bluuebunny/crossref_metadata_2025 huggingface dataset:
Landscape Pattern Metrics
Authors: McGarigal Kevin
Published: September 2006

Landscape ecology is largely founded on the notion that environmental patterns strongly influence ecological processes. The habitats in which organisms live, for example, are spatially structured at a number of scales, and these patterns interact with organism perception and behavior to drive the higher‐level processes of population dynamics and community structure. A disruption in landscape patterns may therefore compromise this structure's functional integrity by interfering with critical ecological processes necessary for population persistence and the maintenance of biodiversity and ecosystem health. For these and other reasons, much emphasis has been placed on developing methods to quantify landscape patterns, which is considered a prerequisite to the study of pattern–process relationships. This has resulted in the development of literally hundreds of indices of landscape patterns.
Lévy Processes
Authors: Wolpert Robert L.
Published: September 2006

Lévy processes are random processes on Euclidean space that are stochastically continuous and have stationary independent increments. They, and their stochastic integrals, have become useful tools in a variety of nonparametric statistical and environmetric applications including density estimation, survival analysis, regression, and spatial modeling.
Likelihood Ratio Tests
Authors: Champely Stephane
Published: September 2006

The LRT is a principal method in a standard hypothesis testing framework. It parallels the maximum likelihood method in estimation theory.
Line‐Transect Sampling
Authors: Cowling Ann
Published: September 2006

Line‐transect sampling methods have been used since the 1930s to estimate the abundance of many biological populations, such as animal, bird, and plant species, and even nonliving things. In a line‐transect survey, an observer moves along a transect line and notes the location of all animals detected relative to the line. It is assumed that not all animals are detected. Factors affecting detectability include distance from the line, habitat, and weather conditions. In the conventional approach to line‐transect sampling, it is assumed that all animals on the line are detected, and that the probability of detection decreases with distance from the line.
Logarithmic Regression
Authors: El‐shaarawi Abdel , Viveros(‐aguilera) Román
Published: September 2006

Log regression (LR) is widely used to model environmental data because the measurements tend to show positively skewed frequency curves and higher variability with higher concentration levels. A compelling reason for the popularity of LR is the simplicity of estimating and making inferences about the regression coefficients using existing software packages for the normal theory linear models.
Logistic Regression
Authors: Gustafson Paul
Published: September 2006

Logistic regression is by far the most common approach to modeling the relationship between some explanatory variables and a binary response variable. It is applicable when the response variable for each study unit can be viewed either as the success or failure of a single trial, or as the number of successes in some fixed number of independent trials.
Lognormal Distribution
Authors: El‐shaarawi Abdel
Published: September 2006

The lognormal distribution is widely used by environmental scientists to model their data. Its popularity is based on the fact that many environmental measurements are non‐negative and their histograms are frequently skewed to the right but the histograms of log‐transformed data resemble those of the normal distribution. Another reason for its popularity is the simplicity of performing the analysis using the familiar normal theory methods. It has been shown that the lognormal distribution arises naturally by applying the central limit theorem when a multiplicative process is used to combine the error.
Longitudinal Studies
Authors: Gotway Crawford Carol A.
Published: September 2006

A longitudinal study is one in which the subjects under investigation are observed repeatedly over time. The same variable is measured on the same subject for at least two time periods. The subjects may be individuals or pre‐existing populations of interest (e.g. species, countries, watersheds). Replication necessary for estimation and inference is provided by the assumption that the subjects respond independently.
Long‐Term Environmental Monitoring
Authors: van der Maarel E.
Published: September 2006

Monitoring (from the Latin monere = to warn) is the act of following or controlling a process through a monitor and being warned if the process deviates from expectation. Environmental monitoring is the controlling of an environmental process, or ‘the intermittent surveillance to ascertain the extent of compliance with a predetermined standard or degree of deviation from an expected norm’. This means in practice a series of carefully planned, repeated observations of parameters indicating changes in a process we do not want to change. Monitoring ‘provides the essential data on how systems are changing and how fast’.
Markov Chain Monte Carlo (MCMC)
Authors: Jones Galin L. , Hobert James P.
Published: September 2006

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 10 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. Any discussion of the Markov chain theory underpinning MCMC algorithms, have intentionally been avoided.
Markov Random Field Models
Authors: Kaiser Mark S.
Published: September 2006

