bluuebunny/crossref_metadata_2025_split huggingface dataset:
Stereology including tessellations
Authors: C. Marriott F. H. 
Published: September 2014

Abstract
Sampling methods used in stereology are briefly discussed. The fundamental formulae give estimates of volume ratios for the volume of a particular phase, the area of two‐dimensional structures, the length of linear features, and the number of particles. Some inference is also possible about curvature of surfaces. Estimation of the size distribution of spherical particles is described, and the extension to ellipsoidal particles, possible only in restricted cases, is discussed. The properties of tesselations, particularly the cell model and the Johnson–Mehl model for crystal growth, are described. Mathematical morphology, developed by Matheron and Serra as a system of transformations of digitized images, is a valuable technique for revealing relevant features, and stereological indices based on the modified images may be compared.
Up‐and‐Down Method
Authors: Gross Alan J. , C. McLean David 
Published: September 2014

AbstractThe Up‐and‐Down method is employed in dose–response studies where the aim is to model the probability of a binary outcome in terms of covariates, one of which is the dose being administered. The method allows for sequential choice of doses, dependent on the outcome of the previous dose. It is used in toxicology experiments in which the outcome is death: following a death, the next unit receives a lower dose, whereas a survival leads to the dose being increased.
Quantal Response Models
Authors: Morgan Byron J.T. 
Published: September 2014

AbstractIn a quantal response experiment, a particular organism is selected and exposed in groups to different concentrations of a drug for a fixed time, and a discrete response is observed (such as death or survival). In the binary response case, a tolerance or threshold assumption yields a model for the probability of response at a particular dose that has the form of the cumulative distribution function of the tolerances. The median effective dose (ED50) is the dose level that results in an expected 50% response under certain model assumptions. The Spearman–Karber estimate is a nonparametric estimate of the ED50. This article also surveys parametric estimates, which can have improved precision. Parametric models are discussed, including extensions for polytomous responses and multivariate responses. Also discussed are the effect of overdispersion, and design issues such as sequential methods for finding the point at which a certain probability of response occurs.
Correspondence Analysis of Longitudinal Data
Authors: Van der Heijden Peter G. M. 
Published: September 2014

Abstract
Correspondence analysis is an exploratory tool for the analysis of associations between categorical variables, the results of which may be displayed graphically. For longitudinal data with two time points, an analysis of the transition matrix (showing the relative frequencies for pairs of categories) provides insight into the structure of departures from independence in the transitions. Transitions between more than two time points can be studied simultaneously. Examples are provided.
Instrumental Variables: Overview
Authors: Dunn Graham 
Published: September 2014

Abstract
We describe the application of instrumental variable methods to cope with model identification problems arising from either hidden selection effects or measurement errors. The problem of hidden selection effects is illustrated by reference to adjustment to non‐ or partial compliance with allocated treatment in a randomized controlled trial. Measurement error problems are illustrated by reference to two potential areas of application: (1) the estimation of the effect of environmental exposure on risk of disease when exposure is measured with error (i.e. measurement error models in epidemiology), and (2) comparative calibration of two measurement methods when both are subject to measurement errors (i.e. method comparison studies).
Intervention Analysis in Time Series
Authors: Helfenstein Ulrich 
Published: September 2014

Abstract
When data are collected in the form of dependent time series data, important questions are concerned with “changes” in the series. Changes may be “man made” or they may arise “naturally”: How efficient was a preventive program to decrease the monthly number of accidents? How did the pattern of morbidity change after an environmental accident? Notifications of diseases or accidents and so on, are often collected in regular intervals. ARIMA models allow the stochastic dependence of consecutive data to be modeled flexibly. Intervention analysis is an extension of ARIMA modeling allowing the study of the structure of changes of ARIMA processes. Since the series may be nonstationary, large changes of the series could occur even when no intervention takes place. Intervention analysis may allow an investigator to distinguish between what can be expected due to nonstationarity alone and what cannot. Analogous questions of “change” may arise when studying time series data recorded in an individual patient. This article reviews basic concepts of intervention analysis. The methods are illustrated by medical applications.
Non Fourier Waveforms
Authors: McCoy E. J. 
Published: September 2014

Abstract
The discrete Fourier transform (DFT), which gives us information about the “frequency” domain characteristics of data, is probably the most ubiquitous orthogonal data transform, and uses basis functions made up of sines and cosines at different frequencies. Often, we have to analyze signals whose frequency behavior changes over time. In such cases, we can utilize transforms with non‐Fourier basis functions, which can better represent nonstationary behavior.
Allometry
Authors: Sprent P. 
Published: September 2014

