lattice data structures.
Species Diversity
Authors: Latimer Andrew M.
Published: January 2013

Species diversity is the number of species present in an area or sample, together with the characteristics of their relative abundance distribution, especially its evenness. Species diversity is only one dimension of biodiversity, but because species are fundamental units of ecology and evolution, and because most diversity data consist of species presence/absence, species diversity is often central to assessing and conserving biodiversity. After noting major conceptual and practical issues with species diversity and species richness, we discuss how best to estimate them from samples both for estimating total species number and for comparing diversity across samples and areas. Despite errors associated with extrapolation, recent research has demonstrated that in many cases, given adequate sampling, both nonparametric and parametric methods can estimate total species richness and effectively standardize across samples. Much research has focused on developing and interpreting compound diversity measures that incorporate patterns of both richness and abundance, some with weightings for additional factors such as rarity, phylogenetic distinctness, and ecological function. For a well‐known set of these indices, including the Shannon and Simpson indices, lognormal mean and variance, log‐series α and related neutral theory parameters, we discuss their consistency in ordering samples and their sensitivity and dependence on sample size. Finally, we touch upon major global patterns of diversity including estimates of the number of species on earth (5 million to 50 million) and large‐scale diversity gradients.
S
pecies
O
verlap
Authors: Gerow Kenneth
Published: January 2013

Species overlap measures the degree to which two species assemblages share common species. There is an abundance of well‐studied indices of species overlap. Some are based on presence/absence of data; more popular ones take relative abundance of species into account. Several important indices are described in this article, as well as an entrée to relevant literature.
Spherical Statistics
Authors: Jupp Peter E.
Published: January 2013

Spherical statistics is concerned with data that lie on the sphere of unit radius, and so are unit vectors representing directions in three‐dimensional space. Typical examples of such data are directions of paleomagnetism in rock or directions of normals to cometary orbits. Spherical statistics also provides methods of analyzing data that are axes or rotations.
Statistical Computing in Environmental Science
Authors: Stein Alfred
Published: January 2013

This article describes statistical computing for the environment. A distinction is made in computing for modeling, statistical analyses, use of large packages, and use of the Internet. Modeling requires the use of basic programming routines; a standard statistical package is recommended for a statistical analysis; typically, geographical information system (GIS) packages and integrating programming environments are interesting large packages; and the Internet offers great opportunities for data and information sharing.
Superfund site, US
Authors: Bowers Teresa Suter
Published: January 2013

The Comprehensive Environmental Response, Compensation, and Liability Act (CERCLA) provides authority for the cleanup of abandoned landfills, warehouses, and other properties sufficiently contaminated by hazardous waste such that they were deemed to represent threats to human health and the environment. Superfund sites become identified as such when they are added to the US National Priorities List (NPL), a list prioritizing sites most in need of remedial response due to contamination.
Surveillance, Environmental
Authors: Järpe Eric
Published: January 2013

In many environmental random processes it is relevant to consider a sudden shift in a parameter of the probability distribution of the random variables. This parameter may be a mean level of the process or the natural variation of the variables. Suddenly the parameter can shift to some other, commonly higher, value or to another, commonly increasing, function in time and/or space. To prevent or mitigate the fatal consequences such shifts could imply, it is often of utter importance to detect the change as accurately and quickly as possible. Therefore, stopping rules which are functions of the random process data observed are evaluated, on‐line or retrospectively, in order to indicate a systematic change. Different shift processes are mentioned. An example with data from the Swedish Radiation Safety Authority is given.
The International Environmetrics Society
Authors: Esterby Sylvia
Published: January 2013

The International Environmetrics Society (TIES) was founded in 1989. The objectives of the society are to foster the development and use of statistical and other quantitative methods in environmental sciences, environmental engineering, and environmental monitoring and protection.
Threshold Models
Authors: Drees Holger
Published: January 2013

Models for exceedances over high thresholds are motivated by limit theorems from extreme value theory. For univariate observations this approach leads to generalized Pareto models. In contrast, natural models for the dependence of vectors of exceedances are infinite dimensional.
Time Series, Periodic
Authors: Lund Robert B.
Published: January 2013

