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: 516
Release: 2018-07-13
Genre: Mathematics
ISBN: 1119246881

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.

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

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.

Introduction to Bayesian Statistics

Introduction to Bayesian Statistics
Author: William M. Bolstad
Publisher: John Wiley & Sons
Total Pages: 608
Release: 2016-09-02
Genre: Mathematics
ISBN: 1118593227

"...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 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

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.

Statistics and Probability with Applications for Engineers and Scientists

Statistics and Probability with Applications for Engineers and Scientists
Author: Bhisham C. Gupta
Publisher: John Wiley & Sons
Total Pages: 896
Release: 2013-04-29
Genre: Mathematics
ISBN: 1118464044

Introducing the tools of statistics and probability from the ground up An understanding of statistical tools is essential for engineers and scientists who often need to deal with data analysis over the course of their work. Statistics and Probability with Applications for Engineers and Scientists walks readers through a wide range of popular statistical techniques, explaining step-by-step how to generate, analyze, and interpret data for diverse applications in engineering and the natural sciences. Unique among books of this kind, Statistics and Probability with Applications for Engineers and Scientists covers descriptive statistics first, then goes on to discuss the fundamentals of probability theory. Along with case studies, examples, and real-world data sets, the book incorporates clear instructions on how to use the statistical packages Minitab® and Microsoft® Office Excel® to analyze various data sets. The book also features: • Detailed discussions on sampling distributions, statistical estimation of population parameters, hypothesis testing, reliability theory, statistical quality control including Phase I and Phase II control charts, and process capability indices • A clear presentation of nonparametric methods and simple and multiple linear regression methods, as well as a brief discussion on logistic regression method • Comprehensive guidance on the design of experiments, including randomized block designs, one- and two-way layout designs, Latin square designs, random effects and mixed effects models, factorial and fractional factorial designs, and response surface methodology • A companion website containing data sets for Minitab and Microsoft Office Excel, as well as JMP ® routines and results Assuming no background in probability and statistics, Statistics and Probability with Applications for Engineers and Scientists features a unique, yet tried-and-true, approach that is ideal for all undergraduate students as well as statistical practitioners who analyze and illustrate real-world data in engineering and the natural sciences.

Bayesian Spectrum Analysis and Parameter Estimation

Bayesian Spectrum Analysis and Parameter Estimation
Author: G. Larry Bretthorst
Publisher: Springer Science & Business Media
Total Pages: 210
Release: 2013-03-09
Genre: Mathematics
ISBN: 146849399X

This work is essentially an extensive revision of my Ph.D. dissertation, [1J. It 1S primarily a research document on the application of probability theory to the parameter estimation problem. The people who will be interested in this material are physicists, economists, and engineers who have to deal with data on a daily basis; consequently, we have included a great deal of introductory and tutorial material. Any person with the equivalent of the mathematics background required for the graduate level study of physics should be able to follow the material contained in this book, though not without eIfort. From the time the dissertation was written until now (approximately one year) our understanding of the parameter estimation problem has changed extensively. We have tried to incorporate what we have learned into this book. I am indebted to a number of people who have aided me in preparing this docu ment: Dr. C. Ray Smith, Steve Finney, Juana Sunchez, Matthew Self, and Dr. Pat Gibbons who acted as readers and editors. In addition, I must extend my deepest thanks to Dr. Joseph Ackerman for his support during the time this manuscript was being prepared.

Statistics with JMP

Statistics with JMP
Author: Peter Goos
Publisher: John Wiley & Sons
Total Pages: 370
Release: 2015-05-04
Genre: Mathematics
ISBN: 1119035708