Statistical models formulated on the basis of Markov random fields (MRFs) constitute an appealing approach to the analysis of data that exhibit complex dependence structures. Such data arise commonly in problems of a spatial or spatiotemporal nature, although MRFs are a general mathematical construct that may be used in other situations such as, for example, the representation of genetic dependence among organisms. Within the context of statistical modeling, a MRF may be defined for any set of random variables defined at a discrete point.
Matrix Population Models
Authors: Caswell Hal
Published: September 2006

Matrix population models are discrete‐time structured population models in which individuals are classified into discrete stages (age classes, size classes, developmental stages, spatial locations, etc.).
Maximum Likelihood Estimation, Nonregular
Authors: Holland David M.
Published: September 2006

For bounded probability distributions capable of J or U shapes, the log‐likelihood function can become unbounded as the boundary parameters approach their respective limits. However, use of penalty function techniques that urge the maximum likelihood (ML) search away from the unbounded region can be used to circumvent this problem. Another approach to nonregular problems is ‘correcting’ the likelihood to estimate the model parameters. In an application to simulated data, this technique was found to be effective with quick convergence to parameter estimates.
Meteorological Adjustment of Air Quality
Authors: Thompson Mary Lou
Published: September 2006

Poor air quality impacts adversely on the health of humans and ecosystems. Air pollutants result both from natural sources and from human activity. Oxides of carbon, nitrogen and sulfur are, for instance, products of combustion activity, such as that generated by motor vehicles. Other secondary pollutants such as ozone result from reactions in the atmosphere between primary pollutants and other chemicals known as precursors. The dispersion of airborne pollutants and the reactions among them are influenced by meteorological conditions. This article describes some of the existing approaches to meteorological adjustment of air quality, i.e. the modeling of (some aspect of) air quality that takes account of (adjusts for) meteorological conditions. In doing so, this article will also highlight challenges that exist and raise issues that need further attention.
Environmental Microbiology
Authors: Hamilton Martin
Published: September 2006

Micro‐organisms are critical to life on earth. They are at the very bottom of the food chain, providing the nutrients required to sustain other forms of life. Scientists are only now discovering the extent to which micro‐organisms control broad biochemical processes, such as the cycling of carbon, nitrogen, and sulfur. Bacteria live in all habitats accessible to any form of life – from Antarctic lakes to deep oceanic hot water vents – even 2000m below the earth's surface, where no fresh organic input has been experienced for millennia. Rigorous investigation of environmental issues must recognize, and take account of, microorganisms.
Missing Data
Authors: Hopke Philip K. , Liu Chuanhai , Rubin Donald B.
Published: September 2006

A common problem with environmental data is that there may be samples or sampling intervals for which there are no data. Environmental studies cannot be designed for experiments that can be reproduced, therefore a sample that was not taken or was lost cannot be recovered. These losses of samples represent a total loss of information about the content of the species that were not directly determined for that sample. Also often there are only sufficient resources to perform partial sampling (every
x
th time interval) instead of contiguous measurements, or to analyze only part of the samples collected. This leads to values that are not obtained, and no information is available about the variables of interest during these sampling intervals. Incomplete data makes analysis using standard complete‐data methods like distribution fitting impossible. Filling in missing values has strong appeal, because then standard complete‐data methods can be applied and existing software can be used without any modification. This general strategy reduces greatly the burden of developing methods and computer codes for analyzing incomplete data.
Mixed Effects
Authors: Drum Melinda
Published: September 2006

Mixed effects refers to the combination of both fixed and random effects in various types of linear and nonlinear regression models.
Mixing Distribution
Authors: Leroux Brian
Published: September 2006

Amixture distributionis any distribution having a density of the formp(y) = ∫f(y; θ) dG(θ) whereGis a distribution function on Θ, called themixing distribution, and {f(x; θ):θ ∈ Θ} is a family of density functions.
Model Uncertainty
Authors: Chatfield Chris
Published: September 2006

The modeling of complex environmental stochastic systems is a difficult task. There may be little or no background theory, the data may be of doubtful quality, and it is not always clear what the objectives are. Nevertheless, scientists have made substantial progress in getting a better insight into environmental relationships and changes. However, much remains to be done, especially in regard to the thorny topic of model uncertainty. Although it is widely recognized that all models are
approximations
and need to be modified and improved as more information becomes available, many scientists continue to make predictions from models as if they really believe them to be true. As a result, the accuracy of out‐of‐sample predictions is typically (much) worse than would be expected from the within‐sample fit.
Model‐Based Inference
Authors: Chambers Ray
Published: September 2006