This entry overviews time series with periodic autocovariance structures. Such series often arise in the environmental sciences. Here, extensions to the class of covariance stationary time series are introduced and used to model and describe the autocovariance periodicities. Detection of autocovariance periodicities is considered. A series of monthly averaged temperatures from Griffin, Georgia (United States) is used to illustrate aspects of the discourse.
Aquatic Toxicity Tests
Authors: Fox John F. , Denton Debra L. , Diamond Jerry
Published: January 2013

Aquatic toxicity tests are used in a variety of regulatory and nonregulatory applications to characterize toxicity of known chemicals and environmental water samples, for effluent compliance testing, and to monitor the ambient environment (watersheds), using a variety of aquatic organisms and biological endpoints. This article covers statistical approaches routinely applied to such tests. Concentration‐response models and point estimates (e.g., EC
25
) based on these models are used to characterize concentration‐response relations for toxic chemicals using toxicity data, and also to characterize single effluent or ambient samples for watershed monitoring. Hypothesis tests can also be used to make yes‐no decisions for compliance and watershed determinations. Test experimental designs and statistical methods have been standardized for regulatory use. New approaches or refinements published in the past 10 years are cited here; these can improve interpretation and application of aquatic toxicity tests.
Epigenetics
Authors: Saunders Ian William
Published: January 2013

Epigenetics is the study of heritable variations within cells that affect gene activity without changing the DNA sequence. Epigenetic responses to environmental changes are common and have potential for early biomarkers of contamination and other environmental effects. This article outlines the basic concepts of epigenetics, the technologies involved in measuring epigenetic changes, the genome‐wide study of such changes, or epigenomics, and the implications for environmetrics.
Groundwater Monitoring, Detection, and Compliance
Authors: Gibbons Robert D. , Bhaumik Dulal K. , Aryal Subhash
Published: January 2013

An overview of statistical issues and methods is provided relevant to the analysis of groundwater detection and compliance‐monitoring problems. The rich methodology that has been used in this area goes well beyond groundwater monitoring applications to many other areas of interest in environmental monitoring and statistics. First, we provide an overview of statistical prediction limits for normal, lognormal, and gamma random variables, as well as nonparametric alternatives. Issues related to multiple comparisons, censored data, nonnormality, and verification sampling (i.e., sequential testing) are considered in the statistical developments. Second, we provide an overview of statistical methods that are relevant for compliance monitoring, where interest is often focused on whether on‐site average concentrations exceed a health‐based regulatory standard. This leads to discussion of a variety of statistical approaches based on confidence limits for normal and nonnormal distributions and nonparametric alternatives. A distinction is made between assessment monitoring where the null hypothesis is that contamination
is not
present and corrective action monitoring where the null hypothesis is that contamination
is
present.
Risk Governance
Authors: Shi Peijun , Jaeger Carlo , Ye Qian , Wang Ming , Henning Elke
Published: January 2013

Examples of recent large‐scale disasters show that the traditional risk management process faces difficulties in dealing with emerging unknowable, unmeasurable, and uncontrollable risks in face of the globalization processes. This article starts with the clarification of the difference between risk management and risk governance, and elaborates the importance of risk governance in terms of addressing the institutional design, the development of legislation system, and the establishment and promotion of paradigms. Following the definition of risk governance, this article emphasizes the large‐scale and emerging risks that risk governance deals with and raises four key questions that need to be answered in the practice. A more recent concept, integrated risk governance, is also discussed from the perspectives of risk governance process, risk‐holders, and outcomes. Although people may still possess different opinions and understanding on many aspects of risk governance, the international scientific risk community and intergovernmental organizations have taken serious and solid steps to tackle the issues of risk governance.
E
xtremes for
P
rocesses in
R
andom
E
nvironment
Authors: Piterbarg Vladimir I.
Published: January 2013

We give definitions for random processes in random environment, in particular, Gaussian random processes in random environment, or, in other words, conditionally Gaussian processes. With some constrains on a random environment, we formulate the large deviation principle for Gaussian processes in the random environment. Further, we consider a class of Gaussian processes in random environment that allows exact calculations for probabilities of large extremes. This is a class of Gaussian stationary processes with smooth bounded random stationary variance. We show how the random environment affects on such probabilities.
Max‐Stable Processes
Authors: Padoan Simone A.
Published: January 2013

