Many people have asked me in person about pointers to good books for ramp-up getting into the field. I’ve casually passed around lists quite often, but I thought I’d share it here.

Below I will begin compiling a list of books (though some may simply be manuscripts from professors) that are well known, read, and/or cited for Ph.D. students to grip the noteworthy theories and practices. I will update this list frequently so please feel free to come back often. (Here I’ve temporarily stripped the correct citation format to be edited later.)

**“Birds-eye-view” textbooks:**

Pattern Recognition and Machine Learning. Christopher Bishop.

Machine Learning: A Probabilistic Perspective. Kevin P. Murphy.

Advanced Data Analysis from an Elementary Point of View. Cosma Rohilla Shalizi.

**Subject-focused textbooks / manuscripts:**

**Graphical Models**

Graphical Models, Exponential Families, and Variational Inference. Martin J. Wainwright, Michael I. Jordan.

An Introduction to Conditional Random Fields. Charles Sutton, Andrew McCallum.

**Discrete Models**

Categorical Data Analysis. Alan Agresti.

**Optimization**

Introductory Lectures on Convex Optimization. Yurii Nesterov.

Convex Optimization. Stephen Boyd, Lieven Vandenberghe.

### Deep Learning

Deep Learning. Ian Goodfellow, Yoshua Bengio, Aaron Courville.

**Probability Theory / Measure Theory**

Introduction to Probability Models. Sheldon M. Ross.

Measure Theory and Fine Properties of Functions. Lawrence Craig Evans, Ronald F. Gariepy

Probability Essentials. Jean Jacod, Philip Protter.

Probabilistic Symmetries and Invariance Principles. Olav Kallenberg.

**Stochastic Process / Stochastic Differential Equations**

Poisson Processes. J. F. C. Kingman.

Stochastic Methods. Crispin Gardiner.

An Introduction to Stochastic Differential Equations. Lawrence Craig Evans.

Stochastic Differential Equations: An Introduction with Applications.Bernt Øksendal.

Determinantal point processes for machine learning. Alex Kulesza, Ben Taskar.

Gaussian Processes for Machine Learning. Carl Edward Rasmussen, Christopher K. I. Williams.

### Optimal Transport

Computational Optimal Transport. Gabriel Peyré, Marco Cuturi.

**Linear Algebra**

-TBA

**Real Analysis**

-TBA

**Complex Analysis**

-TBA

**Functional Analysis**

Introductory Functional Analysis with Applications. Erwin Kreyszig.

**Ordinary / Partial Differential Equations**

Partial Differential Equations. Lawrence Craig Evans.

**Differential Geometry**

**Statistical Inference**

Statistical Inference. George Casella, Roger L. Berger.

Testing Statistical Hypotheses. Erich L. Lehmann, Joseph P. Romano.

Semiparametric Theory and Missing Data. Anastasios A. Tsiatis.

Computer Age Statistical Inference: Algorithms, Evidence and Data Science. Bradley Efron, Trevor Hastie.

The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Trevor Hastie, Robert Tibshirani, Jerome Friedman.

**Bayesian Statistics**

Bayesian Data Analysis. Andrew Gelman, John B. Carlin, Hal S. Stern, David B. Dunson, Aki Vehtari, Donald B. Rubin.

**Bayesian Approximate Inference**

Handbook of Markov Chain Monte Carlo. Steve Brooks, Andrew Gelman, Galin L. Jones, Xiao-Li Meng.

**Reinforcement Learning**

Reinforcement Learning: An Introduction. Richard S. Sutton, Andrew G. Barto.

**Causal Inference**

Causal Inference for Statistics, Social, and Biomedical Sciences: An Introduction. Guido W. Imbens, Donald B. Rubin.

Causality: Models, Reasoning and Inference. Judea Pearl.

Counterfactuals and Causal Inference: Methods and Principles for Social Research. Christopher Morgan, Stephen Winship.

Causal Inference. Miguel A. Hernán, James M. Robins.

Elements of Causal Inference: Foundations and Learning Algorithms. Jonas Peters, Dominik Janzing, Bernhard Schölkopf.

**Information Retrieval**

Information Retrieval. Christopher Manning, Prabhakar Raghavan,

**Data Mining**

-TBA

**Econometrics**

Mostly Harmless Econometrics: An Empiricist’s Companion. Joshua D. Angrist, Jörn-Steffen Pischke.

**Mathematical & Computational Finance**

-TBA

**Quantum Physics / Chemistry**

-TBA

**Algebraic & Computational Game Theory**

-TBA

Enjoy.