Abstract
Allometry is a study of shape changes associated with size. Most living organisms change shape as they grow in order to overcome biological or physical constraints. Simply, allometry occurs when two size measurements exhibit an approximately linear relationship between their logarithms. Suggestions made for multivariate extensions range from applications of principal component analysis to studies of size variables and shape vectors. The limitations imposed by Euclidean geometry and other disadvantages with these approaches have been removed by considering curvature and tangential directions at a series of points called landmarks and by coordinate transformations.
Chronomedicine
Authors: CornÉlissen Germaine , Halberg Franz 
Published: September 2014

AbstractChronobiology (fromchronos, time;bios, life; andlogos, science) investigates the mechanisms underlying variability in the otherwise unassessed physiological range, including rhythms found in us, resonating with cycles around us. Broad time structures (chronomes) consisting of deterministic chaos and trends organized by rhythms are found in organisms and in their environments. They are mapped by chronomics as the reference values for both an applied chronomedicine and a basic chronobiology. Chronomics quantify health, identifying new disease risks, diagnosing predisease and overt illness, enabling timely and timed treatment (Rx), and validating the short‐ and long‐term efficacy of a givenRxon an inferential statistical individualized (as well as population) basis.
Critical Care
Authors: Corwin Howard L. 
Published: September 2014

AbstractThe randomized controlled trial (RCT) has become the “gold” standard for clinical research. However, the complex nature of critical illness has made the design and conduct of RCTs difficult. Research in critically ill patients presents unique challenges. The disease processes are often not well defined. There are also multiple therapeutic interventions being administered and the disease processes themselves often have a variable clinical course. Finally, outcome selection is a challenge, mortality (short or long) versus nonmortality outcomes. The last few years have seen the publication of the results of five RCTs that have had a major impact on the practice of critical care.
Medico–Legal Cases and Statistics
Authors: Gastwirth Joseph L. 
Published: September 2014

AbstractMedico‐legal statistics concerns the use of data from animal studies, case–control and cohort studies and clinical trials in the context of the legal and regulatory system. Statistical findings are submitted to courts and governmental agencies to demonstrate that a new drug is safe and efficacious; exposure to a chemical in the workplace is harmful or not as well as in product liability cases. The validity of clinical findings that are used in advertisements claiming a product is superior to a competitor's or in support of a patent are subject to legal challenge. Recently, the adequacy of the information provided to patients who participate in clinical trials and similar studies has become an issue. This aspect of trials is especially important when the main investigators or the University have a financial interest in the outcome either through stock ownership or options or a royalty agreement.
Sampling With Probability Proportional to Size
Authors: Czaja Ronald 
Published: September 2014

Abstract
Sampling with probability to proportionate to size (PPS), as the name implies, involves sampling elements that are typically arranged into natural groupings of different sizes. Sampling PPS is an efficient design when a list of the population is not available; the elements are in clusters or natural groups that differ greatly in size; it is important to control the sample size; costs and equalizing interviewer workloads are important; the use of natural divisions is possible and supplementary information is available by the natural divisions; and when the sample must be drawn in multiple stages. This entry presents a detailed example of a PPS design, a multistage area probability design, and discusses a random digit telephone sample design that uses PPS sampling.
Systematic Sampling Methods
Authors: Bellhouse D. R. 
Published: September 2014

AbstractSystematic sampling is a sampling technique that is used for its simplicity and convenience. At its simplest, a systematic sample is obtained by selecting a random start near the beginning of the population list and then taking every unit equally spaced thereafter. The technique can be generalized to include systematic sampling schemes with probability proportional to an auxiliary variable. In many situations, systematic sampling is statistically efficient when compared to other sampling schemes. This is especially true in populations with linear and quadratic trends and autocorrelated populations. For populations in random order systematic sampling, it is equivalent to simple random sampling. A major drawback to systematic sampling is that it does not admit an unbiased estimator of variance with respect to the sampling design. Variance estimation must rely on an assumed underlying structure in the population.
Forward Search
Authors: Atkinson A. C. , Riani Marco 
Published: September 2014

Abstract
This is a powerful robust statistical method for exploring the relationship between data and fitted models. It aids discovery of clusters of observations and previously unidentified important subsets of the data as well as revealing groups of outliers. Examples are given with regard to the use of the forward search for regression and generalized linear models, and for multivariate data. The method is to search through the data, fitting subsets of increasing numbers of observations, with outliers being included towards the end.
Dummy Variables
Authors: Darlington G. A. 
Published: September 2014