A basic problem in survey sampling is that of using the sample data for a survey variableYto infer the value of the totalTofYover the sampled population. The model‐based approach to this problem is to base this inference on a joint statistical model for both the population values ofYand, where appropriate, for the sampling method. This is in contrast to design‐based sampling inference, where the only source of uncertainty is the outcome of the sampling method.
Modeling, Environmental
Authors: Solow Andrew R.
Published: September 2006

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, while 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.
Multiple Outcomes
Authors: Legler Julie
Published: September 2006

It has long been recognized that many environmental exposures do not affect a single, well‐defined outcome, but rather induce subtle effects on a host of outcomes. Focusing on a single outcome can be inefficient therefore global tests provide an opportunity for analyzing multiple outcomes using methods that are more efficient and relevant to the overall question of interest in environmental studies.
Multistage Design
Authors: Christman Mary C.
Published: September 2006

A multistage sampling design is one in which an initial sample is taken, some characteristics about the sample are observed, and a subsample is then taken from among the units selected in the initial sample.
Multivariate Data Visualization
Authors: McLeod A.I. , Provost S.B.
Published: September 2006

Multivariate data visualization is an exciting area of current research by statisticians, engineers and those involved in data mining. This article first gives a brief overview of the most important current software available for data visualization and then discusses the general principles or philosophy involved in data visualization. This is followed by a discussion of some of the most interesting and useful multivariate graphical techniques.
Natural Disasters
Authors: Davenport A.G. , Kopp G.A.
Published: September 2006

Natural disasters are the interaction of naturally occurring hazards with human population. Natural disasters are often defined in social and economic terms, one common definition being that the community involved cannot recover without external help. Meteorologist Joseph Golden of the National Oceanic and Atmospheric Administration says that ‘a hazard only becomes a disaster when it occurs where people live’. Where people live is an important aspect of natural disasters because it defines the vulnerability to natural hazards. According to Flageollet, ‘vulnerability is often assessed in terms of the probable cost of the damage the hazard has done or may do’. The risk of a natural disaster is a combination of both the hazard and the vulnerability to the hazard.
Natural Resources Modeling
Authors: Rathbun Stephen L.
Published: September 2006

Environmental resources are biotic, including fish and game populations, timber, and grasslands, or abiotic, including water, air, and soil. Interest may focus on either the quantity of available resources (e.g. volume of available timber, or size of fish populations), or their quality (e.g. the concentration of contaminants in air, water, or soil samples). Environmental resource models can lead to a better understanding of environmental processes, and assist managers in making decisions regarding sustainable levels of resource exploitation, remediation of impaired habitats, and the maintenance of biodiversity. This article describes univariate and multivariate methods for predicting the data at unsampled sites from observations at sampled sites. Univariate models are used when the values of the explanatory variables are available at all sites for which predictions are desired. A multivariate approach is required when the explanatory variables are measured only at a sample of sites. For both approaches, models for the spatial correlation structure of the data are considered, including both parametric and nonparametric forms. Methods for model fitting and spatial prediction are described.
Nearest Neighbor Methods
Authors: Dixon Philip M.
Published: September 2006

This entry 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 related quantities, 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 variabiltiy.
Nonlinear Regression
Authors: Smyth Gordon K.
Published: September 2006

The basic idea of nonlinear regression is the same as that of linear regression, namely to relate a response to a vector of predictor variables. Nonlinear regression is characterized by the fact that the prediction equation depends nonlinearly on one or more unknown parameters. Whereas linear regression is often used for building a purely empirical model, nonlinear regression usually arises when there are physical reasons for believing that the relationship between the response and the predictors follows a particular functional form. The unknown parameters in the regression function are typically estimated by minimizing the residual sum of squares, although other criteria can be used if it is desired to protect against non‐normal errors. Popular nonlinear regression models include sums of exponential functions, rational functions or growth curves such as logistic or Gompertz curves. The estimates usually have to be computed iteratively by using numerical optimization methods such as the Gauss–Newton algorithm. Good‐quality algorithms usually incorporate step‐length modifications designed to ensure a reduction in the residual sum of squares at each step. In some cases, the complexity of the fitting process can be reduced by taking advantage of conditionally linear parameters. Inference for nonlinear regression is classically based on analogies with linear regression using the gradient matrix from the Gauss–Newton algorithm, but recent work on curvature measures has led to new diagnostics and higher‐order approximations.
Nonparametric Regression Model
Authors: Opsomer Jean D.
Published: September 2006

