STATISTICAL INFERENCE : THEORY OF ESTIMATION

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Publisher : PHI Learning Pvt. Ltd.
ISBN 13 : 812034930X
Total Pages : 817 pages
Book Rating : 4.1/5 (23 download)

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Book Synopsis STATISTICAL INFERENCE : THEORY OF ESTIMATION by : MANOJ KUMAR SRIVASTAVA

Download or read book STATISTICAL INFERENCE : THEORY OF ESTIMATION written by MANOJ KUMAR SRIVASTAVA and published by PHI Learning Pvt. Ltd.. This book was released on 2014-04-03 with total page 817 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is sequel to a book Statistical Inference: Testing of Hypotheses (published by PHI Learning). Intended for the postgraduate students of statistics, it introduces the problem of estimation in the light of foundations laid down by Sir R.A. Fisher (1922) and follows both classical and Bayesian approaches to solve these problems. The book starts with discussing the growing levels of data summarization to reach maximal summarization and connects it with sufficient and minimal sufficient statistics. The book gives a complete account of theorems and results on uniformly minimum variance unbiased estimators (UMVUE)—including famous Rao and Blackwell theorem to suggest an improved estimator based on a sufficient statistic and Lehmann-Scheffe theorem to give an UMVUE. It discusses Cramer-Rao and Bhattacharyya variance lower bounds for regular models, by introducing Fishers information and Chapman, Robbins and Kiefer variance lower bounds for Pitman models. Besides, the book introduces different methods of estimation including famous method of maximum likelihood and discusses large sample properties such as consistency, consistent asymptotic normality (CAN) and best asymptotic normality (BAN) of different estimators. Separate chapters are devoted for finding Pitman estimator, among equivariant estimators, for location and scale models, by exploiting symmetry structure, present in the model, and Bayes, Empirical Bayes, Hierarchical Bayes estimators in different statistical models. Systematic exposition of the theory and results in different statistical situations and models, is one of the several attractions of the presentation. Each chapter is concluded with several solved examples, in a number of statistical models, augmented with exposition of theorems and results. KEY FEATURES • Provides clarifications for a number of steps in the proof of theorems and related results., • Includes numerous solved examples to improve analytical insight on the subject by illustrating the application of theorems and results. • Incorporates Chapter-end exercises to review student’s comprehension of the subject. • Discusses detailed theory on data summarization, unbiased estimation with large sample properties, Bayes and Minimax estimation, separately, in different chapters.

Statistical Inference: Theory of Estimation

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Publisher : Blue Rose Publishers
ISBN 13 :
Total Pages : 271 pages
Book Rating : 4./5 ( download)

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Book Synopsis Statistical Inference: Theory of Estimation by : Prakash S. Chougule

Download or read book Statistical Inference: Theory of Estimation written by Prakash S. Chougule and published by Blue Rose Publishers. This book was released on 2022-01-24 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book “Statistical Inference: Theory of Estimation” aims to help the student in gaining knowledge about Statistical Inference. This book contains five chapters like Point estimation, Likelihood function and Sufficiency, Cramer Rao Inequality, methods of estimation and Interval estimation. Every chapter has been divided into several headings and sub headings to offer clarity and conciseness. The authors have tried his best to simplify units and are written in very simple and lucid language. so that the reader can get an intuitive understanding the contains of the book. The number of examples included in the book will really make the study very easy and yet efficient. The question bank of simple and relative exercise included lot of multiple choice questions at the end of each chapter is given which helps the students to evaluate themselves. The book will particularly help students of B.Sc. and M.Sc. statistics classes.

