Bücher der Reihe SpringerBriefs in Statistics

Through real-world datasets, this book shows the reader how to work with material in biostatistics using the open source software R.

This monograph presents a radical rethinking of how elementary inferences should be made in statistics, implementing a comprehensive alternative to hypothesis testing in which the control of the probabilities of the errors is replaced by selecting the course of action (one of the available options) associated with the smallest expected loss.Its strength is that the inferences are responsive to the elicited or declared consequences of the erroneous decisions, and so they can be closely tailored to the client's perspective, priorities, value judgments and other prior information, together with the uncertainty about them.

This book discusses the payout phase of the old-age pension saving scheme, the so-called effective premium, and offers detailed actuarial models and analyses of five old-age pension saving products used in practice. These include the basic permanent monthly annuity, without any benefits for survivors, as well as products which, in addition, also include benefits for survivors or authorized persons in the event of the pensioner¿s death. The purpose of the book is to point out the method of determining future old-age pensions from old-age pension savings, and to present the advantages and disadvantages of such a pension. The book also emphasizes the role of the profitability testing of the products and answers questions concerning the effectiveness of old-age pension savings and insurance. The book is primarily intended for students of actuarial and financial mathematics and future economists.

The book shows how risk, defined as the statistical expectation of loss, can be formally decomposed as the product of two terms: hazard probability and system vulnerability. This requires a specific definition of vulnerability that replaces the many fuzzy definitions abounding in the literature. The approach is expanded to more complex risk analysis with three components rather than two, and with various definitions of hazard. Equations are derived to quantify the uncertainty of each risk component and show how the approach relates to Bayesian decision theory. Intended for statisticians, environmental scientists and risk analysts interested in the theory and application of risk analysis, this book provides precise definitions, new theory, and many examples with full computer code. The approach is based on straightforward use of probability theory which brings rigour and clarity. Only a moderate knowledge and understanding of probability theory is expected from the reader.

This book discusses important applications of the Behrens-Fisher statistic and the False Discovery Rate (FDR). Covered applications include ANOVA and MANOVA under potentially non-normal errors and heteroscedasticity; and an intuitive method of analyzing s x r contingency tables when the column variable is ordinal. This book also explores the novel possibility that these applications may be deemed nonparametric.

This brief monograph is an in-depth study of the infinite divisibility and self-decomposability properties of central and noncentral Student's distributions, represented as variance and mean-variance mixtures of multivariate Gaussian distributions with the reciprocal gamma mixing distribution. These results allow us to define and analyse Student-Lévy processes as Thorin subordinated Gaussian Lévy processes. A broad class of one-dimensional, strictly stationary diffusions with the Student's t-marginal distribution are defined as the unique weak solution for the stochastic differential equation. Using the independently scattered random measures generated by the bi-variate centred Student-Lévy process, and stochastic integration theory, a univariate, strictly stationary process with the centred Student's t- marginals and the arbitrary correlation structure are defined. As a promising direction for future work in constructing and analysing new multivariate Student-Lévy type processes, the notion of Lévy copulas and the related analogue of Sklar's theorem are explained.

In statistics, the Kalman filter is a mathematical method whose purpose is to use a series of measurements observed over time, containing random variations and other inaccuracies, and produce estimates that tend to be closer to the true unknown values than those that would be based on a single measurement alone. This Brief offers developments on Kalman filtering subject to general linear constraints. There are essentially three types of contributions: new proofs for results already established; new results within the subject; and applications in investment analysis and macroeconomics, where the proposed methods are illustrated and evaluated. The Brief has a short chapter on linear state space models and the Kalman filter, aiming to make the book self-contained and to give a quick reference to the reader (notation and terminology). The prerequisites would be a contact with time series analysis in the level of Hamilton (1994) or Brockwell & Davis (2002) and also with linear state models and the Kalman filter - each of these books has a chapter entirely dedicated to the subject. The book is intended for graduate students, researchers and practitioners in statistics (specifically: time series analysis and econometrics).