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.
Nuclear Risk
Authors: Grimston M.
Published: September 2006

The concept of ‘risk’ is inherently linked with that of uncertainty. In the field of energy, uncertainty manifests itself in a number of areas. For example, there is considerable uncertainty about future demands for energy. It seems highly likely that global energy demand will continue to grow rapidly for some decades, but credible projections for energy use in the year 2050, say, can vary by a factor of 2 or more depending on assumptions made. Even more uncertainty surrounds the atmospheric effects of burning fossil fuels. In order to stabilize carbon dioxide concentrations in the atmosphere at double preindustrial levels, it would be necessary to reduce emission of the gas by 60% but global emissions in 2010 are projected to be 30% higher than in 1990. The risks of non‐fossil sources of electricity production such as nuclear power and renewables need to be judged against such a background.
Nutrient Cycling
Authors: Ashman Mark
Published: September 2006

Nutrients are constantly exchanged between the nonliving and living components of an ecosystem. This process is referred to as nutrient cycling.
Occupancy Problem
Authors: Mcdonald Trent L.
Published: September 2006

The ‘occupancy problem’ has also been called the ‘sequential occupancy problem’ and the ‘coupon‐collector's problem’. Although there exist many variations, one popular statement of the problem asks, ‘What is the probability that a set ofnindependent multinomial trials yield at least one member ofyclasses?’ The answer to this question has direct application in many sampling situations, particularly when sampling for members of a population with certain characteristics (such as species members, members with defects, etc.). An answer to this question, under general probabilities of class membership, is given in this article through the occupancy probability mass function and cumulative mass function. This article also mentions the corresponding waiting‐time question that asks how many multinomial trials need to be conducted (i.e. how large shouldnbe) in order to have a certain chance of obtaining at least one member ofyclasses.
Official Statistics, Environmental
Authors: Ross N. Phillip
Published: September 2006

Official statistics can be defined as any set of data produced by a governmental agency. This article addresses some of the important statistical issues relating to the generation and use of ‘official statistics’ on the environment. The majority of environmental statistics is generated by governmental agencies and is
official
. The environmental data collected are usually for the purpose of developing standards and measuring compliance to those standards; however, they are often used for generating a number of secondary statistics that are also considered
official
statistics. A number of statistical issues arise in the generation of official environmental statistics. The remainder of the article focuses on some of the major issues and the approaches being taken to deal with them.
Optimization
Authors: Smyth Gordon K.
Published: September 2006

Optimization means to find that value which maximizes or minimizes a given function. The idea is intimately connected with statistical methods such as least squares, maximum likelihood, posterior mode and so on. Many optimization algorithms are based on the idea of solving the nonlinear equation that arises from setting the derivative vector equal to zero. Except in linear cases, optimization almost invariably proceeds by iteration. This article is concerned with unconstrained optimization in which function arguments not specially restricted.

In general, optimization methods which use derivatives are more powerful than those that do not, although the increase in speed may not always outweigh the overhead in computing the derivatives. If first and second derivatives of the function are available, Newton's method is simple and works well. Some sort of backtracking strategy, such as a line‐search or Levenberg–Marquardt damping, is necessary, though, to prevent divergence from a poor starting value. If second derivatives are not available, then quasi‐Newtonian methods, of which Fisher's method of scoring is one, are recommended. Particular applications of Fisher scoring to nonlinear regression and to generalized linear models are described. General purpose quasi‐Newtonian algorithms build up a working approximation to the second‐derivative matrix from successive values of the first derivative. If even first derivatives are unavailable, the Nelder–Mead downhill simplex algorithm is compact and reasonably robust. However, the slightly more complex direction‐set methods or Newtonian methods with finite‐difference approximations to the derivatives should minimize most functions more quickly. The one‐dimensional problem is considered separately. In one dimension, once one can provide an interval that contains the solution, there exist efficient ‘low‐technology’ algorithms robust enough to take on all problems.

