bossanova verifies its mathematical correctness through property-based testing: every algorithm must satisfy formal theorems for any valid input, checked automatically across thousands of random test cases. This section teaches the math behind those theorems.
You don’t need a strong linear algebra or statistics background. Each page starts with concrete examples and builds intuition before introducing formal statements. Code cells let you see the math in action.
How the pages connect¶
The dependency graph below shows how mathematical domains build on each other. An arrow from A to B means “understanding A helps with B.”
Reading guide¶
Pick a path based on what you want to understand:
| Goal | Pages to read |
|---|---|
| “How does OLS work?” | Linear Algebra → OLS |
| “What are p-values doing?” | OLS → Inference |
| “Are my results reliable?” | OLS → Diagnostics |
| “What are marginal means?” | OLS → Inference → Marginal Means |
| “How do mixed models work?” | Linear Algebra → OLS → Mixed Models |
| “Marginal vs conditional?” | Mixed Models → Marginal vs Conditional |
| “Bootstrap and permutation” | OLS → Resampling |
| “Everything, start to finish” | Read pages in order, top to bottom |
Theorem coverage by page¶
| Page | Theorems | Domain |
|---|---|---|
| Linear Algebra | LA.1–5, LA.7 | Matrix decompositions |
| Ordinary Least Squares | OLS.1, OLS.4–7 | Normal equations, hat matrix |
| Generalized Linear Models | WLS.1–3 | Weighted LS, IRLS |
| Statistical Inference | INF.1–2, INF.4–5 | SE, CI, hypothesis tests |
| Diagnostics | DX.1–4 | Leverage, influence |
| Marginal Means | EMM.1–2 | EMMs, variance propagation |
| Mixed Models | LMM.1–5 | PLS, random effects |
| Marginal vs Conditional | MAR.1–7 | Link scale effects |
| Resampling | BS.1–4 | Bootstrap, permutation |
| Theorem Reference | All | Formal statements |