bluuebunny/crossref_metadata_2025 huggingface dataset:
Parallel Computing: Statistical and Environmetric Uses
Authors: Kulperger Reg , Yu Hao
Published: September 2014

The common use of parallel computing has greatly evolved since the original encyclopedia article of 2001. Multicore processors are now quite common, so many computer users have this readily available on their desktop computers and laptops.

Now increasingly large datasets and simulation of complex statistical models are important in the study of many physical systems. Models in various areas, such as environment, biology, and other physical sciences, play an important role in prediction or detection of changes. All these require lots of computing power. Many of these computations can take advantage of parallel or distributed computing. This article discusses some of these ideas and then discusses how these are implemented in one specific language, R. In the present time, one generally no longer has to work at a low‐level programming language, as was the case a decade or two ago, but now certain types of parallel computations can be implemented at a relatively higher user‐friendly level, even with desktop computing.

Parallel computing consists of a computing environment connecting many processors. Instead of the previous generation where dedicated computer architecture was required, a more loose structure of distributed computing is now more common. This article is intended to give the reader an overview of the parallel computing environment, focusing on the statistical uses that can be made as opposed to a more detailed computing or engineering description.
Resampling Methods
Authors: Tu Wanzhu
Published: September 2014

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.
S + SpatialStats
Authors: Vega Silvia C. , Kaluzny Stephen P.
Published: September 2014

S+SpatialStats is an add‐on module to the S‐Plus system for data analysis and graphics. S‐Plus is an environment for data analysis that provides an object‐oriented programming language and a multitude of functions for the statistical analysis of data. +patialStats provides a comprehensive suite of tools designed for the statistical analysis of
spatial
data. The current version, 1.5, features a graphical user interface (GUI), that is menus and dialogs designed for convenient access to the functionality described in this article.
Sensitivity Analysis of Computer Models
Authors: Fassò Alessandro
Published: September 2014

Sensitivity analysis of computer models has been developed over the last decades paralleling the development of massive computer simulations of engineering, chemical, and environmental systems.

Through extensive simulations, global sensitivity analysis is aimed at assessing the importance of each input to the model outputs by means of variance decomposition.

Depending on model complexity and simulation costs, various techniques are available ranging from design of experiments (DOE) to intensive Monte Carlo, metamodeling, and Bayesian inference.
Simulated Annealing
Authors: Høst Gudmund
Published: September 2014

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.
Singular Value Decomposition and High Dimensional Data
Authors: Allen Genevera I. , Perry Patrick O.
Published: September 2014

The singular value decomposition and related principal component analysis are foundational multivariate methods used for dimension reduction and exploratory analysis of high‐dimensional data. Studying this decomposition using random matrix theory, however, reveals troubling behavior when the number of variables is larger than the number of samples. This article surveys random matrix theory results related to the singular value decomposition and high‐dimensional data as well as recent developments such as sparse principal component analysis. Software on the random matrix theory distributions related to the singular value decomposition can be found elsewhere; several software packages implementing methods for sparse principal component analysis are also available.
Uncertainty and Computer Models
Authors: Sain Stephan R.
Published: September 2014

With the explosion of computing power in recent years, computer models have become important tools for scientists to study the behavior of different phenomena as well as for prediction and decision making. However, there are many sources of uncertainty in computer models that can have significant impact on what is learned from such models. The field of uncertainty quantification, which combines elements from statistics, applied mathematics, and computational science, is emerging to provide tools to better understand, quantify, and mitigate the many uncertainties in computer models, and this article covers some of the key issues and problems facing researchers in this area.
Adaptive Designs
Authors: Flournoy Nancy , Oron Assaf P.
Published: September 2014

The designs described in this article involve treatment allocation probabilities that change according to prior data. Such designs are useful to protect from extreme results that might result from unrestricted randomization, to improve power (e.g., when group variances are unknown and unequal), when prior information is too limited to fix the sampling space a priori (e.g., regions of desirable efficacy and unacceptable toxicity are unknown). Procedures are described for studying K‐groups, but emphasis is placed on dose‐finding experiments. Some procedures involve randomization and some are deterministic given past data. Some are model based and others are nonparametric. Some procedures have a specific optimization criterion as a goal (e.g., maximize power or some other utility) and others are heuristically formulated, with large variation in ease of application and subsequent data analysis.
Incomplete Block Designs, an Example
Authors: Federer Walter T. , Nguyen Nam‐ky
Published: September 2014