Environmental problems such as floods require statistical analysis that takes into account the complex nature of the data, namely, the observations that are sampled at different spatial points in a given region for a certain time. Thus the spatial dependence structure cannot be ignored. Extreme statistics for the design of structures for flood protection, for the study of the structural failures such as those in bridges, dams, and so on, for the prediction of heat waves, and other spatial extremes should be based on a solid theoretical framework. Max‐stable processes provide such a theory and in the last decade have emerged as fertile ground for research and have become a common tool for the statistical modeling of spatial extremes. This article provides a summary of max‐stable processes.
Sampling Agricultural Resources
Authors: Nusser Sarah M. , Zimmer Stephanie A.
Published: January 2013

Agricultural surveys gather data about agricultural production, land management practices, and economic outcomes for farms. Because they involve a complex mix of estimation goals and reporting units, probability samples for agricultural surveys are challenging to design. Two types of sampling frames are used: list frames of agricultural producers and area frames that represent units of land. List frames are cheaper to maintain and easier to select samples from, but may be incomplete. Area frames, which involve selecting land areas or points on the land, are expensive to use, but have full coverage of the population. Some surveys use both types of frames to control costs and estimate coverage bias of the list frame. Regardless of the frame, stratification and multistage sampling are commonly used to balance operational constraints and precision goals for agricultural surveys.
Adaptive Management
Authors: Nichols James D. , Williams Byron K.
Published: January 2013

Adaptive management (AM) is a form of decision analysis developed to deal with recurrent problems that are characterized by uncertainty. This article introduces the concept of AM and provides a brief history of its development in natural resource management, focusing on the relevance of recurrence and uncertainty to decision‐making. The central components of AM include objectives, potential actions, models of system response to actions, monitoring, and a solution algorithm. These components are described, and their respective roles in the iterative AM process specified. “Active” and “passive” forms of AM are defined, with the distinction depending on the degree to which each decision anticipates learning and the resultant improvement in future management. AM has substantial potential for improving natural resource management, but its increased use will depend on our ability to produce many more managers and scientists capable of developing and implementing AM programs.
Environmental Hydrology
Authors: St‐hilaire André , Daigle Anik , Caissie Daniel
Published: January 2013

Environmental hydrology is the component of water science that focuses on the hydrological cycle with an emphasis on its interface with humans and other organisms. Most studies in environmental hydrology deal with ecohydrology, environmental flows or instream flow requirements, and water quality/quantity analysis and modeling. Ecohydrology deals with interactions between ecosystems and the hydrological cycle at different spatiotemporal scales. Historically, most ecohydrological studies focused on the role of vegetation within the hydrologic cycle (e.g., forest hydrology) with the objective of better quantifying its impact (e.g., timber harvesting) on soil water content, evapotranspiration rates, or rainfall interception.Instream flow needsgenerally refer to the amount of water or flow that is required to maintain ecological functions within a river. Water quality variations in rivers depend on water quantity and movement as well as exchange processes within the river. As an example, water temperature is discussed in greater details. Both deterministic and statistical water temperature models are briefly described.
Massive Data, Models for
Authors: Zhang Hao
Published: January 2013

Massive data present a challenge to the use and manipulation of well‐studied inferential strategies such as maximum likelihood estimation, Bayesian methods, and best linear prediction (kriging) since these methods require the inversion of a large covariance matrix. This entry introduces statistical models that circumvent computational issues, which include local models, covariance tapering, low‐rank models, and Markovian models.
Multivariate Covariogram Models
Authors: Zhang Hao
Published: January 2013

When multiple variables are observed at various spatial locations, it may greatly improve spatial prediction if spatial cross correlation is employed. A multivariate covariogram is a matrix‐valued function that consists of marginal and cross covariograms. This article provides some classes of multivariate covariogram models.
Spectral Methods
Authors: Fuentes Montserrat
Published: January 2013

