Constrained Statistical Inference

Constrained Statistical Inference

Author: Mervyn J. Silvapulle

Publisher: John Wiley & Sons

Published: 2011-09-15

Total Pages: 560

ISBN-13: 1118165632

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An up-to-date approach to understanding statistical inference Statistical inference is finding useful applications in numerous fields, from sociology and econometrics to biostatistics. This volume enables professionals in these and related fields to master the concepts of statistical inference under inequality constraints and to apply the theory to problems in a variety of areas. Constrained Statistical Inference: Order, Inequality, and Shape Constraints provides a unified and up-to-date treatment of the methodology. It clearly illustrates concepts with practical examples from a variety of fields, focusing on sociology, econometrics, and biostatistics. The authors also discuss a broad range of other inequality-constrained inference problems that do not fit well in the contemplated unified framework, providing a meaningful way for readers to comprehend methodological resolutions. Chapter coverage includes: Population means and isotonic regression Inequality-constrained tests on normal means Tests in general parametric models Likelihood and alternatives Analysis of categorical data Inference on monotone density function, unimodal density function, shape constraints, and DMRL functions Bayesian perspectives, including Stein’s Paradox, shrinkage estimation, and decision theory


Statistical Inference as Severe Testing

Statistical Inference as Severe Testing

Author: Deborah G. Mayo

Publisher: Cambridge University Press

Published: 2018-09-20

Total Pages: 503

ISBN-13: 1108563309

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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.


Principles of Statistical Inference

Principles of Statistical Inference

Author: D. R. Cox

Publisher: Cambridge University Press

Published: 2006-08-10

Total Pages: 227

ISBN-13: 1139459139

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In this definitive book, D. R. Cox gives a comprehensive and balanced appraisal of statistical inference. He develops the key concepts, describing and comparing the main ideas and controversies over foundational issues that have been keenly argued for more than two-hundred years. Continuing a sixty-year career of major contributions to statistical thought, no one is better placed to give this much-needed account of the field. An appendix gives a more personal assessment of the merits of different ideas. The content ranges from the traditional to the contemporary. While specific applications are not treated, the book is strongly motivated by applications across the sciences and associated technologies. The mathematics is kept as elementary as feasible, though previous knowledge of statistics is assumed. The book will be valued by every user or student of statistics who is serious about understanding the uncertainty inherent in conclusions from statistical analyses.


Foundations of Info-metrics

Foundations of Info-metrics

Author: Amos Golan

Publisher: Oxford University Press

Published: 2018

Total Pages: 489

ISBN-13: 0199349525

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Info-metrics is the science of modeling, reasoning, and drawing inferences under conditions of noisy and insufficient information. It is at the intersection of information theory, statistical inference, and decision-making under uncertainty. It plays an important role in helping make informed decisions even when there is inadequate or incomplete information because it provides a framework to process available information with minimal reliance on assumptions that cannot be validated. In this pioneering book, Amos Golan, a leader in info-metrics, focuses on unifying information processing, modeling and inference within a single constrained optimization framework. Foundations of Info-Metrics provides an overview of modeling and inference, rather than a problem specific model, and progresses from the simple premise that information is often insufficient to provide a unique answer for decisions we wish to make. Each decision, or solution, is derived from the available input information along with a choice of inferential procedure. The book contains numerous multidisciplinary applications and case studies, which demonstrate the simplicity and generality of the framework in real world settings. Examples include initial diagnosis at an emergency room, optimal dose decisions, election forecasting, network and information aggregation, weather pattern analyses, portfolio allocation, strategy inference for interacting entities, incorporation of prior information, option pricing, and modeling an interacting social system. Graphical representations illustrate how results can be visualized while exercises and problem sets facilitate extensions. This book is this designed to be accessible for researchers, graduate students, and practitioners across the disciplines.


Regression Analysis

Regression Analysis

Author: Richard A. Berk

Publisher: SAGE

Published: 2004

Total Pages: 286

ISBN-13: 9780761929048

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PLEASE UPDATE SAGE INDIA AND SAGE UK ADDRESSES ON IMPRINT PAGE.


