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The Bayesian Way: Introductory Statistics for Economists and Engineers

The Bayesian Way: Introductory Statistics for Economists and Engineers
Author: Svein Olav Nyberg
Publisher: John Wiley & Sons
Total Pages: 512
Release: 2018-08-28
Genre: Mathematics
ISBN: 1119246873

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A comprehensive resource that offers an introduction to statistics with a Bayesian angle, for students of professional disciplines like engineering and economics The Bayesian Way offers a basic introduction to statistics that emphasizes the Bayesian approach and is designed for use by those studying professional disciplines like engineering and economics. In addition to the Bayesian approach, the author includes the most common techniques of the frequentist approach. Throughout the text, the author covers statistics from a basic to a professional working level along with a practical understanding of the matter at hand. Filled with helpful illustrations, this comprehensive text explores a wide range of topics, starting with descriptive statistics, set theory, and combinatorics. The text then goes on to review fundamental probability theory and Bayes' theorem. The first part ends in an exposition of stochastic variables, exploring discrete, continuous and mixed probability distributions. In the second part, the book looks at statistical inference. Primarily Bayesian, but with the main frequentist techniques included, it covers conjugate priors through the powerful yet simple method of hyperparameters. It then goes on to topics in hypothesis testing (including utility functions), point and interval estimates (including frequentist confidence intervals), and linear regression. This book: Explains basic statistics concepts in accessible terms and uses an abundance of illustrations to enhance visual understanding Has guides for how to calculate the different probability distributions, functions , and statistical properties, on platforms like popular pocket calculators and Mathematica / Wolfram Alpha Includes example-proofs that enable the reader to follow the reasoning Contains assignments at different levels of difficulty from simply filling out the correct formula to the complex multi-step text assignments Offers information on continuous, discrete and mixed probability distributions, hypothesis testing, credible and confidence intervals, and linear regression Written for undergraduate and graduate students of subjects where Bayesian statistics are applied, including engineering, economics, and related fields, The Bayesian Way: With Applications in Engineering and Economics offers a clear understanding of Bayesian statistics that have real-world applications.


Bayesian Data Analysis, Third Edition

Bayesian Data Analysis, Third Edition
Author: Andrew Gelman
Publisher: CRC Press
Total Pages: 677
Release: 2013-11-01
Genre: Mathematics
ISBN: 1439840954

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Now in its third edition, this classic book is widely considered the leading text on Bayesian methods, lauded for its accessible, practical approach to analyzing data and solving research problems. Bayesian Data Analysis, Third Edition continues to take an applied approach to analysis using up-to-date Bayesian methods. The authors—all leaders in the statistics community—introduce basic concepts from a data-analytic perspective before presenting advanced methods. Throughout the text, numerous worked examples drawn from real applications and research emphasize the use of Bayesian inference in practice. New to the Third Edition Four new chapters on nonparametric modeling Coverage of weakly informative priors and boundary-avoiding priors Updated discussion of cross-validation and predictive information criteria Improved convergence monitoring and effective sample size calculations for iterative simulation Presentations of Hamiltonian Monte Carlo, variational Bayes, and expectation propagation New and revised software code The book can be used in three different ways. For undergraduate students, it introduces Bayesian inference starting from first principles. For graduate students, the text presents effective current approaches to Bayesian modeling and computation in statistics and related fields. For researchers, it provides an assortment of Bayesian methods in applied statistics. Additional materials, including data sets used in the examples, solutions to selected exercises, and software instructions, are available on the book’s web page.


An Introduction to Bayesian Inference in Econometrics

An Introduction to Bayesian Inference in Econometrics
Author: Arnold Zellner
Publisher: New York : J. Wiley
Total Pages: 456
Release: 1971-11-26
Genre: Business & Economics
ISBN:

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Remarks on inference in economics; Principles of bayesian analysis with selected applications; The univariate normal linear regression model; Special problems in regression analysis; On error in the variables; Analysis of single equation nonlinear models; Time series models: some selected examples; Multivariate regression models; Simultaneous equation econometric models; On comparing and testing hypotheses; Analysis of some control problems.