The subject of statistics deals with variability and how to deal with it. In the planning and conduct of an environmental or ecological investigation, the items used to control variability are (a) refinement of experimental technique, (b) selection of homogeneous material and/or environments, (c) grouping (blocking, stratifying) material into homogeneous subgroups (blocks, strata), and (d) measurement of related variables and use of covariance. There are many ways of blocking (arranging) the experimental units (EUs) in a comparative experiment withvtreatments. If the sample of EUs is from a homogeneous population, then no blocking is required and a completely randomized experiment design (ED) of thevtreatments randomly allotted to thervEUs is used. The replicate number (sample size) for each treatment isrunless unequal replication is desired. If homogeneous blocks of sizevare available to accommodate allvtreatments, a randomized complete block ED (allvtreatments in each block, not necessarily an equal number of times) is used. In many situations, the block size,k, is less thanvand an incomplete block ED (not all treatments in each of the blocks) is used.
Up‐and‐Down Designs
Authors: Flournoy Nancy , Oron Assaf P.
Published: September 2014

Up‐and‐down designs are useful for evaluating and comparing the toxicity of pesticides and other chemical compounds. In particular, the primary goal of an up‐and‐down design in toxicity studies is to estimate the dose having a prespecified toxicity rate Γ,0 < Γ < 1. A secondary goal is to limit the experimental subjects that are given highly toxic exposure. Up‐and‐down designs can be sequential or group sequential.
Generalized Extreme Value Distribution
Authors: Walshaw David
Published: September 2014

Historically, flood frequency analysis constitutes the prime important example in environmental sciences where annual maxima‐based inference on return levels is the ultimate research goal. Meanwhile other ecological variables such as wind, temperature, air pollution concentration, or the thickness of the ozone layer have also become intensive research topics for extreme value analysis in view of possible negative impacts as a result of extremes.

For these purposes the (generalized) extreme value (GEV) distribution is the basic distributional tool. This is in contrast to most statistical inference, which focuses on central measures of a distribution, and where the normal distribution is the most standard model. We review the GEV model, its mathematical motivation, and the statistical estimation of the parameters under the assumption of independent random sample from the model. Our ultimate aim in this respect is the accurate estimation of return levels. The idea of GEV models for block maxima is extended to allow for (short‐range) dependence and clusters in the data, bringing in the idea of theextremal indexas a measure of the degree of clustering at extreme levels.

Throughout the text a practical example illustrates the application of the GEV method. We finish with a brief discussion of the software which we believe will be the most relevant for some time to come, and the related literature.
Lognormal Distribution ‐ Applications
Authors: El‐shaarawi Abdel
Published: September 2014

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.
Matric t‐Distribution: Overview
Authors: Sun Li
Published: September 2014

The
t
distribution was first introduced by W.S. Gosset in 1908. Many environmental processes are modeled by
t
instead of Gaussian distributions in order to incorporate uncertainties fully. Successful applications of this kind include air pollution, health impact and epidemiology. A random variable that possesses a
t
distribution can be represented as a ratio of an independent normal and the square root of a χ
2
random variable divided by its degrees of freedom. The degrees of freedom of the χ
2
distribution represent the uncertainty one has about the location of the distribution. In sampling theory, a
t
distribution can be derived from a sample mean and sample variance.
Skew Distributions
Authors: Ley Christophe
Published: September 2014

Interest in skew distributions has been growing tremendously over the past two decades, driven mostly by applications. Indeed, datasets exhibiting evidence of nonsymmetric distributions are the rule rather than the exception. From a more theoretical perspective, skew distributions have been used as privileged alternatives in the construction of tests for symmetry and related inferential procedures. We review the history and development of skew distributions, describe the most important skewing methods, and present some examples for each method.
Spatial Distribution
Authors: Waller Lance A.
Published: September 2014

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.
Weibull Distribution
Authors: Mateu Jorge
Published: September 2014

The article brings together various results on the Weibull distribution in a unified manner. The introduction contains numerous references regarding applications of the Weibull distribution and the subsequent sections address a variety of theoretical developments. Some of the theoretical developments covered include characterization, extreme value theory, parameter estimation, and goodness‐of‐fit.
Bayesian Graphical Models
Authors: Jensen Finn Verner
Published: September 2014

