Stats index
Statistics is the mathematical toolkit for learning from data under uncertainty. It connects probability models, observed samples, and decisions: probability asks what data a model would generate, while statistics asks which model is plausible given data.
Core route
- Stats Key concepts — probability, random variables, expectation, variance, sampling, estimation, inference.
- Stats Equations and definitions — compact formula sheet for probability, likelihood, estimators, and common summaries.
- Stats Examples — worked examples for Bayes’ rule, confidence intervals, and regression-style thinking.
- Stats Common pitfalls — traps around correlation, -values, variance, and overfitting.
- Normal distribution — the main continuous distribution for errors and averages.
How to think about the subject
A statistical model is a simplified story: it says the data were generated by some distribution with unknown parameters. Inference updates beliefs or estimates those parameters. Diagnostics then ask whether the story is credible. Good statistics is therefore not just formula use; it is modelling, checking assumptions, and communicating uncertainty.
Bridges
Statistics supports ML through likelihoods, losses, validation, and uncertainty. It links naturally to Residuals in NF2 and PINNs where model errors and physical residuals must be interpreted carefully rather than treated as magic scores. It also supports experimental physics by distinguishing measurement noise, systematic error, and real signal.