classical_filtering#

Series: lecture-python-advanced.myst
File: lectures/classical_filtering.md
Audit date: 2026-08-26
Corpus snapshot: b83d6da399
Categories audited: writing, math, code, references, links, admonitions (JAX out of scope)
Overall score: 7.4 / 10
Priority: HIGH

Score breakdown#

Category	Score	One-line note
Writing	4.5/10	`qe-writing-001` ×2; `qe-writing-005` ×3; `qe-writing-002` ×3, +4 more.
Math	3.5/10	`qe-math-002` ×17; `qe-math-003` ×5.
Code	10/10	no mechanical violations detected.
JAX	out of scope	JAX rules target `lecture-jax`.
Figures	N/A	no figures or plotting code.
References	8.5/10	`qe-ref-001` ×2.
Links	8/10	`qe-link-002` ×3.
Admonitions	10/10	no mechanical violations detected.

Issues#

Critical#

None found.

High severity#

[qe-math-002] — Use \top for transpose notation. Count: 17. Lines: 77, 113, 119, 129, 429, 430, 982, 983, 989, 1001, …. Example: \prime transpose.
[qe-math-003] — Use square brackets for matrix notation. Count: 5. Lines: 371, 444, 461, 484, 491. Example: matrix environment.
[qe-writing-008] — Remove excessive whitespace between words. Count: 40. Lines: 27, 39, 59, 81, 87, 93, 106, 107, 122, 132, …. Example: 2 spaces.

Medium severity#

[qe-link-002] — Use doc links for cross-series references. Count: 3. Lines: 43. Example: raw link to python-intro.quantecon.org.
[qe-ref-001] — Use correct citation style. Count: 2. Lines: 602, 724. Example: {cite} in narrative flow: ‘in {cite}’.
[qe-writing-001] — Use one sentence per paragraph. Count: 2. Lines: 52, 938. Example: 2 sentences in one paragraph.
[qe-writing-002] (reviewer) — Keep writing clear, concise, and valuable. Count: 3. Lines: 210, 240, 384. Example: line 210-212 is a 44-word sentence that names both halves of an orthogonal decomposition, the space each lies in, and defines “orthogonal complement” on the way past; 240-241 is 38 words of forward reference before the point of the example arrives; 384-388 is 41 words with the covariance-stationarity qualification nested inside the claim it qualifies.
[qe-writing-004] — Avoid unnecessary capitalization in narrative text. Count: 1. Lines: 973. Example: mid-sentence ‘Prediction’.
[qe-writing-005] (reviewer) — Use bold for definitions, italic for emphasis. Count: 3. Lines: 767, 907, 973. Example: bold is used as a substitute for a heading or a directive in three places - **Proposition** at 767 (which should be a {prf:proposition}), **Blaschke factors** at 907 (a subsection in all but markup), and **Multivariable Prediction:** at 973 (an exercise title) - none of the three is a definition or an emphasis, which is what the rule reserves bold and italic for.
[qe-writing-007] (reviewer) — Use visual elements to enhance understanding. Count: 3. Lines: 278, 390, 909. Example: 1047 lines with no figure at all, and three passages that ask for one: line 278 and 286 tell the reader to “notice how the lower rows … are converging” in the raw print(Li) / print(L) output of 281-291; lines 390-401 state the central convergence result (bottom rows of \(L^{-1}\) tend to the Wold moving-average coefficients) without plotting a single coefficient sequence; and the Blaschke-factor section at 909-930 turns entirely on which zeros lie inside the unit circle, which is a picture of the complex plane.

Low severity#

[qe-writing-003] (reviewer) — Maintain logical flow. Count: 1. Lines: 312. Example: Example 2 (294-341) says “We proceed in the same way as in example 1” and then fires five code cells in a row (314, 324, 328, 333, 338) with no prose between any of them, dropping the step-by-step narration that made Example 1 readable at 255, 267-271, 278 and 286; line 335 silently switches to Li[-3:, :] and never says that the last three rows are the point.

Strengths#

\mathbb{E} is written with braces in all 40 places it appears, and the conditional-expectation operator is consistently the distinct \mathbb{\hat E} - the notation for expectation never wobbles across 1047 lines.
Duality between LQ control and least-squares prediction is set up as the organising idea in the Overview (32-48) and then actually used: the finite-dimensional prediction formula {eq}`eq_58` is reused to represent the solution of the control problem at 378 and again in the combined section at 417.
Labelled equations are genuinely cross-referenced rather than decorative - eq_36 is cited forward at 241 and 309, eq_54/eq_55 back at 380-382, eq_57 at 210, onetwenty at 994.
The relationship to the companion lecture is stated in the first line with a {doc} reference to lu_tricks (25) and the shared implementation is loaded from it rather than duplicated (225).
The two problem statements the whole lecture serves - the linear least squares prediction problem (548) and filtering problem (555) - are bolded at exactly the point they are defined, each with its own minimand written out.

Recommended actions#

Replace ^\prime with ^\top throughout - 22 occurrences starting at 77, 113, 119, 129, 408, 409, 429, 430, 470, 982 - the single largest mechanical fix in this file (qe-math-002).
Fix the orthogonal decomposition at 210-212: both parts are written \sum^{t-1}_{j=m} L^{-1}_{t,t-j}\varepsilon_{t-j}, but per {eq}`eq_57` the component orthogonal to the span of \([x_{t-m}, \ldots, x_1]\) is \(\sum_{j=0}^{m-1}\); as written the sentence says a term is orthogonal to its own span (and “knowns as” at 212 is a typo for “known as”).
Correct the exercise statement at 954: \mathbb{E} \widehat X_{t+1} \mid X_t, \ldots puts the hat on \(X\) instead of on \(\mathbb{E}\) and drops the brackets round the conditioning set; line 961 has the same missing brackets - both should read \mathbb{\hat E}\left[X_{t+2} \mid X_t, X_{t-1}, \ldots\right] as the body of the lecture writes it (e.g. 1032).
Add the three figures the argument is missing: the Wold coefficient sequences from the bottom rows of \(L^{-1}\) as \(T\) grows (near 291 and 340), and a unit-circle plot of \(\pi(z)\)’s zeros before and after root flipping (near 917) - the Blaschke section is the one part of the lecture with no computational counterpart at all.
Convert the five \begin{matrix} / \begin{array} blocks at 371, 444, 461, 484 and 491 to bmatrix and drop the hand-written \left[ \right] delimiters around them (qe-math-003, 5 occurrences).
Collapse the 40 double spaces (27, 39, 59, 81, 87, 93, 106, 107, 122, 132 and 30 more) - they are dense enough to be a source-formatting habit rather than isolated slips (qe-writing-008); while there, replace the raw links at 43 with {doc} references (qe-link-002, 3 on that one line), move the four narrative {cite} calls at 345, 602, 724 and 1007 out of the sentence flow (qe-ref-001), lower-case Prediction at 973 (qe-writing-004), split the two-sentence paragraphs at 52 and 938 (qe-writing-001), and swap the legacy \hbox at 310 for \text.
Give the two exercises at 934 and 968 gated {solution-start} / {solution-end} blocks - both currently end at {exercise-end} with no solution anywhere in the file, which is the only place in the lecture where the reader is left without a check.