Mathematically, a Bayesian graphical model is a representation of the joint probability distribution for a set of variables. The most frequently used type of Bayesian graphical models are Bayesian networks, but other types exist and Bayesian networks can be seen as a special type of Chain Graphs. The structural part of a Bayesian graphical model is a graph consisting of nodes and edges. The nodes represent variables. The set of all variables, called the universe, is denotedU. A variable may be discrete or continuous. For the sake of simplicity this article focuses on models with only discrete variables, and refers to the variable values as states. An edge between two nodesAandBindicates a direct influence between the state ofAand the state ofB.
Boxplot
Authors: Iglewicz Boris
Published: September 2014

Tukey introduced several basic exploratory data analytic tools that have since found great popularity and extensive usage. These tools include the stem‐and‐leaf display, the five‐number summary, and a graphical univariate data summary called a box‐and‐whisker plot, which is now typically called a boxplot. The five‐number summary is the basis of a boxplot. It consists of the median, the lower and upper quartiles, and the smallest and largest observation.
Multivariate data visualisation
Authors: McLeod A.I. , Provost S.B.
Published: September 2014

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.
Statistical Graphics
Authors: Wickham Hadley
Published: September 2014

Statistical graphics (let alone visualisation) is a very broad field. This article is my personal take on it, focussing on the works that are most useful for creating insightful graphics. Visualisations work because they display data in a way that is easy for the brain to parse and interpret: this means we need to know a little bit about cognitive psychology, particularly the perception of continuous values, colour and differences. It's also helpful to be aware of what's already been done, so I also summarise the origins the most common statistical graphics, plots of statistical summaries, graphics for high‐dimensional data, display spatial data, and the grammar of graphics.
A
symptotic
R
elative
E
fficiency: Theory
Authors: Hallin Marc
Published: September 2014

The purpose of asymptotic relative efficiency is to compare two statistical procedures by comparing the sample sizes,
n
1
and
n
2
, say, at which those procedures achieve some given measure of performance; the ratio
n
2
/
n
1
is called the
relative efficiency
of procedure one with respect to procedure two. Finite‐sample evaluations being difficult or impossible, a sequence of measures of performances requiring that those sample sizes go to infinity is generally considered. If those measures of performance are indexed by
n
, say, so that
n
1
and
n
2
take the form
n
1
(
n
) and
n
2
(
n
), the limit lim

n
→∞

n
2
(
n
)/
n
1
(
n
), if it exists, is called the
asymptotic relative efficiency
of procedure one with respect to procedure two.
Covariance Matrix Estimation (Estimated Parameters)
Authors: Wu Wei Biao
Published: September 2014

Estimation of covariance matrices of estimated parameters from common estimation procedures are considered. The consistency issue of the covariance matrix estimates is addressed for dependent and nonstationary data. As an application, hypothesis testing for trends in global annual temperature series is performed.
Covariance Matrix Estimation (High‐Dimensional)
Authors: Pourahmadi Mohsen , Wu Wei Biao
Published: September 2014

The article concerns estimation of high‐dimensional covariance matrices. In this case, the sample covariance matrix estimate is typically not consistent. For an improvement, we present various regularization procedures including shrinkage, penalized likelihood estimation, Cholesky decomposition, sparse principal component analysis, and elementwise shrinkage by banding, tapering, and thresholding.
Extreme Value Analysis
Authors: Padoan Simone A.
Published: September 2014

Extreme value theory concerns the behavior of the extremes of a process or processes. The fundamentals of this probability theory have been known since about the beginning of the twentieth century, but the relevant statistical methods for modeling extreme values emerged in the literature only in the past three decades. In fact, since 1980 the literature has seen a flood of applications of statistical extreme values, covering a wide range of areas. These application areas include environmental sciences, including climate, engineering and hydrology, performance assessment as in sports or policing, astronomy, finance, chemometrics, mortality studies, and outlier detection. Further references to specific applications are noted throughout this article.

