Probability and statistics

See also the Probability Puzzles section of the blog.

General probability and statistics
  1. Random variables as vectors
  2. Covariance matrix and Mahalanobis distance
  3. Moments as tensors; tensor notation for moments
  4. Causation, partial covariance matrix, Bayesian networks
  5. MGFs
  6. Sample statistics: moments
  7. Sample statistics: order statistics
  8. Distribution of means with non-vanishing variance: intuition for the Cauchy distribution
  9. Heavy tails, perhaps some generalisations
  10. Introduction to Bayesian inference
  11. Special cases of Bayesian inference
  12. Estimators [1] [2], bias-variance decomposition [1]
  13. p-hacking, jelly beans
  14. Fisher information, Bernstein-von Mises theorem, Rao-Cramer inequality
  15. Decision theory
  16. Relationship between median and absolute error/absolute deviation in regression, Lasso, Tikhonov regularisation, Generalised SVD [1][2][3]
  17. OLD: Convolutions, generating functions and the central limit theorem
Inequalities (Markov etc.), convergence of random variables in distribution/probability, law of large numbers and related simple laws (stuff like large samples, Bayes convergence etc.). Sufficient statistics.

Reference: special distributions
This is not to be read "in order" or after the above section or whatever -- it's just some reference material on special cases.
  1. Important distributions: normal (inflection pt, rot. invar., Gaussian process, etc.), nomial
  2. Important distributions: poisson (derivation, indep to memoryless), geometric, exponential, gamma
  3. Important distributions: beta, Dirichlet -- also: beta is order statistic of uniform
  4. Important distributions: t
  5. Important distributions: Gumbell, Frechet, Weibull
Random processes
Time series...

ARIMA/differential equations, characteristic functions intuition, ambit stochastics

Markov chains, random walks, martingales

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