bluuebunny/crossref_metadata_2025_split huggingface dataset:
Incomplete Block Designs, an Example
Authors: Federer Walter T. , Nguyen Nam‐ky 
Published: September 2014

AbstractThe 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

AbstractUp‐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

AbstractHistorically, 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

AbstractThe 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

Abstract

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

Abstract
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.
Bayesian Graphical Models
Authors: Jensen Finn Verner 
Published: September 2014

AbstractMathematically, 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

Abstract
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

Abstract
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

AbstractStatistical 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

Abstract

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 (High‐Dimensional)
Authors: Pourahmadi Mohsen , Wu Wei Biao 
Published: September 2014

AbstractThe 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

AbstractExtreme 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

Abstract

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

AbstractFor 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

Abstract
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

Abstract

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

Abstract

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

Abstract

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

Abstract
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

Abstract
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

Abstract
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

AbstractRobust 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

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

AbstractA 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

Abstract

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

Abstract
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

AbstractThis 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

AbstractMany 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.