A maximum or minimum of the function can be either global or local, and various heuristics have been used to distinguish one from the other. Any method that relies on the iterative refinement of a single working approximation will fail in the presence of a large number of local optima. Algorithms that are specially designed to cope these circumstances include simulated annealing and genetic algorithms.
Organizations, Environmental Statistics
Authors: Marker David A.
Published: September 2006

Environmental statistics is by its very nature an international endeavor. Every nation in the world must address environmental issues ranging from pollution assessment to biodiversity, global warming to ecosystem monitoring. To solve these issues, any one nation must cooperate with one or more other nations. It is therefore not surprising that many international organizations have formed to work on solutions to environmental statistical issues. This entry provides brief summaries of the major environmental statistical organizations. The list is not intended to be all‐inclusive, rather to provide a short introduction to some of the primary sources for professional information on environmental statistics.
Ozone
Authors: Cocchi Daniela , Trivisano Carlo
Published: September 2006

Ozone gas is produced by photochemical dissociation of atmospheric oxygen as a result of shortwave solar ultraviolet radiation. It is highly concentrated in the stratosphere, mainly between 15 and 40 km. Stratospheric ozone is necessary for life on Earth, since it absorbs solar ultraviolet radiation, which should have mutagenetic effects on living tissues of plants and animals. In recent years it has been discovered that the ozone layer is thinned in the ozonosphere above Antarctica. This has been caused mainly by chlorofluorocarbures (CFCs) from human activities, which are emitted into the stratosphere. This phenomenon, commonly known as the ‘ozone hole’, is different from the increase of ozone in the troposphere, which is the lowest part of the atmosphere near the earth’s surface, i.e. a thin stratum of atmosphere which on average occurs at 10 km altitude. The chemical and biological processes that regulate life on earth, and most of the meteorological processes, occur in the troposphere.
P Value
Authors: Delampady Mohan
Published: September 2006

ThePvalue is one of the tools from classical statistics that is used very widely in applied sciences. It is also one of the concepts that is highly misunderstood and misused. The basic idea behind Fisher's original (1925) definition ofPvalue did have a great deal of appeal: it is the probability under a (simple) null hypothesis of obtaining a value of a test statistic that is at least as extreme as that observed in the sample data.
Plant strategies
Authors: Fang Wei
Published: September 2006

Plant strategies are a complex set of approaches that plants use to maximize their success in particular environments or under particular conditions. These strategies can be characterized by identifiable suites of specific traits. The search for plant strategies is inspired by a long‐standing desire of ecologists to seek simplified patterns in plant diversity and the complexity of ecosystems. The effort to define and quantify plant strategies will clarify patterns of the geographical distribution of flora, enhance generalizations about their physiological, phenological and ecological functions, and improve predictions about ecosystem sensitivity to changes in the environment. Accurate descriptions of plant strategies will also help in synthesizing results from individual studies and enhance our understanding of ecological patterns and processes at landscape and global scales. This article emphasizes descriptions of plant strategies and the development of associated quantitative approaches.
Point Processes, Temporal
Authors: Brillinger David R. , Guttorp Peter M. , Schoenberg Frederic Paik
Published: September 2006

A temporal point process is a random process whose realizations consist of the times {τ

j

}, τ

j

 ∈ ℝ,
j
 = 0, ±1, ±2, … of isolated events scattered in time. A point process is also known as a counting process or a random scatter. The times may correspond to events of several types.
Point Processes, Spatial
Authors: Guttorp Peter M. , Brillinger David R. , Schoenberg Frederic Paik
Published: September 2006

The general theory of point processes has usually been focused on temporal developments. The special case of events that occur in space (or, more precisely, on a plane) has developed some particular approaches, usually assuming spatial stationarity and isotropy (i.e. the distribution of the process is invariant under translations and rotations, respectively). This article focuses on this type of process. Points, or events, take place at spatial locations, and each event is identified with its location.
Pollutant Measurements
Authors: Mole Nils , Palmgren Finn , Zhang Hao
Published: September 2006

Measurements of pollutant concentrations are needed in monitoring to determine when an emergency response is required, for example close to installations that store or process hazardous chemicals; to determine whether legal standards are complied with; and to gain knowledge and understanding that can be used to improve modeling, prediction and mitigation of the effects of pollution. This article deals with measurement techniques and strategies appropriate to major pollutants in both air and water, and also with the effects of unavoidable measurement errors.
Posterior Distribution
Authors: Gelman Andrew
Published: September 2006

The posterior distribution summarizes the current state of knowledge about all the uncertain quantities in a Bayesian analysis.
Proportional Hazards Model
Authors: Piegorsch Walter W.
Published: September 2006

A short introduction is given into construction and use of the proportional hazards model with time‐to‐event data. Applications include environmetric settings where analysis of the survival pattern(s) from a set of observations is studied. The presentation includes material on a form of distribution‐free proportional hazards model, known as the Cox regression model.
Pseudo‐Replication
Authors: Stewart‐Oaten Allan
Published: September 2006

