“It is by logic that we prove, but by intuition that we discover. To know how to criticize is good, to know how to create is better.” — Henri Poincaré

Probability inequalities

I explain and prove some common concentration and expectation inequalities

Fisher information and the Cramér–Rao lower bound

Why curvature of the log-likelihood controls estimation precision

Likelihood and the score

What the likelihood function is, why it is not a probability, and what the score tells you

Stochastic convergence

A visual guide to convergence in distribution, in probability, and almost surely