Statistical Inference

The twenty-first century has seen a breathtaking expansion of statistical methodology, both in scope and influence. 'Data science' and 'machine learning' have become familiar terms in the news, as statistical methods are brought to bear upon the enormous data sets of modern science and commerce. How did we get here? And where are we going? How does it all fit together? Now in paperback and fortified with exercises, this book delivers a concentrated course in modern statistical thinking. Beginning with classical inferential theories - Bayesian, frequentist, Fisherian - individual chapters take up a series of influential topics: survival analysis, logistic regression, empirical Bayes, the jackknife and bootstrap, random forests, neural networks, Markov Chain Monte Carlo, inference after model selection, and dozens more. The distinctly modern approach integrates methodology and algorithms with statistical inference. Each chapter ends with class-tested exercises, and the book concludes wit

Statistical Inference via Data Science: A ModernDive into R and the Tidyverse provides a pathway for learning about statistical inference using data science tools widely used in industry, academia, an

This textbook provides a concise and engaging introduction to the concepts of statistical inference aimed at a non-mathematical audience. The book uses very little calculus and lots of illustrative ex

One of Ian Hacking's earliest publications, this book showcases his early ideas on the central concepts and questions surrounding statistical reasoning. He explores the basic principles of statistical reasoning and tests them, both at a philosophical level and in terms of their practical consequences for statisticians. Presented in a fresh twenty-first-century series livery, and including a specially commissioned preface written by Jan-Willem Romeijn, illuminating its enduring importance and relevance to philosophical enquiry, Hacking's influential and original work has been revived for a new generation of readers.

Exact Statistical Inference for Categorical Data discusses the way asymptotic approaches have been often used in practice to make statistical inference. This book introduces both conditional and uncon

?This monograph provides the fundamentals of statistical inference for financial engineering and covers some selected methods suitable for analyzing financial time series data. In order to describe th

This book covers statistical inference based on the likelihood function. Discusses frequentist likelihood-based inference from a Fisherian viewpoint, Bayesian inference techniques including point and

This work is an overview of statistical inference in stationary, discrete time stochastic processes. Results in the last fifteen years, particularly on non-Gaussian sequences and semi-parametric and n

This book is based upon lecture notes developed by Jack Kiefer for a course in statistical inference he taught at Cornell University. The notes were distributed to the class in lieu of a textbook, and

This book offers a brief course in statistical inference that requires only a basic familiarity with probability and matrix and linear algebra. Ninety problems with solutions make it an ideal choice f

The dynamics of financial returns varies with the return period, from high-frequency data to daily, quarterly or annual data. Multifractal Random Walk models can capture the statistical relation betwe

Aimed at advanced undergraduate and graduate students in mathematics and related disciplines, this book presents the concepts and results underlying the Bayesian, frequentist and Fisherian approaches, with particular emphasis on the contrasts between them. Computational ideas are explained, as well as basic mathematical theory. Written in a lucid and informal style, this concise text provides both basic material on the main approaches to inference, as well as more advanced material on developments in statistical theory, including: material on Bayesian computation, such as MCMC, higher-order likelihood theory, predictive inference, bootstrap methods and conditional inference. It contains numerous extended examples of the application of formal inference techniques to real data, as well as historical commentary on the development of the subject. Throughout, the text concentrates on concepts, rather than mathematical detail, while maintaining appropriate levels of formality. Each chapter

This book builds theoretical statistics from the first principles of probability theory. Starting from the basics of probability, the authors develop the theory of statistical inference using techniqu

Nonparametric techniques in statistics are those in which the data are ranked in order according to some particular characteristic. When applied to measurable characteristics, the use of such techniques often saves considerable calculation as compared with more formal methods, with only slight loss of accuracy. The field of nonparametric statistics is occupying an increasingly important role in statistical theory as well as in its applications. Nonparametric methods are mathematically elegant, and they also yield significantly improved performances in applications to agriculture, education, biometrics, medicine, communication, economics and industry.

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.

Originally published in 1984, this textbook offers a unified treatment of probability and statistics. It analyzes the relationship between the two fields, with particular attention to utility and con

The book discusses the estimation theory for the wide class of inhomogeneous Poisson processes. The consistency, limit distributions and the convergence of moments of parameter estimators are establis

Originally published in 1962 by Van Nostrand, Princeton, NJ. A textbook emphasizing the inferential and decision-making aspects of statistics. For undergraduate students with a knowledge of elementary

The study of spatial processes and their applications is an important topic in statistics and finds wide application particularly in computer vision and image processing. This book is devoted to statistical inference in spatial statistics and is intended for specialists needing an introduction to the subject and to its applications. One of the themes of the book is the demonstration of how these techniques give new insights into classical procedures (including new examples in likelihood theory) and newer statistical paradigms such as Monte-Carlo inference and pseudo-likelihood. Professor Ripley also stresses the importance of edge effects and of lack of a unique asymptotic setting in spatial problems. Throughout, the author discusses the foundational issues posed and the difficulties, both computational and philosophical, which arise. The final chapters consider image restoration and segmentation methods and the averaging and summarising of images. Thus, the book will find wide appeal

This monograph develops an approach to statistical inference that is both comprehensive in its treatment of statistical principles and sufficiently powerful to be applicable to a variety of important

Empirical researchers, for whom Iversen's volume provides an introduction, have generally lacked a grounding in the methodology of Bayesian inference. As a result, applications are few. After outlinin

This book is a philosophical study of the basic principles of statistical reasoning. Professor Hacking has sought to discover the simple principles which underlie modern work in mathematical statistics and to test them, both at a philosophical level and in terms of their practical consequences fort statisticians. The ideas of modern logic are used to analyse these principles, and results are presented without the use of unfamiliar symbolism. It begins with a philosophical analysis of a few central concepts and then, using an elementary system of logic, develops most of the standard statistical theory. the analysis provides answers to many disputed questions about how to test statistical hypotheses and about how to estimate quantities in the light of statistical data. One product of the analysis is a sound and consistent rationale for R. A. Fisher's controversial concept of 'fiducial probability'.

An accessible and illuminating exploration of the conceptual basisof scientific and statistical inference and the practical impact this has on conducting psychological research. The book encourages a