Theory of Statistical Inference

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Publisher : CRC Press
ISBN 13 : 1000488012
Total Pages : 470 pages
Book Rating : 4.0/5 (4 download)

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Book Synopsis Theory of Statistical Inference by : Anthony Almudevar

Download or read book Theory of Statistical Inference written by Anthony Almudevar and published by CRC Press. This book was released on 2021-12-30 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory of Statistical Inference is designed as a reference on statistical inference for researchers and students at the graduate or advanced undergraduate level. It presents a unified treatment of the foundational ideas of modern statistical inference, and would be suitable for a core course in a graduate program in statistics or biostatistics. The emphasis is on the application of mathematical theory to the problem of inference, leading to an optimization theory allowing the choice of those statistical methods yielding the most efficient use of data. The book shows how a small number of key concepts, such as sufficiency, invariance, stochastic ordering, decision theory and vector space algebra play a recurring and unifying role. The volume can be divided into four sections. Part I provides a review of the required distribution theory. Part II introduces the problem of statistical inference. This includes the definitions of the exponential family, invariant and Bayesian models. Basic concepts of estimation, confidence intervals and hypothesis testing are introduced here. Part III constitutes the core of the volume, presenting a formal theory of statistical inference. Beginning with decision theory, this section then covers uniformly minimum variance unbiased (UMVU) estimation, minimum risk equivariant (MRE) estimation and the Neyman-Pearson test. Finally, Part IV introduces large sample theory. This section begins with stochastic limit theorems, the δ-method, the Bahadur representation theorem for sample quantiles, large sample U-estimation, the Cramér-Rao lower bound and asymptotic efficiency. A separate chapter is then devoted to estimating equation methods. The volume ends with a detailed development of large sample hypothesis testing, based on the likelihood ratio test (LRT), Rao score test and the Wald test. Features This volume includes treatment of linear and nonlinear regression models, ANOVA models, generalized linear models (GLM) and generalized estimating equations (GEE). An introduction to decision theory (including risk, admissibility, classification, Bayes and minimax decision rules) is presented. The importance of this sometimes overlooked topic to statistical methodology is emphasized. The volume emphasizes throughout the important role that can be played by group theory and invariance in statistical inference. Nonparametric (rank-based) methods are derived by the same principles used for parametric models and are therefore presented as solutions to well-defined mathematical problems, rather than as robust heuristic alternatives to parametric methods. Each chapter ends with a set of theoretical and applied exercises integrated with the main text. Problems involving R programming are included. Appendices summarize the necessary background in analysis, matrix algebra and group theory.

STATISTICAL INFERENCE

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Publisher : PHI Learning Pvt. Ltd.
ISBN 13 : 8120346351
Total Pages : 408 pages
Book Rating : 4.1/5 (23 download)

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Book Synopsis STATISTICAL INFERENCE by : M. RAJAGOPALAN

Download or read book STATISTICAL INFERENCE written by M. RAJAGOPALAN and published by PHI Learning Pvt. Ltd.. This book was released on 2012-07-08 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended as a text for the postgraduate students of statistics, this well-written book gives a complete coverage of Estimation theory and Hypothesis testing, in an easy-to-understand style. It is the outcome of the authors’ teaching experience over the years. The text discusses absolutely continuous distributions and random sample which are the basic concepts on which Statistical Inference is built up, with examples that give a clear idea as to what a random sample is and how to draw one such sample from a distribution in real-life situations. It also discusses maximum-likelihood method of estimation, Neyman’s shortest confidence interval, classical and Bayesian approach. The difference between statistical inference and statistical decision theory is explained with plenty of illustrations that help students obtain the necessary results from the theory of probability and distributions, used in inference.

Asymptotic Theory of Statistical Inference

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Publisher :
ISBN 13 :
Total Pages : 458 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Asymptotic Theory of Statistical Inference by : B. L. S. Prakasa Rao

Download or read book Asymptotic Theory of Statistical Inference written by B. L. S. Prakasa Rao and published by . This book was released on 1987-01-16 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability and stochastic processes; Limit theorems for some statistics; Asymptotic theory of estimation; Linear parametric inference; Martingale approach to inference; Inference in nonlinear regression; Von mises functionals; Empirical characteristic function and its applications.

