Table of Contents
Preface
1 Bayes's Theorem
2 Computational Statistics
3 Estimation
4 More Estimation
5 Odds and Addends
6 Decision Analysis
7 Prediction
8 Observer Bias
9 Two Dimensions
10 Approximate Bayesian Computation
11 Hypothesis Testing
12 Evidence
13 Simulation
14 A Hierarchical Model
15 Dealing with Dimensions
About the Book
Think Bayes is an introduction to Bayesian statistics using computational methods.
The premise of this book, and the other books in the Think X series, is that if you know how to program, you can use that skill to learn other topics.
Most books on Bayesian statistics use mathematical notation and present ideas in terms of mathematical concepts like calculus. This book uses Python code instead of math, and discrete approximations instead of continuous mathematics. As a result, what would be an integral in a math book becomes a summation, and most operations on probability distributions are simple loops.
I think this presentation is easier to understand, at least for people with programming skills. It is also more general, because when we make modeling decisions, we can choose the most appropriate model without worrying too much about whether the model lends itself to conventional analysis. Also, it provides a smooth development path from simple examples to real-world problems.
About the Contributors
Author
Allen B. Downey is an American computer scientist, Professor of Computer Science at the Franklin W. Olin College of Engineering and writer of free textbooks. Downey received in 1989 his BS and in 1990 his MA, both in Civil Engineering from the Massachusetts Institute of Technology, and his PhD in Computer Science from the University of California at Berkeley in 1997. He started his career as Research Fellow in the San Diego Supercomputer Center in 1995. In 1997 he became Assistant Professor of Computer Science at Colby College, and in 2000 at Wellesley College. He was Research Fellow at Boston University in 2002 and Professor of Computer Science at the Franklin W. Olin College of Engineering since 2003. In 2009-2010 he was also Visiting Scientist at Google Inc.
Bayesian Theory by Adrian F. M. Smith; José M. BernardoThis 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