The aim of this article is to review some fundamentals of extreme value theory and the relevant statistical methods. The emphasis will be on the latter and the applications it has attracted in the literature so far. The article is in two parts. The first part considers univariate extremes and the remainder is for multivariate extremes. Each part begins with a discussion of fundamental theoretical results. This is then followed by a discussion of relevant statistical models, inference, and simulation.
Fuzzy Numbers and Non‐Precise Data
Authors: Viertl Reinhard
Published: September 2014

Real data obtained from measurements of continuous quantities are not precise numbers or vectors but more or less nonprecise. This uncertainty is different from measurement errors and has to be described formally in order to obtain realistic results of data analysis. Real‐life examples are poisons in different environmental media at a fixed time. These are typically not a precise multiple of the scale unit for the measurements. Such data are called
nonprecise
. In the past, this kind of uncertainty was neglected in statistical analysis. The reason behind this was the philosophical idea of the existence of a ‘true’ value which is identified with a real number times the measurement unit; but this is not realistic. The formal description of such nonprecise measurements can be given using so‐called
fuzzy numbers
.
Maximum Likelihood Estimation, Non Regular
Authors: Holland David M.
Published: September 2014

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.
Meta‐Analysis in Environmental Science
Authors: Weerasinghe Swarna
Published: September 2014

Meta‐analysis is an analytical method of synthesizing, systematically combining, and integrating results across different studies with similar research focuses. While limiting the analytical methods applicable to environmental studies, this article presents a step‐by‐step approach to meta‐analysis. Brief descriptions presented in each section of this article cover the initial steps of meta‐analysis such as formulation of a research question, development of a literature search strategy, and assessment of quality of the published literature by reviewing possible biases. Next steps provide essentials of data extraction, methods of meta‐data analysis as well as interpretation of results. An attempt is made to provide hypothetical examples to illustrate each meta‐analytical step. The goal of this article is to provide an overview of the fundamentals of meta‐analysis of environmental studies.
Model Uncertainty
Authors: Chatfield Chris
Published: September 2014

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.
Multiple Comparisons ‐ Applications
Authors: Edwards D.G.
Published: September 2014

In comparing several unknowns, e.g. the means
μ
1
, μ
2
, …, μ
k
of
k
> 2 populations, the classical approach would recommend starting with a test of equality, i.e. test the hypothesis H
0
: 
μ
1
 = μ
2
 = … = μ
k
. The process known as multiple comparisons has historically been considered as the logical next step following a rejection of this ‘omnibus’ test: if we can be confident that some differences among the

μ
i

exist, then
which
pairs μ
i
,

μ
i

'
are different (1 ≤ 
i
 ≠ 
i
′ ≤ 
k
) and (perhaps) how large are these differences? Modern multiple comparisons analysis retains the goal of answering these sorts of questions, though the preliminary test of equality is no longer sacrosanct.
N
eyman‐
P
earson Lemma
Authors: Hallin Marc
Published: September 2014

Named after Jerzy Neyman and Egon Pearson, who published the result in 1933 [1], the Neyman–Pearson lemma can be considered as the theoretical cornerstone of the modern theory of hypothesis testing. Although the situation it is addressing (a
simple
null hypothesis versus a
simple
alternative) is of limited practical value, this lemma paved the way for all further developments of the theory; see Ref. [2] for an overview. We briefly state that fundamental result, and describe some immediate applications to standard one‐sided one‐parameter problems.
Permutation Tests
Authors: Hallin Marc , Ley Christophe
Published: September 2014

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.
Power Analysis
Authors: Conn Paul B.
Published: September 2014

Power analysis is a tool for investigating trade‐offs between error rates, sample size, and precision, and has several different connotations depending on the underlying problem or objective. In the hypothesis testing context, power analysis can be used to investigate trade‐offs between Type I and Type II errors or to investigate the effect of varying sample size on statistical power. Power analysis has a broader definition in the context of environmental statistics, however, being widely used by statisticians to examine trade‐offs when designing sampling programs. In this context, power analysis largely refers to the allocation of survey effort in relation to some desired level of precision. The investigator might compare the effects of different design options (e.g., simple random sampling, stratified random sampling) or different types of estimators (model‐based estimators versus design‐based estimators). Power analysis is best viewed as a prospective tool for optimizing study design to meet objectives with a given set of constraints. In contrast, retrospective power analyses, whereby researchers fail to achieve a “significant” result and argue that it was likely due to insufficient sample size, are flawed and should be avoided.
Regularization Methods
Authors: Lukas Mark A.
Published: September 2014

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.
Robust Inference
Authors: Hampel Frank
Published: September 2014

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.
S
ensitivity
A
nalysis of
S
tatistical
M
odels
Authors: Fassò Alessandro
Published: September 2014

Sensitivity analysis of statistical models is aimed here at finding influential observations that affect the model considered.