Statistical Inference: Testing Of Hypotheses

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Publisher : PHI Learning Pvt. Ltd.
ISBN 13 : 812033728X
Total Pages : 414 pages
Book Rating : 4.1/5 (23 download)

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Book Synopsis Statistical Inference: Testing Of Hypotheses by : Srivastava & Srivastava

Download or read book Statistical Inference: Testing Of Hypotheses written by Srivastava & Srivastava and published by PHI Learning Pvt. Ltd.. This book was released on 2009-12 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: it emphasizes on J. Neyman and Egon Pearson's mathematical foundations of hypothesis testing, which is one of the finest methodologies of reaching conclusions on population parameter. Following Wald and Ferguson's approach, the book presents Neyman-Pearson theory under broader premises of decision theory resulting into simplification and generalization of results. On account of smooth mathematical development of this theory, the book outlines the main result on Lebesgue theory in abstract spaces prior to rigorous theoretical developments on most powerful (MP), uniformly most powerful (UMP) and UMP unbiased tests for different types of testing problems. Likelihood ratio tests their large sample properties to variety of testing situations and connection between confidence estimation and testing of hypothesis have been discussed in separate chapters. The book illustrates simplification of testing problems and reduction in dimensionality of class of tests resulting into existence of an optimal test through the principle of sufficiency and invariance. It concludes with rigorous theoretical developments on non-parametric tests including their optimality, asymptotic relative efficiency, consistency, and asymptotic null distribution.

Models for Probability and Statistical Inference

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Publisher : John Wiley & Sons
ISBN 13 : 0470183403
Total Pages : 466 pages
Book Rating : 4.4/5 (71 download)

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Book Synopsis Models for Probability and Statistical Inference by : James H. Stapleton

Download or read book Models for Probability and Statistical Inference written by James H. Stapleton and published by John Wiley & Sons. This book was released on 2007-12-14 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise, yet thorough, book is enhanced with simulations and graphs to build the intuition of readers Models for Probability and Statistical Inference was written over a five-year period and serves as a comprehensive treatment of the fundamentals of probability and statistical inference. With detailed theoretical coverage found throughout the book, readers acquire the fundamentals needed to advance to more specialized topics, such as sampling, linear models, design of experiments, statistical computing, survival analysis, and bootstrapping. Ideal as a textbook for a two-semester sequence on probability and statistical inference, early chapters provide coverage on probability and include discussions of: discrete models and random variables; discrete distributions including binomial, hypergeometric, geometric, and Poisson; continuous, normal, gamma, and conditional distributions; and limit theory. Since limit theory is usually the most difficult topic for readers to master, the author thoroughly discusses modes of convergence of sequences of random variables, with special attention to convergence in distribution. The second half of the book addresses statistical inference, beginning with a discussion on point estimation and followed by coverage of consistency and confidence intervals. Further areas of exploration include: distributions defined in terms of the multivariate normal, chi-square, t, and F (central and non-central); the one- and two-sample Wilcoxon test, together with methods of estimation based on both; linear models with a linear space-projection approach; and logistic regression. Each section contains a set of problems ranging in difficulty from simple to more complex, and selected answers as well as proofs to almost all statements are provided. An abundant amount of figures in addition to helpful simulations and graphs produced by the statistical package S-Plus(r) are included to help build the intuition of readers.

Essential Statistical Inference

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Publisher : Springer Science & Business Media
ISBN 13 : 1461448182
Total Pages : 567 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Essential Statistical Inference by : Dennis D. Boos

Download or read book Essential Statistical Inference written by Dennis D. Boos and published by Springer Science & Business Media. This book was released on 2013-02-06 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: ​This book is for students and researchers who have had a first year graduate level mathematical statistics course. It covers classical likelihood, Bayesian, and permutation inference; an introduction to basic asymptotic distribution theory; and modern topics like M-estimation, the jackknife, and the bootstrap. R code is woven throughout the text, and there are a large number of examples and problems. An important goal has been to make the topics accessible to a wide audience, with little overt reliance on measure theory. A typical semester course consists of Chapters 1-6 (likelihood-based estimation and testing, Bayesian inference, basic asymptotic results) plus selections from M-estimation and related testing and resampling methodology. Dennis Boos and Len Stefanski are professors in the Department of Statistics at North Carolina State. Their research has been eclectic, often with a robustness angle, although Stefanski is also known for research concentrated on measurement error, including a co-authored book on non-linear measurement error models. In recent years the authors have jointly worked on variable selection methods. ​

