Probability Books: Recommended Reading
Probability theory is essential for statistics, machine learning, finance, and physics. These books cover everything from combinatorial probability through measure theory and stochastic processes.
Introductory Probability
Standard introductory probability textbooks.
| Book | Author | Year | Level | Description |
|---|---|---|---|---|
| Introduction to Probability 2nd Edition, CRC Press | Joseph K. Blitzstein, Jessica Hwang | 2019 | Intermediate | Harvard's Stat 110 textbook, the best modern introduction to probability. Free lectures on YouTube. |
| A First Course in Probability 10th Edition, Pearson | Sheldon M. Ross | 2018 | Beginner-Intermediate | The most widely used introductory probability textbook. |
| Introduction to Probability 2nd Edition, Athena Scientific | Dimitri P. Bertsekas, John N. Tsitsiklis | 2008 | Intermediate | MIT-based textbook with strong emphasis on conditioning and intuition. |
Measure-Theoretic Probability
Rigorous graduate-level probability based on measure theory.
| Book | Author | Year | Level | Description |
|---|---|---|---|---|
| Probability: Theory and Examples 5th Edition, Cambridge | Rick Durrett | 2019 | Advanced | The standard graduate probability textbook, freely available. Rigorous measure-theoretic treatment with many examples. |
| Probability and Measure Anniversary Edition, Wiley | Patrick Billingsley | 2012 | Advanced | Classic rigorous probability textbook. |
| Foundations of Modern Probability 2nd Edition, Springer | Olav Kallenberg | 2002 | Advanced | Comprehensive advanced probability reference. |
Stochastic Processes
Markov chains, martingales, and Brownian motion.
| Book | Author | Year | Level | Description |
|---|---|---|---|---|
| Introduction to Stochastic Processes 2nd Edition, Chapman & Hall | Gregory F. Lawler | 2006 | Advanced | Clear introduction to major stochastic processes. |
| Markov Chains and Mixing Times 2nd Edition, AMS | David A. Levin, Yuval Peres | 2017 | Advanced | Modern treatment of Markov chains with mixing time focus. Free online. |
| Brownian Motion and Stochastic Calculus 2nd Edition, Springer | Ioannis Karatzas, Steven E. Shreve | 1998 | Advanced | Standard reference on Brownian motion and stochastic integration. |
Applied Probability
Probability with applications to specific domains.
| Book | Author | Year | Level | Description |
|---|---|---|---|---|
| Probability and Random Processes 3rd Edition, Oxford | Geoffrey Grimmett, David Stirzaker | 2001 | Intermediate-Advanced | Broad coverage of probability and stochastic processes. |
| Introduction to Probability Models 12th Edition, Academic Press | Sheldon M. Ross | 2019 | Intermediate | Applied probability emphasizing stochastic models. |
| Stochastic Processes 3rd Edition, Wiley | Sheldon M. Ross | 1995 | Intermediate-Advanced | Classic applied stochastic processes textbook. |
Probability for ML and Physics
Probability with specific applications to machine learning and physics.
| Book | Author | Year | Level | Description |
|---|---|---|---|---|
| Information Theory, Inference, and Learning Algorithms Cambridge | David J.C. MacKay | 2003 | Advanced | Unique integrated treatment of information theory and ML. Free PDF. |
| Probabilistic Graphical Models MIT Press | Daphne Koller, Nir Friedman | 2009 | Advanced | Definitive treatment of probabilistic graphical models. |
| High-Dimensional Probability Cambridge | Roman Vershynin | 2018 | Advanced | Modern probability for data science and ML applications. |