Peter Goos, Department of Statistics, University of Leuven, Faculty of Bio-Science Engineering and University of Antwerp, Faculty of Applied Economics, Belgium David Meintrup, Department of Mathematics and Statistics, University of Applied Sciences Ingolstadt, Faculty of Mechanical Engineering, Germany Thorough presentation of introductory statistics and probability theory, with numerous examples and applications using JMP JMP: Graphs, Descriptive Statistics and Probability provides an accessible and thorough overview of the most important descriptive statistics for nominal, ordinal and quantitative data with particular attention to graphical representations. The authors distinguish their approach from many modern textbooks on descriptive statistics and probability theory by offering a combination of theoretical and mathematical depth, and clear and detailed explanations of concepts. Throughout the book, the user-friendly, interactive statistical software package JMP is used for calculations, the computation of probabilities and the creation of figures. The examples are explained in detail, and accompanied by step-by-step instructions and screenshots. The reader will therefore develop an understanding of both the statistical theory and its applications. Traditional graphs such as needle charts, histograms and pie charts are included, as well as the more modern mosaic plots, bubble plots and heat maps. The authors discuss probability theory, particularly discrete probability distributions and continuous probability densities, including the binomial and Poisson distributions, and the exponential, normal and lognormal densities. They use numerous examples throughout to illustrate these distributions and densities. Key features: Introduces each concept with practical examples and demonstrations in JMP. Provides the statistical theory including detailed mathematical derivations. Presents illustrative examples in each chapter accompanied by step-by-step instructions and screenshots to help develop the reader’s understanding of both the statistical theory and its applications. A supporting website with data sets and other teaching materials. This book is equally aimed at students in engineering, economics and natural sciences who take classes in statistics as well as at masters/advanced students in applied statistics and probability theory. For teachers of applied statistics, this book provides a rich resource of course material, examples and applications.

Introduction to Modern Bayesian Econometrics

Introduction to Modern Bayesian Econometrics
Author: Tony Lancaster
Publisher: Wiley-Blackwell
Total Pages: 401
Release: 2004-06-28
Genre: Business & Economics
ISBN: 9781405117197

Almost two hundred and forty years ago, an English clergyman named Thomas Bayes developed a method to calculate the chances of uncertain events. While his method has extensive applications to the work of applied economists, it is only recent advances in computing that have made it possible to exploit the full power of the Bayesian way of doing applied economics.In this new and expanding area, Tony Lancasters text provides a comprehensive introduction to the Bayesian way of doing applied economics. Using clear explanations and practical illustrations and problems, the text presents innovative, computer-intensive ways for applied economists to use the Bayesian method.The Introduction emphasizes computation and the study of probability distributions by computer sampling, showing how these techniques can provide exact inferences about a wide range of econometric problems. Covering all the standard econometric models, including linear and non-linear regression using cross-sectional, time series, and panel data, it also details causal inference and inference about structural econometric models. In addition, each chapter includes numerical and graphical examples and demonstrates their solutions using the S programming language and Bugs software.

The Book of Why

The Book of Why
Author: Judea Pearl
Publisher: Basic Books
Total Pages: 432
Release: 2018-05-15
Genre: Computers
ISBN: 0465097618

A Turing Award-winning computer scientist and statistician shows how understanding causality has revolutionized science and will revolutionize artificial intelligence "Correlation is not causation." This mantra, chanted by scientists for more than a century, has led to a virtual prohibition on causal talk. Today, that taboo is dead. The causal revolution, instigated by Judea Pearl and his colleagues, has cut through a century of confusion and established causality -- the study of cause and effect -- on a firm scientific basis. His work explains how we can know easy things, like whether it was rain or a sprinkler that made a sidewalk wet; and how to answer hard questions, like whether a drug cured an illness. Pearl's work enables us to know not just whether one thing causes another: it lets us explore the world that is and the worlds that could have been. It shows us the essence of human thought and key to artificial intelligence. Anyone who wants to understand either needs The Book of Why.

Bayesian Theory

Bayesian Theory
Author: José M. Bernardo
Publisher: John Wiley & Sons
Total Pages: 608
Release: 2009-09-25
Genre: Mathematics
ISBN: 047031771X

This highly acclaimed text, now available in paperback, provides a thorough account of key concepts and theoretical results, with particular emphasis on viewing statistical inference as a special case of decision theory. Information-theoretic concepts play a central role in the development of the theory, which provides, in particular, a detailed discussion of the problem of specification of so-called prior ignorance . The work is written from the authors s committed Bayesian perspective, but an overview of non-Bayesian theories is also provided, and each chapter contains a wide-ranging critical re-examination of controversial issues. The level of mathematics used is such that most material is accessible to readers with knowledge of advanced calculus. In particular, no knowledge of abstract measure theory is assumed, and the emphasis throughout is on statistical concepts rather than rigorous mathematics. The book will be an ideal source for all students and researchers in statistics, mathematics, decision analysis, economic and business studies, and all branches of science and engineering, who wish to further their understanding of Bayesian statistics