Statistics

Statistics
Author: David W. Scott
Publisher: John Wiley & Sons
Total Pages: 180
Release: 2020-07-13
Genre: Mathematics
ISBN: 1119675847

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Statistic: A Concise Mathematical Introduction for Students and Scientists offers a one academic term text that prepares the student to broaden their skills in statistics, probability and inference, prior to selecting their follow-on courses in their chosen fields, whether it be engineering, computer science, programming, data sciences, business or economics. The book places focus early on continuous measurements, as well as discrete random variables. By invoking simple and intuitive models and geometric probability, discrete and continuous experiments and probabilities are discussed throughout the book in a natural way. Classical probability, random variables, and inference are discussed, as well as material on understanding data and topics of special interest. Topics discussed include: • Classical equally likely outcomes • Variety of models of discrete and continuous probability laws • Likelihood function and ratio • Inference • Bayesian statistics With the growth in the volume of data generated in many disciplines that is enabling the growth in data science, companies now demand statistically literate scientists and this textbook is the answer, suited for undergraduates studying science or engineering, be it computer science, economics, life sciences, environmental, business, amongst many others. Basic knowledge of bivariate calculus, R language, Matematica and JMP is useful, however there is an accompanying website including sample R and Mathematica code to help instructors and students.


Introduction to Bayesian Statistics

Introduction to Bayesian Statistics
Author: William M. Bolstad
Publisher: John Wiley & Sons
Total Pages: 353
Release: 2013-06-05
Genre: Mathematics
ISBN: 1118619218

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Praise for the First Edition "I cannot think of a better book for teachers of introductory statistics who want a readable and pedagogically sound text to introduce Bayesian statistics." —Statistics in Medical Research "[This book] is written in a lucid conversational style, which is so rare in mathematical writings. It does an excellent job of presenting Bayesian statistics as a perfectly reasonable approach to elementary problems in statistics." —STATS: The Magazine for Students of Statistics, American Statistical Association "Bolstad offers clear explanations of every concept and method making the book accessible and valuable to undergraduate and graduate students alike." —Journal of Applied Statistics The use of Bayesian methods in applied statistical analysis has become increasingly popular, yet most introductory statistics texts continue to only present the subject using frequentist methods. Introduction to Bayesian Statistics, Second Edition focuses on Bayesian methods that can be used for inference, and it also addresses how these methods compare favorably with frequentist alternatives. Teaching statistics from the Bayesian perspective allows for direct probability statements about parameters, and this approach is now more relevant than ever due to computer programs that allow practitioners to work on problems that contain many parameters. This book uniquely covers the topics typically found in an introductory statistics book—but from a Bayesian perspective—giving readers an advantage as they enter fields where statistics is used. This Second Edition provides: Extended coverage of Poisson and Gamma distributions Two new chapters on Bayesian inference for Poisson observations and Bayesian inference for the standard deviation for normal observations A twenty-five percent increase in exercises with selected answers at the end of the book A calculus refresher appendix and a summary on the use of statistical tables New computer exercises that use R functions and Minitab® macros for Bayesian analysis and Monte Carlo simulations Introduction to Bayesian Statistics, Second Edition is an invaluable textbook for advanced undergraduate and graduate-level statistics courses as well as a practical reference for statisticians who require a working knowledge of Bayesian statistics.


Data Analysis

Data Analysis
Author: Devinderjit Sivia
Publisher: OUP Oxford
Total Pages: 259
Release: 2006-06-02
Genre: Mathematics
ISBN: 0191546704

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One of the strengths of this book is the author's ability to motivate the use of Bayesian methods through simple yet effective examples. - Katie St. Clair MAA Reviews.