Hurlbert defines pseudo‐replication as ‘testing for treatment effects with an error term inappropriate to the hypothesis being considered’. An alternative definition is ‘estimating the size of chance variation without accounting for all its likely sources’.
Radioactivity
Authors: Scott E. Marian
Published: September 2006

Radioactivity is present in all components of the environment, it has two main sources: the first is natural, created at the time of the Earth's formation, the second is anthropogenic, created more recently as a result of man's activities. The presence of radioactive elements in the environment has stimulated a great deal of research on the distribution, transport and biological effects of environmental radioactivity. Statistical methods have an important role to play in many areas of the scientific study of radioactivity, including construction of sampling plans, monitoring and mapping, predictive modeling (in the presence of uncertainty), and risk assessment.
Random Field, Gaussian
Authors: Worsley Keith J.
Published: September 2006

The
Gaussian
random field
Y
(
t
),
t
 ∈ 
T
, is one of the most common models used to describe spatial stochastic processes. In many applications, the domain
T
is a subset of
D
‐dimensional Euclidean space (usually
D
 = 2 or
D
 = 3), and the function
Y
(
t
) is almost surely continuous or smooth in
t
. The definition is simple: the Gaussian random field must be multivariate Gaussian at all finite sets of points, that is, [
Y
(
t
1
), …,
Y
(

t
n

)] must be multivariate Gaussian for all
n
 > 0 and all

t
j

 ∈ 
T
. Since the multivariate Gaussian is specified uniquely by its mean vector and variance matrix, then the Gaussian random field is defined uniquely by its mean function
μ
(
t
) = E[
Y
(
t
)] and its covariance function
C
(
s
,
t
) = cov[
Y
(
s
),
Y
(
t
)].
Randomized Branch Sampling
Authors: Valentine Harry T.
Published: September 2006

Randomized branch sampling (RBS) is a special application of multistage probability sampling, which was developed originally by Jessen to estimate fruit counts on individual orchard trees. In general, the method can be used to obtain estimates of many different attributes of trees or other branched plants. The usual objective of RBS is the estimation of a total quantity for a tree or a branch, for example, woody dry matter or volume, leaf dry matter, or counts of tree‐inhabiting insects. RBS also has potential application in the estimation of attributes of river networks and other branched structures.
Ranked Set Sampling
Authors: Patil G.P.
Published: September 2006

Environmental monitoring and assessment typically requires observational data, as opposed to data obtained from controlled experiments. Obtaining such data requires identification of sample units to represent the population of concern, followed by selection of particular units to quantify the characteristic(s) of interest. Sample units are generally the smallest possible units of measurement, such as plots, soil cores, individuals, etc., while typical characteristics of interest include biomass, chemical concentrations or ‘head counts’. Typically the most expensive part of this process is laboratory analysis, while identification of potential sample units is a comparatively simple matter. One can therefore achieve great observational economy if able to identify a large number of sample units to represent the population of interest, yet only have to quantify a carefully selected subsample. This potential for observational economy was recognized for estimating mean pasture and forage yields in the early 1950s when McIntyre proposed a method, later coined ranked set sampling (RSS) by Halls and Dell, and currently under active investigation in various quarters.
Record Linkage
Authors: Winkler William E.
Published: September 2006

Record linkage is the methodology of identifying pairs of records associated with entities from two or more files. Entities may be persons or businesses. Record linkage also refers to finding duplicates within files. Sometimes, records are linked using unique identification numbers such as a Social Security Number. Typically, non‐unique identifiers such as names, addresses, and other information are used. These methods of record linkage are called exact matching. Methods for exact matching may be based on
ad hoc
rules that may be applicable in a limited number of situations. Methods may also be based on a formal mathematical model as discussed in this article.
Regression Trees
Authors: Leblanc Michael
Published: September 2006

Regression trees are a flexible statistical method for modeling the conditional distribution of a response variable given a vector of predictors or covariates. Trees have several advantages compared with classical parametric regression methods: they are completely nonparametric; they include powerful variable subset selection; they are robust to outliers in the covariate space and are used easily on a wide variety of data structures.
Regularization Methods
Authors: Lukas Mark A.
Published: September 2006

