Chapter 3: Further Reading

An annotated bibliography of resources for deepening your understanding of probability theory, Bayesian statistics, and their applications to prediction markets.

Foundational Probability Textbooks

1. Introduction to Probability by Joseph K. Blitzstein and Jessica Hwang (2nd Edition, 2019)

The best modern introduction to probability for anyone with basic calculus. Blitzstein's approach emphasizes intuition and storytelling alongside rigorous mathematics. The accompanying Harvard Stat 110 lectures (freely available online) are among the finest probability lectures ever recorded. Particularly relevant chapters: conditional probability (Ch. 2), Bayes' theorem (Ch. 2), random variables and distributions (Ch. 3-5), expected value and variance (Ch. 4). The book's numerous examples from games, strategy, and decision-making translate naturally to prediction market contexts.

2. Probability and Statistics for Engineering and the Sciences by Jay Devore (9th Edition, 2016)

A widely used textbook that balances theory and application. The treatment of discrete and continuous distributions is thorough and accessible. The chapters on point estimation and hypothesis testing provide a bridge to Chapter 4 of this textbook. Best suited for readers who want a structured, problem-set-driven approach to learning probability.

3. A First Course in Probability by Sheldon Ross (10th Edition, 2019)

A classic text that has been the standard introduction for decades. Ross covers all the foundational material in this chapter with clarity and precision. The book is denser than Blitzstein but more concise. The sections on conditional probability and Bayes' theorem are particularly well-written.

4. Probability Theory: The Logic of Science by E.T. Jaynes (2003)

A philosophical and mathematical tour de force that presents probability as an extension of logic. Jaynes argues passionately for the Bayesian interpretation and demonstrates its power across science and engineering. The first few chapters provide deep insight into why probability is the right framework for reasoning under uncertainty. This book is advanced but profoundly rewarding. Its perspective is essential for anyone who wants to understand why prediction markets work.

Bayesian Statistics

5. Bayesian Statistics the Fun Way by Will Kurt (2019)

The most accessible introduction to Bayesian thinking available. Kurt uses vivid examples (alien invasions, cookie jars, superheroes) to build intuition for priors, likelihoods, and posteriors. Despite the playful tone, the mathematical content is sound. An excellent starting point for readers who find traditional statistics textbooks intimidating. The chapters on Bayes' theorem and the Beta distribution are directly applicable to this chapter.

6. Statistical Rethinking: A Bayesian Course with Examples in R and Stan by Richard McElreath (2nd Edition, 2020)

A remarkable textbook that teaches Bayesian statistics through modeling and simulation rather than mathematical proofs. McElreath's writing is engaging and his emphasis on building generative models aligns perfectly with the prediction market mindset. The treatment of Beta-Binomial models (Ch. 2) is one of the best available. Accompanying video lectures are freely available.

7. Doing Bayesian Data Analysis by John Kruschke (2nd Edition, 2015)

Known as the "Puppy Book" for its cover art, this is a comprehensive, hands-on guide to Bayesian methods. Kruschke covers everything from basic Bayes' theorem to hierarchical models, with extensive R and JAGS code examples. The early chapters on Bayesian updating with Beta priors are directly relevant to this chapter. The book excels at visual explanations.

8. Think Bayes by Allen Downey (2nd Edition, 2021)

A Python-centric introduction to Bayesian statistics. Downey builds up from simple examples to complex models using computational approaches rather than analytical solutions. The code-first pedagogy makes this book ideal for programmers learning Bayesian methods. Freely available online. The chapters on estimating proportions and comparing hypotheses connect directly to prediction market analysis.

Probability Applied to Decision-Making and Markets

9. Thinking in Bets by Annie Duke (2018)

A former professional poker player applies probabilistic thinking to everyday decision-making. Duke's central argument --- that all decisions are bets under uncertainty --- maps directly to prediction market participation. The book provides excellent intuition about separating decision quality from outcome quality, calibrating confidence, and updating beliefs. Not a technical book, but essential reading for the prediction market mindset.