Theory of Point Estimation

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Publisher : Springer Science & Business Media
ISBN 13 : 0387227288
Total Pages : 590 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Theory of Point Estimation by : Erich L. Lehmann

Download or read book Theory of Point Estimation written by Erich L. Lehmann and published by Springer Science & Business Media. This book was released on 2006-05-02 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second, much enlarged edition by Lehmann and Casella of Lehmann's classic text on point estimation maintains the outlook and general style of the first edition. All of the topics are updated, while an entirely new chapter on Bayesian and hierarchical Bayesian approaches is provided, and there is much new material on simultaneous estimation. Each chapter concludes with a Notes section which contains suggestions for further study. This is a companion volume to the second edition of Lehmann's "Testing Statistical Hypotheses".

Introduction to the Theory of Statistical Inference

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Publisher : CRC Press
ISBN 13 : 1466503203
Total Pages : 280 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Introduction to the Theory of Statistical Inference by : Hannelore Liero

Download or read book Introduction to the Theory of Statistical Inference written by Hannelore Liero and published by CRC Press. This book was released on 2016-04-19 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the authors' lecture notes, this text presents concise yet complete coverage of statistical inference theory, focusing on the fundamental classical principles. Unlike related textbooks, it combines the theoretical basis of statistical inference with a useful applied toolbox that includes linear models. Suitable for a second semester undergraduate course on statistical inference, the text offers proofs to support the mathematics and does not require any use of measure theory. It illustrates core concepts using cartoons and provides solutions to all examples and problems.

Asymptotic Theory of Statistical Inference for Time Series

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Publisher : Springer Science & Business Media
ISBN 13 : 146121162X
Total Pages : 671 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Asymptotic Theory of Statistical Inference for Time Series by : Masanobu Taniguchi

Download or read book Asymptotic Theory of Statistical Inference for Time Series written by Masanobu Taniguchi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 671 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary aim of this book is to provide modern statistical techniques and theory for stochastic processes. The stochastic processes mentioned here are not restricted to the usual AR, MA, and ARMA processes. A wide variety of stochastic processes, including non-Gaussian linear processes, long-memory processes, nonlinear processes, non-ergodic processes and diffusion processes are described. The authors discuss estimation and testing theory and many other relevant statistical methods and techniques.

Statistical Theory and Inference

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Publisher : Springer
ISBN 13 : 3319049720
Total Pages : 438 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Statistical Theory and Inference by : David J. Olive

Download or read book Statistical Theory and Inference written by David J. Olive and published by Springer. This book was released on 2014-05-07 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is for a one semester graduate course in statistical theory and covers minimal and complete sufficient statistics, maximum likelihood estimators, method of moments, bias and mean square error, uniform minimum variance estimators and the Cramer-Rao lower bound, an introduction to large sample theory, likelihood ratio tests and uniformly most powerful tests and the Neyman Pearson Lemma. A major goal of this text is to make these topics much more accessible to students by using the theory of exponential families. Exponential families, indicator functions and the support of the distribution are used throughout the text to simplify the theory. More than 50 ``brand name" distributions are used to illustrate the theory with many examples of exponential families, maximum likelihood estimators and uniformly minimum variance unbiased estimators. There are many homework problems with over 30 pages of solutions.

The Theory of Statistical Inference

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Publisher : John Wiley & Sons
ISBN 13 :
Total Pages : 640 pages
Book Rating : 4.:/5 (44 download)

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Book Synopsis The Theory of Statistical Inference by : Shelemyahu Zacks

Download or read book The Theory of Statistical Inference written by Shelemyahu Zacks and published by John Wiley & Sons. This book was released on 1971 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: Synopsis; Sufficient statistics; Unbiased estimation; The efficiency of estimators under quadratic loss; Maximum likelihood estimation; Bayes and minimax estimation; Equivariant estimators; Admissibility of estimators; Confidence and tolerance intervals.