This book focuses on multiple comparisons of proportions in multi-sample models with Bernoulli responses. First, the author explains the one-sample and two-sample methods that form the basis of multiple comparisons. Then, regularity conditions are stated in detail. Simultaneous inference for all proportions based on exact confidence limits and based on asymptotic theory is discussed. Closed testing procedures based on some one-sample statistics are introduced. For all-pairwise multiple comparisons of proportions, the author uses arcsine square root transformation of sample means. Closed testing procedures based on maximum absolute values of some two-sample test statistics and based on chi-square test statistics are introduced. It is shown that the multi-step procedures are more powerful than single-step procedures and the Ryan-Einot-Gabriel-Welsch (REGW)-type tests. Furthermore, the author discusses multiple comparisons with a control. Under simple ordered restrictions of proportions, the author also discusses closed testing procedures based on maximum values of two-sample test statistics and based on Bartholomew's statistics. Last, serial gatekeeping procedures based on the above-mentioned closed testing procedures are proposed although Bonferroni inequalities are used in serial gatekeeping procedures of many.

This short book elaborates on selected aspects of stochastic-statistical dependencies in multivariate statistics. Each chapter provides a rigorous and self-contained treatment of one specific topic, poses a particular problem within its scope, and concludes by presenting its solution. The presented problems are not only relevant for research in mathematical statistics, but also entertaining, with elegant proofs and appealing solutions. The chapters cover correlation coefficients of bivariate normal distributions, empirical likelihood ratio tests for the population correlation, the rearrangement algorithm, covariances of order statistics, equi-correlation matrices, skew-normal distributions and the weighted bootstrap. This book is primarily intended for early-career researchers in mathematical statistics, but will also be interesting for lecturers in the field. Its goal is to rouse the reader's interest, further their knowledge of the subject and provide them with some useful mathematical techniques.

This book covers some biostatistical methods and several case studies useful to interpret and analyze dental research in the areas of orofacial pain and temporomandibular disorders. It will guide practitioners in these fields who would like to interpret research findings or find examples on the design of clinical investigations. After an introduction dealing with the basic issues, the central sections of the textbook are dedicated to the different types of investigations in sight of specific goals researchers may have. The final section contains a recent approach based on nonparametric permutation tests which can be adopted in many practical situations. The field of orofacial pain and temporomandibular disorders is emerging as one of the most critical areas of clinical research in dentistry. Due to the complexity of clinical pictures, the multifactorial etiology, and the importance of psychosocial factors in all aspects of the TMD practice, clinicians often find it hard to appraise their modus operandi, and researchers must constantly increase their knowledge in epidemiology and medical statistics. Indeed, proper methodological designs are fundamental to reaching high levels of internal and external validity of findings in this specific area.

Strategic Economic Decision-Making: Using Bayesian Belief Networks to Solve Complex Problems is a quick primer on the topic that introduces readers to the basic complexities and nuances associated with learning Bayes' theory and inverse probability for the first time. This brief is meant for non-statisticians who are unfamiliar with Bayes' theorem, walking them through the theoretical phases of set and sample set selection, the axioms of probability, probability theory as it pertains to Bayes' theorem, and posterior probabilities. All of these concepts are explained as they appear in the methodology of fitting a Bayes' model, and upon completion of the text readers will be able to mathematically determine posterior probabilities of multiple independent nodes across any system available for study. Very little has been published in the area of discrete Bayes' theory, and this brief will appeal to non-statisticians conducting research in the fields of engineering, computing, life sciences, and social sciences.

This monograph provides an extensive treatment of the theory and applications of the celebrated Borel-Cantelli Lemma. Starting from some of the basic facts of the axiomatic probability theory, it embodies the classical versions of these lemma, together with the well known as well as the most recent extensions of them due to Barndorff-Nielsen, Balakrishnan and Stepanov, Erdos and Renyi, Kochen and Stone, Petrov and the present author. The versions of the second Borel-Cantelli Lemma for pair wise negative quadrant dependent sequences, weakly *-mixing sequences, mixing sequences (due to Renyi) and for many other dependent sequences are all included. The special feature of the book is a detailed discussion of a strengthened form of the second Borel-Cantelli Lemma and the conditional form of the Borel-Cantelli Lemmas due to Levy, Chen and Serfling. All these results are well illustrated by means of many interesting examples.All the proofs are rigorous, complete and lucid. An extensive listof research papers, some of which are forthcoming, is provided. The book can be used for a self study and as an invaluable research reference on the present topic.

