Here is an attempt to add material on probability and statistic subjects affecting the field of Artificial Intelligence.

  1. Introduction slides
    • The Basics and intuition on counting
    • Frequentist views of probability
    • Introduction to random variables
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  2. Families of Distributions
    • Discrete Distributions
    • Continuous Distributions
    • Exponential Families
    • Location and Scale Families
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  3. Functions of Random Variable
    • Transformations
    • Expectations
    • Moments
    • Method of Moments
    • Bivariate Transformations
    \[\]
  4. Bayesian Estimation slides
    • The likelihood principle, \(\ell \left( \theta \right)\).

    • General A Posteriori methods

      \[P\left( \theta \vert x \right) \approx P \left( x \vert \theta \right) P\left( \theta \right)\]
  5. Priors and Estimation
    • A Problem with subjectivity
    • Priors
    • Exponential Priors
    • Conjugate Priors
    • Local/Scale Family
    • Improper Priors
    • The Great Jeffrey
    \[\]
  6. Hierarchical Bayes
    • The Posterior
    • A Graphical View
    • Plate Notation
    • Why Hierarchical Models?
    • Examples
    \[\]
  7. Introduction to Markov Chain Monte Carlo
    • The History of the Monte Carlo
    • The Basics
    • Monte Carlo Integration
    • Rejection Sampling
    • Slice Sampler
    • Importance Sampling
    • Metropolis-Hasting
    • Gibbs Sampler
    \[\]
  8. More Advanced Methods in Markov Chain Monte Carlo
    • Bayesian Estimation
    • Simulated Annealing and Beyond
    • Population-Based MCMC Methods
    • Hamiltonian Monte Carlo
    • Rao-Blackwellisation
    • Divide & Conquer strategies
    • Pseudo-marginal strategies
    \[\]
  9. Theory of Point Estimation
    • The main problem
    • Unbiasdness Estimators
    • Equivariance
    • Average Risk Optimality
    • Minimaxity and Admissibility
    • Asymptotic Optimality
    \[\]

UNDER CONSTRUCTION