**General probability and statistics**

- Random variables as vectors
- Covariance matrix and Mahalanobis distance
- Moments as tensors; tensor notation for moments
- Causation, partial covariance matrix, Bayesian networks
- MGFs
- Sample statistics: moments
- Sample statistics: order statistics
- Distribution of means with non-vanishing variance: intuition for the Cauchy distribution
- Heavy tails, perhaps some generalisations
- Introduction to Bayesian inference
- Special cases of Bayesian inference
- Estimators [1] [2], bias-variance decomposition [1]
- p-hacking, jelly beans
- Fisher information, Bernstein-von Mises theorem, Rao-Cramer inequality
- Decision theory
- Relationship between median and absolute error/absolute deviation in regression, Lasso, Tikhonov regularisation, Generalised SVD [1], [2], [3]
- 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.

- Important distributions: normal (inflection pt, rot. invar., Gaussian process, etc.), nomial
- Important distributions: poisson (derivation, indep to memoryless), geometric, exponential, gamma
- Important distributions: beta, Dirichlet -- also: beta is order statistic of uniform
- Important distributions: t
- 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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