In this article, using the so‐called influence curve, a number of techniques are presented for assessing the sensitivity to a single or a group of data in regression analysis, time series, and spatiotemporal models.
Spherical Statistics
Authors: Jupp Peter E.
Published: September 2014

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.
Proportional Hazards Model: Introduction
Authors: Piegorsch Walter W.
Published: September 2014

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.
Zero‐Inflated Data
Authors: Tu Wanzhu
Published: September 2014

As its name suggests, zero inflation indicates that a dataset contains an excessive number of zeros. The word
inflation
is used to emphasize that the probability mass at the point zero exceeds that allowed under a standard parametric family of distributions. Zero‐inflated data are abundant in many disciplines, including the environmental sciences. If not properly modeled, the presence of excess zeros can invalidate the distributional assumptions of the analysis, jeopardizing the integrity of the scientific inferences. The zeros can also create many computational difficulties. Recently, a fair amount of interest has concentrated on the analysis of zero‐inflated Poisson (ZIP) counts. Strictly speaking, however, the data need not follow a Poisson distribution in order to be zero inflated. In this article, a broader definition of the subject is taken; zero inflation is considered as a practical data phenomenon that can be associated with any parametric family of distributions.
Kronecker Product
Authors: Hallin Marc
Published: September 2014

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.
Morphometrics
Authors: Reyment Richard A.
Published: September 2014

Morphometrics is defined as the application of multivariate statistical procedures to the study of variation in morphological characteristics of organisms. As originally implemented, the analyses are based on standard measures (“distances”) spanning critical sites. A more recent introduction is concerned with quantifying outlines of organisms, the data then being a suite of arbitrary coordinate‐pairs around the circumference of the object, obtained by some automatically operating digitization procedure (e.g., the Zahn‐Rosskies method). Geometric morphometrics is the latest class to appear. It relies on diagnostically located “landmarks” that form the basis for superimposition of coordinate systems, visualizations by deformation grids. The first and third of these categories can, without particular difficulty, be allied with environmental indicators by appropriate techniques.
Multivariate Extremes
Authors: Bortot Paola , Gaetan Carlo
Published: September 2014

This paper reviews the main probabilistic results on multivariate extremes. Historically, this branch of probability focused on the limiting distribution of the componentwise maximum of independent and identically distributed random vectors. A number of equivalent asymptotic characterizations are available and are summarized. Inferential issues arising from the statistical application of classical results are discussed. They motivate the development of alternative models for multivariate extremes, based on multivariate threshold exceedances, which have received increasing attention in the literature; these will also be reviewed.
Transformations, Multivariate
Authors: Ruppert David
Published: September 2014

Many of the classical techniques of multivariate analysis, e.g. principal components, factor analysis, canonical correlations, and linear discriminant analysis are based upon the assumption that the data have been sampled from a multivariate normal distribution. These techniques can be quite nonrobust towards some types of deviations from normality, for example heavy‐tails or skewness. When the data deviate from normality, multivariate transformation can re‐express the data as a sample closer to being multivariate normal. In principle, the methodologies developed for transformation to multivariate normality could be used to transform to other multivariate distributions. However, the normal distribution plays such a central role in multivariate analysis that transformation to other multivariate targets has not been considered as important and will not be discussed in this article.
Tree‐Structured Methods
Authors: Leblanc Michael
Published: September 2014

Tree‐structured methods are a class of adaptive statistical procedures used for exploratory data analysis and classification. An important feature of tree‐structured models is that they yield results that can be expressed as a binary decision tree which can often facilitate data exploration.
Nonparametric Curve Estimator
Authors: Tarter Michael E.
Published: September 2014

The roles that nonparametric curve estimators can play are illustrated in studies of polluting chemicals that have built up in the environment and of crop forecasting techniques. The multivariate normal model and model‐free curve estimator representations are compared. Equations and approaches are described that enable researchers to input prior information that divides variates into two categories, variates of primary importance and variates that are nuisances in the sense that their detained distributional structure is relevant solely insofar as its effects on variates of primary importance. It is shown that conditional density estimators can be computed given user‐selected values of nuisance variates, not computed as a second step that follows a first step, which requires the estimation of a high‐dimensional joint distribution. It is argued that this approach resembles parametric methodology that has long been fruitfully employed in the field of experimental design.
Gauss–Markov Theorem in Statistics
Authors: Hallin Marc
Published: September 2014

