Nonparametric Predictive Inference For Multiple Comparisons
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| Author | : Tahani Maturi |
| Publisher | : |
| Total Pages | : |
| Release | : 2010 |
| Genre | : Analysis of variance |
| ISBN | : |
This thesis presents Nonparametric Predictive Inference (NPI) for several multiple comparisons problems. We introduce NPI for comparison of multiple groups of data including right-censored observations. Different right-censoring schemes discussed are early termination of an experiment, progressive censoring and competing risks. Several selection events of interest are considered including selecting the best group, the subset of best groups, and the subset including the best group. The proposed methods use lower and upper probabilities for some events of interest formulated in terms of the next future observation per group. For each of these problems the required assumptions are Hill's assumption A(n) and the generalized assumption rc-A(n) for right-censored data. Attention is also given to the situation where only a part of the data range is considered relevant for the inference, where in addition the numbers of observations to the left and to the right of this range are known. Throughout this thesis, our methods are illustrated and discussed via examples with data from the literature.
| Author | : Frank Coolen |
| Publisher | : Wiley-Blackwell |
| Total Pages | : 256 |
| Release | : 2012-06-15 |
| Genre | : |
| ISBN | : 9780470723340 |
This book will be the first on NPI and will provide an introduction to and overview of, the approach′s current state of the art. It will be a self-contained treatment of the subject, introducing it to readers, and leading them on to a more advanced and specialist understanding. The Author compares and contrasts NPI theory with classical statistical theory, pointing out the ways in which NPI can enhance current research in areas ranging from operations research to engineering and artificial intelligence. After the initial introductory chapter, the book provides a series of chapters outlining the use of NPI in specific settings, e.g. for real-valued random quantities or for multinomial data. This will be followed by chapters detailing further applications in statistics, providing examples such as NPI for statistical quality and process control, reliability and operations research, with a variety of examples such as maintenance and replacement problems, queuing situations and risk reliability inferences. The foundations and ideas behind NPI will be presented along with an examination and comparison of more traditional approaches of classical and Bayesian statistics, providing further insights into the advantages of NPI. Future directions and the accommodation of multivariate data will also be discussed.
| Author | : Ahmad Mohammad Abdalmonem Aboalkhair |
| Publisher | : |
| Total Pages | : 104 |
| Release | : 2012 |
| Genre | : Predictive statistics |
| ISBN | : |
Abstract:This thesis provides a new method for statistical inference on system reliability on the basis of limited information resulting from component testing. This method is called Nonparametric Predictive Inference (NPI). We present NPI for system reliability, in particular NPI for k-out-of-m systems, and for systems that consist of multiple ki-out-of-mi subsystems in series configuration. The algorithm for optimal redundancy allocation, with additional components added to subsystems one at a time is presented. We also illustrate redundancy allocation for the same system in case the costs of additional components differ per subsystem. Then NPI is presented for system reliability in a similar setting, but with all subsystems consisting of the same single type of component. As a further step in the development of NPI for system reliability, where more general system structures can be considered, nonparametric predictive inference for reliability of voting systems with multiple component types is presented. We start with a single voting system with multiple component types, then we extend to a series configuration of voting subsystems with multiple component types. Throughout this thesis we assume information from tests of nt components of type t.
| Author | : Zhimei Ren |
| Publisher | : |
| Total Pages | : |
| Release | : 2021 |
| Genre | : |
| ISBN | : |
Recent advances in technology have allowed us to collect, store and process an enormous amount of data, bringing unprecedented challenges to interpretable data analysis: first, the structure of data is often complicated, while model assumptions are hard to justify in practice; second, the algorithms used to analyze the data can be extremely complex--think of the convolutional neural nets--making it difficult to develop validity guarantees for the results. Indeed, it has been noticed by researchers that many of the classical statistical methods fail when applied to the modern type of problems--we need a new set of tools to conduct statistical data analysis in the modern era. This dissertation contributes to the toolbox of statistical data analysis in the modern world by presenting several model-free methods for multiple testing and predictive inference. The methods proposed in this dissertation, building upon knockoffs and conformal inference, bypass the modelling of the data structure and the analysis of complex algorithms, and work as wrappers of other (potentially black-box) existing algorithms. Despite the flexibility of these methods, they are guaranteed to achieve statistical validity under the minimal set of assumptions. The validity and efficacy of these methods are evaluated in extensive numerical experiments. Applying these methods to real genetic and clinical data has led to new scientific insights.
| Author | : Deborah G. Mayo |
| Publisher | : Cambridge University Press |
| Total Pages | : 503 |
| Release | : 2018-09-20 |
| Genre | : Mathematics |
| ISBN | : 1108563309 |
Mounting failures of replication in social and biological sciences give a new urgency to critically appraising proposed reforms. This book pulls back the cover on disagreements between experts charged with restoring integrity to science. It denies two pervasive views of the role of probability in inference: to assign degrees of belief, and to control error rates in a long run. If statistical consumers are unaware of assumptions behind rival evidence reforms, they can't scrutinize the consequences that affect them (in personalized medicine, psychology, etc.). The book sets sail with a simple tool: if little has been done to rule out flaws in inferring a claim, then it has not passed a severe test. Many methods advocated by data experts do not stand up to severe scrutiny and are in tension with successful strategies for blocking or accounting for cherry picking and selective reporting. Through a series of excursions and exhibits, the philosophy and history of inductive inference come alive. Philosophical tools are put to work to solve problems about science and pseudoscience, induction and falsification.