Statistical Inference for Diffusion Type Processes

Statistical Inference for Diffusion Type Processes

Author: B.L.S. Prakasa Rao

Publisher: Wiley

Published: 2010-05-24

Total Pages: 0

ISBN-13: 9780470711125

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Decision making in all spheres of activity involves uncertainty. If rational decisions have to be made, they have to be based on the past observations of the phenomenon in question. Data collection, model building and inference from the data collected, validation of the model and refinement of the model are the key steps or building blocks involved in any rational decision making process. Stochastic processes are widely used for model building in the social, physical, engineering, and life sciences as well as in financial economics. Statistical inference for stochastic processes is of great importance from the theoretical as well as from applications point of view in model building. During the past twenty years, there has been a large amount of progress in the study of inferential aspects for continuous as well as discrete time stochastic processes. Diffusion type processes are a large class of continuous time processes which are widely used for stochastic modelling. the book aims to bring together several methods of estimation of parameters involved in such processes when the process is observed continuously over a period of time or when sampled data is available as generally feasible.


Modern Statistical Methods for HCI

Modern Statistical Methods for HCI

Author: Judy Robertson

Publisher: Springer

Published: 2016-03-22

Total Pages: 359

ISBN-13: 3319266330

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This book critically reflects on current statistical methods used in Human-Computer Interaction (HCI) and introduces a number of novel methods to the reader. Covering many techniques and approaches for exploratory data analysis including effect and power calculations, experimental design, event history analysis, non-parametric testing and Bayesian inference; the research contained in this book discusses how to communicate statistical results fairly, as well as presenting a general set of recommendations for authors and reviewers to improve the quality of statistical analysis in HCI. Each chapter presents [R] code for running analyses on HCI examples and explains how the results can be interpreted. Modern Statistical Methods for HCI is aimed at researchers and graduate students who have some knowledge of “traditional” null hypothesis significance testing, but who wish to improve their practice by using techniques which have recently emerged from statistics and related fields. This book critically evaluates current practices within the field and supports a less rigid, procedural view of statistics in favour of fair statistical communication.


Geometry Driven Statistics

Geometry Driven Statistics

Author: Ian L. Dryden

Publisher: John Wiley & Sons

Published: 2015-09-03

Total Pages: 436

ISBN-13: 1118866606

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A timely collection of advanced, original material in the area of statistical methodology motivated by geometric problems, dedicated to the influential work of Kanti V. Mardia This volume celebrates Kanti V. Mardia's long and influential career in statistics. A common theme unifying much of Mardia’s work is the importance of geometry in statistics, and to highlight the areas emphasized in his research this book brings together 16 contributions from high-profile researchers in the field. Geometry Driven Statistics covers a wide range of application areas including directional data, shape analysis, spatial data, climate science, fingerprints, image analysis, computer vision and bioinformatics. The book will appeal to statisticians and others with an interest in data motivated by geometric considerations. Summarizing the state of the art, examining some new developments and presenting a vision for the future, Geometry Driven Statistics will enable the reader to broaden knowledge of important research areas in statistics and gain a new appreciation of the work and influence of Kanti V. Mardia.


Nonparametric Estimation under Shape Constraints

Nonparametric Estimation under Shape Constraints

Author: Piet Groeneboom

Publisher: Cambridge University Press

Published: 2014-12-11

Total Pages: 429

ISBN-13: 1316194124

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This book treats the latest developments in the theory of order-restricted inference, with special attention to nonparametric methods and algorithmic aspects. Among the topics treated are current status and interval censoring models, competing risk models, and deconvolution. Methods of order restricted inference are used in computing maximum likelihood estimators and developing distribution theory for inverse problems of this type. The authors have been active in developing these tools and present the state of the art and the open problems in the field. The earlier chapters provide an introduction to the subject, while the later chapters are written with graduate students and researchers in mathematical statistics in mind. Each chapter ends with a set of exercises of varying difficulty. The theory is illustrated with the analysis of real-life data, which are mostly medical in nature.


Informative Hypotheses

Informative Hypotheses

Author: Herbert Hoijtink

Publisher: CRC Press

Published: 2011-10-26

Total Pages: 243

ISBN-13: 1439880514

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When scientists formulate their theories, expectations, and hypotheses, they often use statements like: ``I expect mean A to be bigger than means B and C"; ``I expect that the relation between Y and both X1 and X2 is positive"; and ``I expect the relation between Y and X1 to be stronger than the relation between Y and X2". Stated otherwise, they formulate their expectations in terms of inequality constraints among the parameters in which they are interested, that is, they formulate Informative Hypotheses. There is currently a sound theoretical foundation for the evaluation of informative hypotheses using Bayes factors, p-values and the generalized order restricted information criterion. Furthermore, software that is often free is available to enable researchers to evaluate the informative hypotheses using their own data. The road is open to challenge the dominance of the null hypothesis for contemporary research in behavioral, social, and other sciences.