Introduction to Bayesian Statistics

Introduction to Bayesian Statistics
Author: William M. Bolstad
Publisher: John Wiley & Sons
Total Pages: 621
Release: 2016-08-23
Genre: Mathematics
ISBN: 1118593154

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"...this edition is useful and effective in teaching Bayesian inference at both elementary and intermediate levels. It is a well-written book on elementary Bayesian inference, and the material is easily accessible. It is both concise and timely, and provides a good collection of overviews and reviews of important tools used in Bayesian statistical methods." There is a strong upsurge in the use of Bayesian methods in applied statistical analysis, yet most introductory statistics texts only present frequentist methods. Bayesian statistics has many important advantages that students should learn about if they are going into fields where statistics will be used. In this third Edition, four newly-added chapters address topics that reflect the rapid advances in the field of Bayesian statistics. The authors continue to provide a Bayesian treatment of introductory statistical topics, such as scientific data gathering, discrete random variables, robust Bayesian methods, and Bayesian approaches to inference for discrete random variables, binomial proportions, Poisson, and normal means, and simple linear regression. In addition, more advanced topics in the field are presented in four new chapters: Bayesian inference for a normal with unknown mean and variance; Bayesian inference for a Multivariate Normal mean vector; Bayesian inference for the Multiple Linear Regression Model; and Computational Bayesian Statistics including Markov Chain Monte Carlo. The inclusion of these topics will facilitate readers' ability to advance from a minimal understanding of Statistics to the ability to tackle topics in more applied, advanced level books. Minitab macros and R functions are available on the book's related website to assist with chapter exercises. Introduction to Bayesian Statistics, Third Edition also features: Topics including the Joint Likelihood function and inference using independent Jeffreys priors and join conjugate prior The cutting-edge topic of computational Bayesian Statistics in a new chapter, with a unique focus on Markov Chain Monte Carlo methods Exercises throughout the book that have been updated to reflect new applications and the latest software applications Detailed appendices that guide readers through the use of R and Minitab software for Bayesian analysis and Monte Carlo simulations, with all related macros available on the book's website Introduction to Bayesian Statistics, Third Edition is a textbook for upper-undergraduate or first-year graduate level courses on introductory statistics course with a Bayesian emphasis. It can also be used as a reference work for statisticians who require a working knowledge of Bayesian statistics.


Bayesian Core: A Practical Approach to Computational Bayesian Statistics

Bayesian Core: A Practical Approach to Computational Bayesian Statistics
Author: Jean-Michel Marin
Publisher: Springer Science & Business Media
Total Pages: 265
Release: 2007-05-26
Genre: Mathematics
ISBN: 0387389830

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This Bayesian modeling book is intended for practitioners and applied statisticians looking for a self-contained entry to computational Bayesian statistics. Focusing on standard statistical models and backed up by discussed real datasets available from the book website, it provides an operational methodology for conducting Bayesian inference, rather than focusing on its theoretical justifications. Special attention is paid to the derivation of prior distributions in each case and specific reference solutions are given for each of the models. Similarly, computational details are worked out to lead the reader towards an effective programming of the methods given in the book.


Introductory Statistics

Introductory Statistics
Author: Douglas S. Shafer
Publisher:
Total Pages: 0
Release: 2022
Genre: Mathematical statistics
ISBN: 9781453388945

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Introduction to Bayesian Statistics

Introduction to Bayesian Statistics
Author: Karl-Rudolf Koch
Publisher: Springer Science & Business Media
Total Pages: 258
Release: 2007-10-08
Genre: Science
ISBN: 3540727264

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This book presents Bayes’ theorem, the estimation of unknown parameters, the determination of confidence regions and the derivation of tests of hypotheses for the unknown parameters. It does so in a simple manner that is easy to comprehend. The book compares traditional and Bayesian methods with the rules of probability presented in a logical way allowing an intuitive understanding of random variables and their probability distributions to be formed.