Probability Topics

  1. Probability models

    1. Probability denstiy functions

    2. Classic distributons

      1. Bernouli

      2. Binomial

      3. Poisson

      4. Gaussian

      5. Chi-Square

      6. Exponential family

    3. Multivariate distributions

      1. Independence

      2. Covariance

      3. Conditional distributions

      4. Marginal distributions

      5. Graphical Models

        1. https://github.com/pgmpy/pgmpy

        2. https://github.com/jmschrei/pomegranate

        3. Video

      6. Copula

    4. Information theory

      1. Entropy

      2. Mutual information

      3. KL divergence

      4. cross entropy

    5. Divergences

      1. KL Divergence

      2. Fisher distance

      3. Optimal Transport

      4. Hellinger distance

      5. f-divergences

      6. Stein divergence

    6. Implicit probabity models

      1. Simulators

      2. Probabilistic Programming

        1. https://docs.pymc.io

        2. ppymc3 vs. stan vs edward

        3. pyro

        4. pyprob

  2. Likelihood function

  3. Axioms of probability

    1. Probability Space

  4. Transformation properties

    1. Change of variables

      1. Propagation of errors

    2. Reparameterization

  5. Bayes Theorem

    1. Subjective priors

    2. Emperical Bayes

    3. Jeffreys’ prior

    4. Unfiform priors

    5. Reference Priors

    6. Transformation Properties

  6. Convolutions and the Central Limit Theorem

    1. Binomial example

    2. Convolutions in Fourier domain

  7. Extreme Value Theory

    1. Weibull law

    2. Gumbel law

    3. Fréchet Law

Preliminaries Random Variables