Order Statistics & Inference

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Publisher : Elsevier
ISBN 13 : 1483297497
Total Pages : 399 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Order Statistics & Inference by : Narayanaswamy Balakrishnan

Download or read book Order Statistics & Inference written by Narayanaswamy Balakrishnan and published by Elsevier. This book was released on 2014-06-28 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: The literature on order statistics and inferenc eis quite extensive and covers a large number of fields ,but most of it is dispersed throughout numerous publications. This volume is the consolidtion of the most important results and places an emphasis on estimation. Both theoretical and computational procedures are presented to meet the needs of researchers, professionals, and students. The methods of estimation discussed are well-illustrated with numerous practical examples from both the physical and life sciences, including sociology,psychology,a nd electrical and chemical engineering. A complete, comprehensive bibliography is included so the book can be used both aas a text and reference.

Asymptotic Theory of Quantum Statistical Inference

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Publisher : World Scientific
ISBN 13 : 981448198X
Total Pages : 560 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Asymptotic Theory of Quantum Statistical Inference by : Masahito Hayashi

Download or read book Asymptotic Theory of Quantum Statistical Inference written by Masahito Hayashi and published by World Scientific. This book was released on 2005-02-21 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: ' Quantum statistical inference, a research field with deep roots in the foundations of both quantum physics and mathematical statistics, has made remarkable progress since 1990. In particular, its asymptotic theory has been developed during this period. However, there has hitherto been no book covering this remarkable progress after 1990; the famous textbooks by Holevo and Helstrom deal only with research results in the earlier stage (1960s-1970s). This book presents the important and recent results of quantum statistical inference. It focuses on the asymptotic theory, which is one of the central issues of mathematical statistics and had not been investigated in quantum statistical inference until the early 1980s. It contains outstanding papers after Holevo's textbook, some of which are of great importance but are not available now. The reader is expected to have only elementary mathematical knowledge, and therefore much of the content will be accessible to graduate students as well as research workers in related fields. Introductions to quantum statistical inference have been specially written for the book. Asymptotic Theory of Quantum Statistical Inference: Selected Papers will give the reader a new insight into physics and statistical inference. Contents:Hypothesis TestingQuantum Cramér-Rao Bound in Mixed States ModelQuantum Cramér-Rao Bound in Pure States ModelGroup Symmetric Approach to Pure States ModelLarge Deviation Theory in Quantum EstimationFuther Topics on Quantum Statistical Inference Readership: Graduate students in quantum physics, mathematical physics, and probability and statistics. Keywords:Quantum Information;Estimation Theory;Statistics;Statistical Inference;Mathematical Physics;Asymptotic Theory;Hypothesis TestingReviews:“This book will give the scholars new insight into physics and statistical inference.”Zentralblatt MATH '

Estimation and Inferential Statistics

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Publisher : Springer
ISBN 13 : 8132225147
Total Pages : 317 pages
Book Rating : 4.1/5 (322 download)

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Book Synopsis Estimation and Inferential Statistics by : Pradip Kumar Sahu

Download or read book Estimation and Inferential Statistics written by Pradip Kumar Sahu and published by Springer. This book was released on 2015-11-03 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the meaning of statistical inference and estimation. Statistical inference is concerned with the problems of estimation of population parameters and testing hypotheses. Primarily aimed at undergraduate and postgraduate students of statistics, the book is also useful to professionals and researchers in statistical, medical, social and other disciplines. It discusses current methodological techniques used in statistics and related interdisciplinary areas. Every concept is supported with relevant research examples to help readers to find the most suitable application. Statistical tools have been presented by using real-life examples, removing the “fear factor” usually associated with this complex subject. The book will help readers to discover diverse perspectives of statistical theory followed by relevant worked-out examples. Keeping in mind the needs of readers, as well as constantly changing scenarios, the material is presented in an easy-to-understand form.

Statistical Inference for Engineers and Data Scientists

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Publisher : Cambridge University Press
ISBN 13 : 1107185920
Total Pages : 423 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Statistical Inference for Engineers and Data Scientists by : Pierre Moulin

Download or read book Statistical Inference for Engineers and Data Scientists written by Pierre Moulin and published by Cambridge University Press. This book was released on 2019 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: A mathematically accessible textbook introducing all the tools needed to address modern inference problems in engineering and data science.