Over the last 40 years there has been rapid growth in the field of inverse problems. In general terms, a direct problem is to find the effect from some cause using a completely specified model. For an inverse problem, the effect is known (in practice, usually imprecisely as measured data), and it is desired to find either the cause or some component of the model itself. Environmental applications of inverse problems occur in different types of remote sensing, image restoration, chemical sorption, ecology, and hydrology. Unlike direct problems, inverse problems are usually ill‐posed. A problem is well‐posed if a solution exists, is unique, and depends continuously on the data. An ill‐posed problem is inherently difficult to solve in practice since, even if it has a unique solution, the solution is sensitive to errors in the data. In order to obtain a reasonable approximate solution, it is essential to stabilize the problem using some method of regularization.
Reproductive Toxicology
Authors: Williams Paige L.
Published: September 2006

Reproductive toxicology is the study of adverse effects of environmental agents on the male and female reproductive systems, including reduced fertility, menstrual disorders, spontaneous abortion, developmental defects including low birth weight, and genetic diseases affecting the reproductive system and offspring. In particular, there is concern regarding the high rate in humans of pregnancy, congenital malformations, and serious developmental defects possibly due to environmental factors. Also of specific interest is an apparent increase in male sexual effects such as reduced sperm production and testicular cancer. Public health concern regarding these reproductive issues has been heightened by an increase in the number of women in the workforce during their childbearing years, and by the large increase in numbers of couples seeking treatment for infertility. While the cause of many of these adverse reproductive outcomes is unknown, at least some proportion can be attributed to known environmental agents.
Residuals
Authors: Lee Alan J. , Seber George A.F.
Published: September 2006

Many scientific problems involve modeling the relationship between variables. Regression analysis is concerned with modeling the behavior of a variableY(the response or dependent variable) in terms of a setx1, …,xpof explanatory variables (also called covariates, regressors, and independent variables). The model takes the form E(Y) = f(x1, ,xp; β) wherefis one of a ‘sensible’ family of functions, and β is a parameter vector which must be estimated from the data. We also need to postulate the statistical distribution ofyfor a fixed covariate vector x = (x1, …,xp)T. The assumed form offis tentative and we need various diagnostic checks to assess its suitability. To do this, we need a measure of the discrepancy between each datumyand the ‘fitted value’ŷpredicted by the model. These measures are known asresiduals. The precise form of the residual depends on the type of data (continuous data, counts, binary data) and the form of the model.
Residuals, Studentized
Authors: Paul Sudhir R.
Published: September 2006

A brief review of the procedures for detecting outliers in linear regression models using studentized residuals is provided. Several single and multiple outlier detection procedures and their advantages and disadvantages are discussed.
Resource Selection
Authors: Thomas Dana L. , McDonald Lyman L.
Published: September 2006

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.
Respiratory Epidemiology
Authors: Coull Brent A. , Schwartz Joel
Published: September 2006

Environmental health scientists now recognize respiratory illness as a potential health effect in both children and adults. Respiratory effects may include asthma, wheezing, altered pulmonary function in the form of respiratory flow or volume, dyspnea (shortness of breath), and bronchitic or chronic bronchitic symptoms. Risk factors having documented associations with respiratory illness or disease include maternal smoking, environmental tobacco smoke, respirable particulate matter, ozone, nitrogen dioxide, and acid aerosols. Other studies have focused on possible protective effects of diet against lung disease in humans. This article focuses on some statistical challenges often encountered in the analysis of respiratory data.
Ripley'sKFunction
Authors: Dixon Philip M.
Published: September 2006

Ripley’sK(t) function is a tool for analyzing completely mapped spatial point process data, i.e. data on the locations of events. These are usually recorded in two dimensions, but they may be locations along a line or in space. This article will only describeK(t) for two‐dimensional spatial data. Completely mapped data include the locations of all events in a predefined study area. Ripley’sK(t) function can be used to summarize a point pattern, test hypotheses about the pattern, estimate parameters and fit models. Bivariate or multivariate generalizations can be used to describe relationships between two or more point patterns. Applications include spatial patterns of trees, herbaceous plants, bird nests and disease cases.
Risk Assessment, Probabilistic
Authors: Carrothers Timothy J. , Thompson Kimberly M. , Burmaster David E.
Published: September 2006