Abstract

Categorical explanatory variables can be included in models via the use of dummy variables. In a regression model with an intercept,
K
− 1 linearly independent dummy variables must be defined to represent a
K
level categorical variable. Indicator variables are commonly used to define a set of dummy variables. In a regression model with an intercept, indicators are derived for
K
− 1 of the
K
possible levels and the remaining level is the referent or baseline category. Overall tests regarding the categorical variable will not depend on the choice of dummy variable definitions. However, the interpretation of the coefficient for each dummy variable will depend on the coding used.
Measurement Scale
Authors: Hand David J. 
Published: September 2014

Abstract
The measured variables analyzed in statistics are reflections of aspects of the system being studied. As such, the relationships between values of the variables must reflect properties of the attributes being studied. Different types of measurement scale, amongst which the most familiar are nominal, ordinal, interval, and ratio, reflect different properties of the attributes. Incorrect conclusions can be drawn if a statistical analysis fails to take appropriate account of this relationship between the objects of study and their numerical representations.
Model, Choice of
Authors: S. Matthews John N. 
Published: September 2014

Abstract
The choice of which statistical model to use in a given application is a complex matter, which draws not only on the technical expertise of the statistician but also on the nature of the application and the purpose of the analysis. Different purposes may require quite different models to be applied to the same dataset. The role of modeling in clinical trials, epidemiology, and general biostatistics is discussed. The relative contribution of expertise both in the area of application and in the relevant statistical issues is explored. The use of sensitivity analyses to ensure that substantive conclusions are not heavily dependent on model assumptions is stressed. A strong theme throughout the article is that the judgment of the biostatistician plays an inescapable role in an activity, which nonstatisticians too often see as wholly objective.
Multiple Linear Regression
Authors: Matthews David E. 
Published: September 2014

AbstractMultiple linear regression involves finding the best‐fitting surface of a suitable functional form that relates the values of explanatory variables,X1, …,Xk, and the mean value of a response variable,Y, given values ofX1, …,Xk. The objectives of regression modeling are to determine whetherYand one or more of the explanatory variables are associated in some systematic way, and to estimate or predict the value ofY, or its mean, corresponding to known values of a selected subset ofX1, …,Xk. We describe methods of estimation, variable selection, statistical inference, and diagnostic checking of the assumed model and any associated unknown parameters, giving due importance to their statistical and scientific interpretations. An example concerning the relationship between oxygen uptake and age, weight, sex, the time required to run 1.5 miles, and various pulse rates for participants in a physical fitness workshop illustrates these concepts concretely. Finally, we outline the close connection between ordinary and weighted linear regression.
Separate Families of Hypotheses
Authors: Braganca Pereira Basilio 
Published: September 2014

AbstractIn the last forty years since statistical procedures were first developed to test separate (nonnested) families of hypotheses, a huge amount of literature has developed for testing a null model against one or more separate alternatives. In the first two decades, mainly statisticians were interested in this problem. During the eighties the econometricians took a great interest and in the nineties, Bayesian statisticians developed some new results on the subject. The purpose of this paper is to given an introductory overview of the subject and an updated bibliography.
Variance Components
Authors: Solomon P. J. 
Published: September 2014

AbstractRandom variation may have a complex structure, with several identifiable sources and corresponding components of variance. In a hierarchical or multilevel model, parameters may change, for example, between individuals, their variation being measured by variance components. This article reviews the history of the study of variance components and describes methods of estimation. Topics include synthesis of variance, empirical Bayes methods, nonnormal models, and model assessment and prediction.
Cox Regression Model
Authors: Sasieni Peter 
Published: September 2014

AbstractIn 1972, D.R. Cox proposed the semiparametric modelfor the hazard at timetfor an individual with covariatesz. Here, the hazard is the instantaneous conditional probability of failure attgiven that failure has not happened beforet.The Cox model has had enormous influence in the theory and practice of biostatistics, and this article surveys its definition, history, basic use, estimators and algorithms, asymptotic properties, use of time‐dependent covariates, model checking, and alternatives and extensions.
Structural Time Series Models
Authors: Harvey A. , Koopman S. J. 
Published: September 2014

AbstractStructural time series models are set up in terms of components, such as trends and cycles, which have a direct interpretation. Their statistical treatment is based on the state space form and the Kalman filter. Signal extraction is carried out by smoothing algorithms. Models may be constructed for multivariate series, and explanatory and intervention variables may be included. Nonlinear and non‐Gaussian models are handled using simulation techniques.
Canonical Correlation
Authors: Das Shubhabrata , Sen Pranab K. 
Published: September 2014

