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.
Table of Contents
Dedication v
Preface ix
1 Introduction 1
Part I Foundations 7
2 Data 9
3 Multivariate Data 31
4 Set Theory and Combinatorics 51
5 Probability 71
6 Bayes’ Theorem 107
7 Stochastic Variables on ℝ 137
8 Stochastic Variables II 171
9 Discrete Distributions 197
10 Continuous Distributions 225
Part II Inference 267
11 Introduction 269
12 Bayes’ Theorem for Distributions 279
13 Bayes’ Theorem with Hyperparameters 299
14 Bayesian Hypothesis Testing 329
15 Estimates 351
16 Frequentist Inference 371
17 Linear Regression 389
A Appendix 405
B Solutions to Exercises 423
C Tables 489
Index 497