10. Superforecasting: The Art and Science of Prediction by Philip Tetlock and Dan Gardner (2015)

Tetlock's research on forecasting tournaments (the predecessors to modern prediction markets) demonstrated that certain thinking habits --- including probabilistic reasoning, Bayesian updating, and calibration --- distinguish excellent forecasters from average ones. This book provides the empirical evidence that the skills taught in this chapter actually matter for real-world prediction. Essential context for understanding why probability fundamentals are worth mastering.

11. The Signal and the Noise by Nate Silver (2012)

Silver's exploration of prediction across domains (weather, elections, earthquakes, poker) provides rich context for understanding how probability theory works in practice. The chapters on Bayesian reasoning and the distinction between signal and noise are particularly relevant. Silver's discussion of calibration and overconfidence connects to the practical considerations in Section 3.11.

12. Fortune's Formula by William Poundstone (2005)

A lively history of the connections between information theory, probability, and gambling/investing. The book covers the Kelly criterion (previewed in Case Study 2), the story of Claude Shannon and Ed Thorp, and the mathematical foundations of betting strategy. Provides historical context for why expected value and variance matter in betting markets.

Academic Papers and Technical References

13. "The Role of Prediction Markets in Forecasting" by Kenneth Arrow et al. (Science, 2008)

A brief but influential essay by a group of prominent economists (including Nobel laureate Arrow) arguing for the value of prediction markets. The paper discusses how market prices aggregate information through what is essentially distributed Bayesian updating. A foundational reference for the prediction markets field.

14. "Prediction Markets: Does Money Matter?" by Emile Servan-Schreiber et al. (Electronic Markets, 2004)

Examines whether prediction markets with real money outperform play-money markets. The paper implicitly tests whether financial incentives improve the Bayesian updating process --- whether putting "skin in the game" leads to more accurate probability estimates. Relevant to understanding whether market prices are truly reliable probability estimates.

15. "A Comparison of Forecasting Methods: Prediction Markets, Polls, and Expert Opinions" by Berg, Nelson, and Rietz (2008)

Compares the accuracy of prediction market probabilities against traditional forecasting methods. The paper provides empirical evidence for the quality of market-implied probabilities, connecting directly to the question of how well markets perform Bayesian updating in practice.

16. "Proper Scoring Rules, Dominated Forecasts, and Coherence" by Tilmann Gneiting and Adrian Raftery (Journal of the American Statistical Association, 2007)

A technical paper on scoring rules --- mathematical functions that evaluate the quality of probabilistic forecasts. Proper scoring rules incentivize honest probability reporting, which is the theoretical foundation for why prediction market prices should reflect true beliefs. The Brier score discussed in Exercise C.6 is a proper scoring rule covered in this paper.

Online Resources

17. Seeing Theory (seeingtheory.brown.edu)

An interactive visual introduction to probability and statistics created by Daniel Kunin at Brown University. The visualizations for basic probability, compound probability, and Bayesian updating are exceptionally well-designed. An excellent supplement to the mathematical treatment in this chapter.

18. 3Blue1Brown: "Bayes' Theorem" YouTube Video

Grant Sanderson's visual explanation of Bayes' theorem is widely regarded as the best short introduction available. The video builds intuition through geometric representations and avoids the common confusion between P(A|B) and P(B|A). A 15-minute investment that pays enormous dividends for understanding.

19. Metaculus Calibration Training (metaculus.com)

Metaculus is a prediction platform that provides calibration training tools. Users can practice assigning probabilities to questions and receive feedback on their calibration. This is the practical application of the probability concepts in this chapter --- you can directly practice and improve your probability estimation skills.

20. Arbital Guide to Bayes' Rule (arbital.com)

Eliezer Yudkowsky's extensive guide to Bayes' theorem on Arbital. It covers everything from the absolute basics to advanced applications, with a focus on building deep intuition. The multiple-level approach (introductory, intermediate, advanced) allows readers of different backgrounds to engage with the material. Particularly strong on the odds form of Bayes' theorem and the concept of likelihood ratios.