Probability spaces · Random variables · Convergence · Conditioning
Notes on the mathematical foundations of probability, including random variables, distribution functions, independence, expectation, conditional expectation, laws of large numbers, and modes of convergence.
- Convergence in probability and distribution
- Almost sure convergence
- Conditional expectation
- Weak and strong laws
- Central limit theorems
Open Probability Notes
Optimization | Duality | Optimization in ML
Notes on Convexity, duality, optimization algorithms
- Primal and dual formulations
- Weak and strong duality
- Complementary slackness
- Simplex geometry
- Sensitivity analysis
Open LP Notes
Rare events | Maxima | Exceedances | Tail risk
Notes on modelling rare and extreme events, including block maxima, threshold exceedances, generalized extreme value distributions, generalized Pareto models, tail index estimation, and extreme quantile inference.
- Block maxima and GEV limits
- Peaks over threshold
- Generalized Pareto distribution
- Tail index estimation
- Extreme quantile estimation
Open EVT Notes