Probabilities and Statistics

Statistics

• Probability and Statistics, DeGroot et al
• [Probability Theory: The Logic of Science], E.T. Jaynes (2003)
• Probabilistic Graphical Models, D. Koller and N. Friedman (2009)
• Introduction to Probability, Blitzstein, Hwang
• D. Applebaum: Probability and Information: An Integrated Approach, 2nd ed (2008)
• M. Jordan preprints
  • The Multivariate Gaussian
  • The Exponential Family: Basics
  • The Exponential Family: Conjugate Priors
• J. Pearl: Causality (2009)

Bayesian Statistics

• Ch. Robert: The Bayesian Choice (2007)
• A. Gelman et al: Bayesian Data Analysis, 2nd ed (2004)
• Ben Lambert: A Student’s Guide to Bayesian Statistics (2018), videos

Variational Bayes

• M. Jordan et al: An Introduction to Variational Methods for Graphical Models (1998)
• M. Wainwright, M. Jordan: Graphical Models, Exponential Families, and Variational Inference (2008)
• D. Blei et al: Variational Inference: A Review for Statisticians (2017)

Courses

• Harvard Stat 110 (2013)
• MIT 14.30 Intro to Statistical Methods in Economics
• Duke: S. Schmidler: Stat 376: Advanced Modeling and Scientific Computing, with many references and papers

Statistics in Machine Learning

• InformationTheory, Inference, and Learning Algorithms, by David MacKay (2005 version)
• A Gentle Introduction to Information Entropy, blog post
• Stochastic approximation: a dynamical systems viewpoint, V. Borkar (2008)

Statistics in Financial Markets

• Theory of Financial Risk and Derivative Pricing: From Statistical Physics to Risk Management, by Jean-Philippe Bouchaud & Marc Potters (2011)

Axiomatic statistics

• A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics, Tobias Fritz (Aug 2019)

Presentations

• Ben Lambert: A Student’s Guide to Bayesian Statistics
  • An introduction to the concept of a sufficient statistic
• ritvikmath:
  • Maximum Likelihood
  • Accept-Reject Sampling
  • Markov Chains
  • Markov Chain Stationary Distribution
  • Markov Chain Monte Carlo (MCMC)
  • Metropolis - Hastings
  • Gibbs Sampling
  • Thompson Sampling
  • Inverse Transform Sampling
  • EM Algorithm
  • Gaussian Mixture Model
  • Hidden Markov Model
  • Multi-Armed Bandit

Other

• Market Trading
• Robotics
• Self Driving Cars