The Gauss–Markov theorem states that, under very general conditions, which do not require Gaussian assumptions, the ordinary least squares method, in linear regression models, provides best linear unbiased estimators (BLUE), a property which constitutes the theoretical justification for that widespread estimation method.
Inverse Prediction
Authors: Brown Philip J.
Published: September 2014

Inverse prediction concerns predicting one set of measurements from another set when the direction of causation and possibly error operates in the opposite direction. An example is that of calibration in which it is desired to use a cheap and quick but error‐prone measurementY, to predict the true amount of a constituentx, which in itself can be measured accurately in laboratory conditions but at much greater effort or cost. After taking data on samples using both measurements (the training or learning data) it is desired to use the cheap measurement in future.
Least Squares, General
Authors: Haslett John
Published: September 2014

As with least squares (more specifically ordinary least squares, OLS), general least squares (GLS) is formally a criterion, and an extension of the OLS criterion. But, even more than OLS, GLS is most frequently discussed as a method for fitting a specific model, often referred to as the general linear model (GLM).
Logarithmic Regression
Authors: El‐shaarawi Abdel , Viveros(‐aguilera) Román
Published: September 2014

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.
Multicollinearity
Authors: Wakefield Jon
Published: September 2014

Multicollinearity is said to occur when at least one column of the design matrix is linearly dependent on the other columns, and can cause problems of both interpretation and computation in regression analysis. The problem manifests itself when a regressor is highly correlated with another regressor, or a linear combination of a number of regressors. This does not guarantee multicollinearity, however, since two vectors may have correlation one, but be orthogonal. Sometimes this phenomenon is referred to as collinearity but, in this article, this term is reserved for the situation in which several points lie on a line.
Nonlinear Regression‐Extensions
Authors: Smyth Gordon K.
Published: September 2014

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.
Quantile Regression
Authors: Koenker Roger
Published: September 2014

Classical least squares regression may be viewed as a natural way of extending the idea of estimating an unconditional mean parameter to the problem of estimating conditional meanfunctions; the crucial link is the formulation of an optimization problem that encompasses both problems. Likewise, quantile regression offers an extension of univariate quantile estimation to estimation of conditional quantile functions via an optimization of a piecewise linear objective function in the residuals. Median regression minimizes the sum of absolute residuals, an idea introduced by Boscovich in the eighteenth century, and developed by Edgeworth in the nineteenth century.

The asymptotic theory of quantile regression closely parallels the theory of the univariate sample quantiles. Computation of quantile regression estimators may be formulated as a linear programming problem and efficiently solved by simplex or barrier methods. A close link to rank‐based inference has been forged from the theory of the dual regression quantile process, or regression rankscore process. Recent work has extended quantile regression into time‐series, spatial models, survival analysis, and nonparametric estimation.
Regression Diagnostics
Authors: Davison Anthony C.
Published: September 2014

Statistical diagnostics are used to help data analysts detect and find the source of any problems that may have arisen with the application of statistical procedures, and if possible to suggest remedies. Often they have two elements: a graph constructed to highlight potential difficulties and a numerical test statistic intended to help gauge their significance. Regression involves studying the dependence of one or a few variables on others and is perhaps the most widespread statistical activity. Consequently, regression diagnostics have been well studied and are incorporated into most statistical packages. Moreover, the general ideas that underlie them are useful much more widely, with close links togoodness of fitandrobustness.
Shrinkage Regression
Authors: Sundberg Rolf
Published: September 2014

Shrinkage regression refers to shrinkage methods of estimation or prediction in regression situations, useful when there is multicollinearity among the regressors. With a term borrowed from approximation theory, these methods are also called regularization methods. Such situations occur frequently in environmetric studies, when many chemical, biological or other explanatory variables are measured.
Variable Selection via Regularization
Authors: Li Runze , Cui Hengjian
Published: September 2014

Variable selection has been an active research topic since the 1970s. There are hundreds of publications on variable selection. This entry describes regularization methods for variable selection developed in the recent literature. The regularization methods include classical variable selection criteria such as AIC and BIC and modern variable selection approaches such as LASSO, SCAD, and LARS.
Composite Sampling
Authors: Patil G.P.
Published: September 2014