| Author | : Seymour Geisser |
| Publisher | : Routledge |
| Total Pages | : 280 |
| Release | : 2017-11-22 |
| Genre | : Mathematics |
| ISBN | : 1351422294 |
The author's research has been directed towards inference involving observables rather than parameters. In this book, he brings together his views on predictive or observable inference and its advantages over parametric inference. While the book discusses a variety of approaches to prediction including those based on parametric, nonparametric, and nonstochastic statistical models, it is devoted mainly to predictive applications of the Bayesian approach. It not only substitutes predictive analyses for parametric analyses, but it also presents predictive analyses that have no real parametric analogues. It demonstrates that predictive inference can be a critical component of even strict parametric inference when dealing with interim analyses. This approach to predictive inference will be of interest to statisticians, psychologists, econometricians, and sociologists.
| Author | : Lesley Walls |
| Publisher | : CRC Press |
| Total Pages | : 2983 |
| Release | : 2016-11-25 |
| Genre | : Technology & Engineering |
| ISBN | : 149878898X |
Risk, Reliability and Safety contains papers describing innovations in theory and practice contributed to the scientific programme of the European Safety and Reliability conference (ESREL 2016), held at the University of Strathclyde in Glasgow, Scotland (25—29 September 2016). Authors include scientists, academics, practitioners, regulators and other key individuals with expertise and experience relevant to specific areas. Papers include domain specific applications as well as general modelling methods. Papers cover evaluation of contemporary solutions, exploration of future challenges, and exposition of concepts, methods and processes. Topics include human factors, occupational health and safety, dynamic and systems reliability modelling, maintenance optimisation, uncertainty analysis, resilience assessment, risk and crisis management.
| Author | : Thomas Augustin |
| Publisher | : John Wiley & Sons |
| Total Pages | : 448 |
| Release | : 2014-04-11 |
| Genre | : Mathematics |
| ISBN | : 1118763149 |
In recent years, the theory has become widely accepted and has beenfurther developed, but a detailed introduction is needed in orderto make the material available and accessible to a wide audience.This will be the first book providing such an introduction,covering core theory and recent developments which can be appliedto many application areas. All authors of individual chapters areleading researchers on the specific topics, assuring high qualityand up-to-date contents. An Introduction to Imprecise Probabilities provides acomprehensive introduction to imprecise probabilities, includingtheory and applications reflecting the current state if the art.Each chapter is written by experts on the respective topics,including: Sets of desirable gambles; Coherent lower (conditional)previsions; Special cases and links to literature; Decision making;Graphical models; Classification; Reliability and risk assessment;Statistical inference; Structural judgments; Aspects ofimplementation (including elicitation and computation); Models infinance; Game-theoretic probability; Stochastic processes(including Markov chains); Engineering applications. Essential reading for researchers in academia, researchinstitutes and other organizations, as well as practitionersengaged in areas such as risk analysis and engineering.
| Author | : Jean Dickinson Gibbons |
| Publisher | : CRC Press |
| Total Pages | : 652 |
| Release | : 2010-07-26 |
| Genre | : Mathematics |
| ISBN | : 1439896127 |
Proven Material for a Course on the Introduction to the Theory and/or on the Applications of Classical Nonparametric Methods Since its first publication in 1971, Nonparametric Statistical Inference has been widely regarded as the source for learning about nonparametric statistics. The fifth edition carries on this tradition while thoroughly revising at least 50 percent of the material. New to the Fifth Edition Updated and revised contents based on recent journal articles in the literature A new section in the chapter on goodness-of-fit tests A new chapter that offers practical guidance on how to choose among the various nonparametric procedures covered Additional problems and examples Improved computer figures This classic, best-selling statistics book continues to cover the most commonly used nonparametric procedures. The authors carefully state the assumptions, develop the theory behind the procedures, and illustrate the techniques using realistic research examples from the social, behavioral, and life sciences. For most procedures, they present the tests of hypotheses, confidence interval estimation, sample size determination, power, and comparisons of other relevant procedures. The text also gives examples of computer applications based on Minitab, SAS, and StatXact and compares these examples with corresponding hand calculations. The appendix includes a collection of tables required for solving the data-oriented problems. Nonparametric Statistical Inference, Fifth Edition provides in-depth yet accessible coverage of the theory and methods of nonparametric statistical inference procedures. It takes a practical approach that draws on scores of examples and problems and minimizes the theorem-proof format. Jean Dickinson Gibbons was recently interviewed regarding her generous pledge to Virginia Tech.
| Author | : Faiza Farag Ali |
| Publisher | : |
| Total Pages | : 129 |
| Release | : 2012 |
| Genre | : Nonparametric statistics |
| ISBN | : |
Abstract:This thesis considers Nonparametric Predictive Inference (NPI) for ordinal data and accuracy of diagnostic tests. We introduce NPI for ordinal data, which are categor- ical data with an ordering of the categories. Such data occur in many application areas, for example medical and social studies. The method uses a latent variable representation of the observations and categories on the real line. Lower and upper probabilities for events involving the next observation are presented, with specic attention to comparison of multiple groups of ordinal data. We introduce NPI for accuracy of diagnostic tests with ordinal outcomes, with the inferences based on data for a disease group and a non-disease group. We intro- duce empirical and NPI lower and upper Receiver Operating Characteristic (ROC) curves and the corresponding areas under the curves. We discuss the use of the Youden index related to the NPI lower and upper ROC curves in order to deter- mine the optimal cut-o point for the test. Finally, we present NPI for assessment of accuracy of diagnostic tests involving three groups of real-valued data. This is achieved by developing NPI lower and upper ROC surfaces and the corresponding volumes under these surfaces, and we also consider the choice of cut-o points for classications based on such diagnostic tests.