A primary criticism of environmental risk assessment as it has been practiced in the last 20 years has been the failure of analysts to properly account for issues of variability and uncertainty. Many risk assessments focused on producing ‘point estimates’ of risks have provided risk managers and decision makers with information that is at best incomplete and at worst dangerously misleading. As the field of risk assessment has matured, techniques for better treatment of variability and uncertainty have been developed and incorporated into what is known as ‘probabilistic’ risk assessments. In contrast to the point estimate approach, where single values are assumed for each model input, the probabilistic approach quantifies the possible range of values that each input may take, as well as the probability associated with each value. Modern computational power then allows the analyst to generate a multidimensional distribution of risk that reflects both the variability of risk across different individuals in the population as well as the uncertainty associated with each estimate.
Risk Assessment, Quantitative
Authors: Stern Alan H.
Published: September 2006

Two different forms of risk assessment are commonly in practice. They have somewhat different orientations and address different regulatory and communications goals. One form of risk assessment can be referred to as safety assessment. This type of assessment seeks to identify the largest level of exposure or dose that can reasonably be expected to be without adverse effect. It does not necessarily provide quantitative information on the risk associated with exposure above this ‘safe’ level. The other type of risk assessment seeks to quantify the risk associated with any exposure or dose of an environmental agent. This latter form of risk assessment is the focus of this article.
Robust Inference
Authors: Hampel Frank
Published: September 2006

Robust inference is inference that is insensitive to (smaller or larger) deviations from the assumptions under which it is derived. Some very commonly used assumptions in statistics are normality, independence, identical distributions, linearity (e.g. in regression), and stationarity of stochastic processes. As a rule, such assumptions are only approximations to reality, and the questions arise as to what deviations tend to occur in practice, what effects they have on known statistical procedures, and how to develop better, ‘more robust’ procedures when deemed desirable. To answer these questions, new statistical concepts have proven useful.
Robust Quantile Regression
Authors: JureČková Jana
Published: September 2006

Robust quantile regression is a collection of statistical procedures based on
regression, autoregression and conditional quantiles
and on
regression and autoregression rank scores
. These procedures can replace the classical estimation and testing procedures in the linear regression and autoregression models, based on least squares, in situations when we cannot guarantee that our observations follow the normal distribution. The character of these methods is nonparametric (i.e. they do not assume any specific probability distribution of the observations), and robust (with respect to outliers in the dependent variables). Moreover, the procedures based on the regression rank scores do not depend on an eventual nuisance regression, because the regression rank scores are invariant to the regression parameters, similarly as the ordinary ranks are invariant to the shift in location. Regression quantiles and regression rank scores are dual in the linear programming sense, but their relation also extends the duality of the quantiles (order statistics) and ranks from the location to the linear regression (autoregression) models.
Sample Support
Authors: Gotway Crawford Carol A.
Published: September 2006

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 article provides: 1. a more complete definition of sample support as used in geostatistics; 2. a description of the problems that arise in working with data of differing supports; 3. a brief overview of the solutions to change of support problems.
Sediment Transport
Authors: James Alec E.
Published: September 2006

Sediment transport occurs when the flow of water over a surface is rapid enough to erode and move surfacial sediments; if the current decreases then deposition of all or some of the sediments will occur. In practice the process is extremely complex and once movement is initiated the properties of the fluid are modified by the presence of the irregularly shaped solid particles from which the bed‐form is comprised. The range of particle size is large and this in itself leads to different ways of describing sediment transport phenomena. There are two fundamental modes of transport, the first in which particles roll or slide along the bed of a river or the sea and the second in which the particles are entrained by the flow and move in suspension with the water mass. Evidently the amount of material transported will depend on factors such as the particle size and shape; the density will be important, as will the local intensity of turbulence and the magnitude of the average advective velocity of the water together with its own density.
Risk Assessment, Seismological
Authors: Brillinger David R.
Published: September 2006

Seismic risk assessment(SRA) may be defined as the process of estimating the probability that certain performance variates at a location of interest exceed relevant critical values, within a specified time period, as a result of nearby seismic events. Possible performance variates include: maximum acceleration, force (on an object), amplitude of vibration at a specified frequency, damage.
Sensitivity and Specificity
Authors: Piegorsch Walter W.
Published: September 2006

A brief introduction is given on the use of the terms ‘sensitivity’ and ‘specificity’ in environmental applications. Emphasis is directed at diagnostic testing/screening, where the terms delineate forms of true positive and true negative rates of the diagnostic outcomes.
Simulated Annealing
Authors: Høst Gudmund
Published: September 2006

Simulated annealing is a Monte Carlo method for combinatorial optimization. It has found wide applications to problems within fields, such as image analysis, electronic circuit design and spatial sampling.