Contents

• Purpose of Slide 1
• Draft Structure
  • Motivation
  • Covariance matrix
  • Eigen-decomposition mechanics
  • Three components / curve shapes
  • Outputs as a list
  • Assumptions as bridge
  • Does the draft structure meet the main steps of pca
• Draft Script

Purpose of Slide 1

The purpose of slide 1 is to (re)familiarise audience with components of classical PCA model and set up the discussion for slide 2 which will detail which components change under the probablistic Bayesian model.

We may want to say why Classical PCA is limited.

Draft Structure

Motivation — 0:45

Covariance matrix — 1:00

• transformations how we get to it (perhaps)

Eigen-decomposition mechanics — 1:30

Three components / curve shapes — 2:00

Outputs as a list — 0:45

Assumptions as bridge — 0:45

6 mins 45... goes over the 5 mins

Does the draft structure meet the main steps of pca

● No — the structure has gaps against the 5 steps:

• Data prep (step 1) — no dedicated section; it only shows up buried in the script (point 10), not in the structure/timing.
• Covariance matrix (step 2) — covered, 1:00.
• Eigen-decompose (step 3) — covered as "Eigen-decomposition mechanics," 1:30.
• Order/select components (step 4) — not really covered. "Three components / curve shapes" (2:00) skips straight to interpreting 3 components as level/slope/curvature rather than explaining the selection/ranking-by-eigenvalue logic.
• Project onto eigenvectors → scores (step 5) — not its own section; scores only appear implicitly under "Outputs as a list."

So the structure is built around motivation → covariance → eigen-decomposition → (interpretation, not selection) → outputs → assumptions. It's missing explicit beats for data prep and for the projection step, and it swaps "component selection" for "component interpretation."

Draft Script

1. the aim is to get eigenvectors and component scores. explain vectors allow factor reduction technique.
4. Loadings are the eigenvectors of the covariance matrix. Each loading vector tells you how much the original variable (interest rate tenor) contributes to that component.
6. Principal components are the projected scores that live in the reduced space. Although it is VERY common to use principal component to refer to the eigenvector. I will therefore use DATA SCORES and LOADINGS.
10. Produce a "calibration \ analysis" dataset: involves differencing, demeaning, taking logs.
11. Covariance matrix encodes the structure and relationships in the data - the variance and covariance between features.
12. information lost as a result of covariance matrix is ....
14. we project raw data onto eigenvectors - the component scores -
17. The reason we take logarithmns....
18. Choice of co-variance or correlation matrix...
22. a justification for using 2016 is that terms greater than 25 not available before 2016
50. Classical PCA gives you a single fixed answer - principal components\ scores and loadings

Soundbites