The high costs of laboratory analytical procedures frequently strain environmental and public health budgets. Whether soil, water, or biological tissue is being analyzed, the cost of testing for chemical and pathogenic contaminants can be quite prohibitive. Composite sampling can substantially reduce analytical costs because the number of required analyses is reduced by compositing several samples into one and analyzing the composited sample. By appropriate selection of the composite sample size and retesting of select individual samples, composite sampling may reveal the same information as would otherwise require many more analyses. Many of the limitations of composite sampling have been overcome by recent research, thus providing more widespread potential for the use of composite sampling to reduce costs of environmental and public health assessments, while maintaining and often increasing the precision of sample‐based inference.
Hansen‐Hurwitz Estimator
Authors: Christman Mary C.
Published: September 2014

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.
Model‐Based Inference
Authors: Chambers Ray
Published: September 2014

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.
Multiphase Sampling
Authors: Lesser Virginia M.
Published: September 2014

Multiphase sampling is an extension of two‐phase sampling, also known as double sampling. Multiphase sampling must be distinguished from multistage sampling since, in multiphase sampling, the different phases of observation relate to sample units of the same type, while in multistage sampling, the sample units are of different types at different stages.
Randomized Branch Sampling
Authors: Valentine Harry T.
Published: September 2014

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.
Sampling Agricultural Resources
Authors: Nusser Sarah M. , Zimmer Stephanie A.
Published: September 2014

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.
Added Risk
Authors: West R. Webster
Published: September 2014

Dose–response studies of environmental toxins are designed to determine the detrimental effects associated with exposure to the toxin, over a particular range of exposures. To properly quantify the toxic effect of a toxin, the
background risk
of no exposure to the toxin, R(0), must first be specified. The additional risk incurred by exposure to a dose,
d
, of the toxin is then called the added risk (AR) at this dose and is given by AR(
d
) = R(
d
) – R(0).
Ames Assay
Authors: Margolin Barry H. , Kim Byung‐Soo
Published: September 2014

Who would have thought that
Salmonella
bacteria, the very same strains that are the bane of travelers, would also contribute to human health via their use in bioassays for genetic mutation? Developed by Ames and colleagues in the early 1970s, the Ames assay continues to hold a preeminent position in genetic toxicology. Its applications have grown increasingly diverse, ranging from attempts at cancer prediction to screening of industrial byproducts for possible mutagens. The assay is currently conducted in thousands of laboratories worldwide. The Ames assay has produced a wealth of experimental data over the last two decades. During the same period many authors have proposed mechanistic models for the analysis of Ames data. Much of this modeling, based on radiation ‘hit theory’, derives from the work of Haynes and Eckardt.
Carcinogenesis, Environmental
Authors: Ryan Louise
Published: September 2014

A significant proportion of cancer cases are likely to be attributable to the environment, especially when broadly interpreted to include lifestyle choices such as smoking and diet, as well as chemical exposures encountered in the workplace, air, water or in our food.
Development Toxicity Study
Authors: Regan Meredith M.
Published: September 2014

Development toxicology investigates the impacts on human development of exposure to potentially toxic substances or conditions. Controlled development toxicity studies in laboratory animals play an important role in the toxicological assessment of foods, drugs and chemicals. In contrast to carcinogenicity studies, methods to extrapolate safe exposure levels from animals to humans are not well developed. The mechanisms of most development toxicants are unknown, and statistical methods for carcinogenicity do not directly apply since the outcomes and the experimental design differ. Manifestations of development toxicity include death, malformations, growth alterations, and functional impairment. Improving methods of quantitative assessment of adverse development effects is a current research focus.
Disease Clustering
Authors: Elliott Paul
Published: September 2014

In recent years there has been heightened awareness about the possible effects of environmental pollution on health, reflecting an increasing public expectation of a clean and healthy environment. The public and media alike have focused on the possible risks to individuals and their communities from local sources of industrial pollution. These concerns have to some extent been fueled by scientific uncertainties about the health effects of low levels of pollution. All these issues tend to come to the fore when disease excesses (
clusters
) in the local community are reported or suspected. This article reviews some of the issues affecting the analysis and interpretation of clusters of disease, including examples where evidence of local disease excess is derived from a disease mapping exercise or a point source investigation.