Spectral methods are a powerful tool for characterizing and modeling spatial dependence, while offering significant computational advantages. Using the spectral representation of a spatial process, we can easily construct valid (positive definite) covariance functions and introduce new models to characterize complex dependence structures of spatial processes. Likelihood approaches for very large spatial datasets are often very difficult, if not infeasible, to implement owing to computational limitations. Even when we can assume normality, exact calculations of the likelihood for a Gaussian spatial process observed at
n
locations requires O(
n
3
) operations. The spectral version of the Gaussian log‐likelihood for gridded data requires O(
n
log2
n
) operations and does not involve calculating determinants.
E
nsemble
M
odels
Authors: Fuentes Montserrat , Foley Kristen
Published: January 2013

An ensemble, or sample, of competing numerical models has been used in many applications to represent different predictions of the true state of a physical system. Ensembles of computer models (e.g. weather, climate, air quality, ocean models) are often used to forecast future states of a physical system and to quantify uncertainty in the numerical model predictions. Various statistical methods have been proposed to improve ensemble predictions from deterministic computer simulations based on actual measurements of the physical systems (e.g. data assimilation, Bayesian model averaging). Ensemble data mining methods have also been developed for a wide variety of applications to combine different versions of a statistical model (e.g. time series models, simple regression models, neural networks) to improve the predictive model performance. We present different statistical criteria that have been proposed to select or weight ensemble members for both numerical model‐based and statistical model‐based ensembles.
Counting process
Authors: Olofsson Peter
Published: January 2013

A counting process is a nonnegative, integer‐valued, increasing stochastic process that is used to count the number of occurrences of some event as time goes by. Special cases include pure birth processes, renewal processes, and the Poisson process.
Brownian Motion
Authors: Riedi Rudolf H.
Published: January 2013

This article on Brownian motion starts with a short historical survey on its discovery and importance and continues with its most relevant properties. Mathematically detailed formulas are given and connections between the properties are indicated, however no derivations or proofs are provided.

The properties covered start with the mathematical modeling of Brownian motion via the Wiener process; equivalent definitions and constructions such as the Lévy characterization, the midpoint displacement, and the rescaled random walks are discussed. Basic properties given include uniqueness, symmetry, restarted Brownian motion, and time inversion. More advanced topics treated cover stopping times, the strong Markov property, the reflection principle, extreme values, escape times from a strip, and last visits. Path oscillations, stationarity, Gaussian white noise, and Karhunen‐Löwe expansions are also discussed. Brownian motion with drift, the Brownian bridge, as well as intersections, recurrence, and transience of Brownian motion in higher dimensions, are mentioned briefly.
Random Walk
Authors: Lasinio Giovanna Jona , Pollice Alessio
Published: January 2013

Random walks (RW's) appeared in the mathematical and statistical literature in 1905 when Karl Pearson, in a letter to the journalNature, introduced the name for the first time. They are a simple kind ofstochastic processesand describe the random movements of an object in a set of possible positions. RW's areMarkov processesas the conditional distribution of a future state given the present and the past depends only on the present state. As a consequence, the classification ofMarkov chainsasirreducible,recurrent, andperiodiccan be applied to characterize their limiting behavior. An important role in this regard is played by asymptotic results in probability theory concerning sums of iid random variables, such as the laws of large numbers and the central limit theorem. At present, a large number of papers in environmental sciences make explicit or implicit use of RW‐based models. Their application has mainly to do with studies of animal movements and microscopic motility and of particle diffusion in fluids. The implicit use of RW models arises when computational algorithms or complex, possibly hierarchical, statistical models are employed.
Elliptical Symmetry
Authors: Paindaveine Davy
Published: January 2013

This article first reviews the definition of elliptically symmetric distributions and discusses identifiability issues. It then presents results related to the corresponding characteristic functions, moments, marginal and conditional distributions, and considers the absolutely continuous case. Some well‐known instances of elliptical distributions are provided. Finally, inference in elliptical families is briefly discussed.
Equivariant Estimation
Authors: Hallin Marc , JureČková Jana
Published: January 2013

The concepts of invariance and equivariance of estimators with respect to various groups of transformations of the sample space are defined. The structure and properties of equivariant and minimum risk equivariant estimators are characterized. Emphasis is put on equivariance with respect to shift, scale, and affine transformations.
Goodness of Fit (Testing)
Authors: Deheuvels Paul
Published: January 2013

We present a selection of some common goodness‐of‐fit tests, with emphasis on the cases for which there exist analytical methods to evaluate their critical levels and asymptotic efficiency.