Statistical shape analysis is a geometrical analysis from a set of shapes in which statistics are measured to describe geometrical properties from similar shapes or different groups, for instance, the difference between male and female Gorilla skull shapes, normal and pathological bone shapes, etc. Some of the important aspects of shape analysis are to obtain a measure of distance between shapes, to estimate average shapes from a (possibly random) sample and to estimate shape variability in a sample[1]. One of the main methods used is principal component analysis. Specific applications of shape analysis may be found in archaeology, architecture, biology, geography, geology, agriculture, genetics, medical imaging, security applications such as face recognition, entertainment industry (movies, games), computer-aided design and manufacturing. This is a proposal for a new Brief on statistical shape analysis and the various new parametric and non-parametric methods utilized to facilitate shape analysis.

This book presents recent advances (from 2008 to 2012) concerning use of the Naïve Bayes model in unsupervised word sense disambiguation (WSD).While WSD, in general, has a number of important applications in various fields of artificial intelligence (information retrieval, text processing, machine translation, message understanding, man-machine communication etc.), unsupervised WSD is considered important because it is language-independent and does not require previously annotated corpora. The Naïve Bayes model has been widely used in supervised WSD, but its use in unsupervised WSD has led to more modest disambiguation results and has been less frequent. It seems that the potential of this statistical model with respect to unsupervised WSD continues to remain insufficiently explored. The present book contends that the Naïve Bayes model needs to be fed knowledge in order to perform well as a clustering technique for unsupervised WSD and examines three entirely different sources of such knowledge for feature selection: WordNet, dependency relations and web N-grams. WSD with an underlying Naïve Bayes model is ultimately positioned on the border between unsupervised and knowledge-based techniques. The benefits of feeding knowledge (of various natures) to a knowledge-lean algorithm for unsupervised WSD that uses the Naïve Bayes model as clustering technique are clearly highlighted. The discussion shows that the Naïve Bayes model still holds promise for the open problem of unsupervised WSD.

This book begins with the fundamental large sample theory, estimating ruin probability, and ends by dealing with the latest issues of estimating the GerberΓÇôShiu function. This book is the first to introduce the recent development of statistical methodologies in risk theory (ruin theory) as well as their mathematical validities. Asymptotic theory of parametric and nonparametric inference for the ruin-related quantities is discussed under the setting of not only classical compound Poisson risk processes (Cram├⌐rΓÇôLundberg model) but also more general L├⌐vy insurance risk processes.The recent development of risk theory can deal with many kinds of ruin-related quantities: the probability of ruin as well as GerberΓÇôShiuΓÇÖs discounted penalty function, both of which are useful in insurance risk management and in financial credit risk analysis. In those areas, the common stochastic models are used in the context of the structural approach of companiesΓÇÖ default. So far, the probabilistic point of view has been the main concern for academic researchers. However, this book emphasizes the statistical point of view because identifying the risk model is always necessary and is crucial in the final step of practical risk management.

This book presents the state of the art in extreme value theory, with a collection of articles related to a seminal paper on the bivariate extreme value distribution written by Professor Masaaki Sibuya in 1960, demonstrating various developments of the original idea over the last half-century.

This volume focuses on predicting users' attendance at a future event at specific time and location based on their common interests. By predicting event attendance, events that better fit users' interests can be recommended, and personalized location-based or topic-based services related to the events can be provided to users.

As explored in this open access book, higher education in STEM fields is influenced by many factors, including education research, government and school policies, financial considerations, technology limitations, and acceptance of innovations by faculty and students.

Singular spectrum analysis (SSA) is a technique of time series analysis and forecasting combining elements of classical time series analysis, multivariate statistics, multivariate geometry, dynamical systems and signal processing.

This book provides an updated account of the regression techniques employed in comparing analytical methods and to test the biases of one method relative to others - a problem commonly found in fields like analytical chemistry, biology, engineering, and medicine.

This concise book for practitioners presents the statistical analysis of operational risk, which is considered the most relevant source of bank risk, after market and credit risk.

New developments in the second edition include: Configural Mediation Models, CFA with covariates, moderator CFA, and CFA modeling branches in tree-based methods.