AbstractThe article starts with the genesis of canonical correlation from the product moment correlation and defines canonical correlation from the various angles including algebraic and geometric approaches. The different issues related to interpreting canonical correlation analysis, for example, canonical coefficients, canonical loadings, and redundancy coefficients are highlighted. Relationship with other multivariate methods like principal component analysis, factor analysis, and MANOVA have also been outlined. Then the article dwells on the sampling distribution of the sample canonical correlation and the related inference problems, while touching upon the relevant resampling methods in this context. Various generalizations and extensions are taken up next, with emphasis on the treatment of dependence between more than two sets of variables as well as constrained dependence under problem specific restrictions on the coefficients. The article concludes with a narration of issues related to applications, specially in the field of Biostatistics and a reference to key articles in this domain.
Biostatistics, an overview
Authors: Byron Brown W. 
Published: September 2014

Abstract
Biostatistics is concerned with the development and use of statistical methods to solve problems and to answer questions that arise in human biology and medicine. Its development is traced through early work in vital and health statistics, and in heredity, with the important influence of R.A. Fisher on experimental design and statistical inference. Applications in clinical trials, epidemiology, psychometrics, and health services research are described. Current challenges include the impact of computers, Bayesian methods, the use of data banks, longitudinal studies, and research on the human genome. The organization of biostatistics as a professional discipline is discussed.
B
ayes' Theorem
Authors: Lindley Dennis V. 
Published: September 2014

Abstract
Bayes' Theorem, which plays a central role in Bayesian inference, relates the probability of an uncertain event after additional knowledge has been obtained, to the probability before the acquisition of that knowledge, by multiplying by the likelihood (i.e. the probability of the additional information given the occurrence of the event). An alternative formulation is that the posterior odds on the event is obtained from the prior odds by multiplying by the likelihood ratio.
Density Estimation
Authors: Scott D. W. 
Published: September 2014

Abstract
The “density estimation” article highlights the dual roles of the graphical exploration of data as well as the nonparametric estimation of probabilities. Estimators described in detail include the histogram, frequency polygon, averaged shifted histogram, and kernel method. The basic theory of estimation is outlined. Data‐based calibration by cross‐validation is described. Several concrete examples are given.
Empirical Bayes, with Application to Genomics
Authors: Morris Carl N. , Christiansen Cindy L. 
Published: September 2014

AbstractWhen certain estimation situations are encountered many times, the data from all these situations can be used to construct estimates for each individual case. This overview shows how empirical Bayes has evolved and expanded since its 1955 origins in order to useful practical procedures, which are good not only asymptotically but also in moderately sized samples. Various distributional models are described, as is an application to gene expression data.
The Theory of Estimating Functions
Authors: Desmond A. F. , Godambe V. P. 
Published: September 2014

AbstractThe aim of this article is twofold. First, we demonstrate that the methodology of estimating functions produces a unification and extensions of approaches to statistical modeling and inference, both parametric and semiparametric. Secondly, we illustrate via selected examples, how this methodology applies in biostatistics. We have limited our discussion, here, to case–control studies, prospective and retrospective sampling, and overdispersion.
Fiducial probabiltiy including confidence intervals, nuisance factors and prediction
Authors: Seidenfeld Teddy 
Published: September 2014

AbstractFiducial probability was introduced by R. A. Fisher in 1930, as a method by which probability statements could (apparently) be made about an unknown parameter value without recourse to the Bayesian tools of prior and posterior probability. In a simple univariate one‐parameter case, this involves inversion of a probability statement from the distribution function. In other cases, it may involve a pivotal quantity whose distribution is independent of the parameter. The resulting statements are often similar to Bayesian posteriors with uniform priors, and fiducial intervals are often numerically equivalent to confidence intervals, although the logical structure is quite different. In some cases, notably the ratio of two normal means (the Creasy–Fieller problem) and the difference between two normal means with different variances (the Behrens–Fisher problem) fiducial and confidence intervals differ. The relationship between fiducial and Bayesian inference is discussed here in some detail.
Law of Large Numbers: Theory
Authors: Janssen Paul 
Published: September 2014

Abstract
It is well known that the sample mean, based on a sequence of independent random variables with common distribution, is a weakly consistent estimator as well as a strongly consistent estimator for the population mean. The first property is the famous weak law of large numbers (Khinchin), the second property is the strong law of large numbers (Kolmogorov). Both laws are key results of modern probability theory. Similar properties hold for more complicated sequences of random variables, for example, for sequences satisfying the stationarity assumption or for martingale sequences. These extensions are of crucial importance for statistical applications in ergodic theory and survival analysis.
Limit Theorems
Authors: Zabell S. L. 
Published: September 2014

Abstract
These concern the asymptotic behavior of distributions of random variables in large samples. Classical results include the weak and strong laws of large numbers, the central limit theorem, and the law of the iterated logarithm. Other results discussed briefly are the ergodic theorem, the martingale convergence theorem, Skorokhod's theorem, and the use of coupling methods.