lq_robust_smoothing#

  • Series: lecture-python.myst

  • File: lectures/lq_robust_smoothing.md

  • Audit date: 2026-08-26

  • Corpus snapshot: e25fdf2345

  • Categories audited: writing, math, code, figures, references, links, admonitions (JAX out of scope)

  • Overall score: 8.4 / 10

  • Priority: LOW

Score breakdown#

Category

Score

One-line note

Writing

5.5/10

qe-writing-005 ×6; qe-writing-002 ×4; qe-writing-003 ×1, +1 more.

Math

7.5/10

qe-math-003 ×9.

Code

8.5/10

qe-code-001 ×3.

JAX

out of scope

JAX rules target lecture-jax.

Figures

7.5/10

qe-fig-003 ×2; qe-fig-001 ×1.

References

10/10

no mechanical violations detected.

Links

10/10

no mechanical violations detected.

Admonitions

10/10

no mechanical violations detected.

Issues#

Critical#

None found.

High severity#

  • [qe-math-003] — Use square brackets for matrix notation. Count: 9. Lines: 105, 107, 108, 110, 111, 133, 136, 222, 469. Example: pmatrix environment.

  • [qe-writing-005] (reviewer) — Use bold for definitions, italic for emphasis. Count: 6. Lines: 189, 622, 768, 862, 1036, 1048. Example: bold is used for emphasis in places the lecture elsewhere italicises, and the clearest evidence is internal: line 491 writes more persistent in italic and line 1036 writes more persistent in bold, the same two words making the same point. The other five are conditional means (189), the whole bolded sentence at 622, the bolded question at 862, and high-frequency / Low-frequency (768, 772) and do (1048). The lecture’s genuine definitions are bolded correctly and abundantly (75-77, 187, 191, 203, 292, 433, 473, 864, 866), and its emphases are italicised correctly eighteen times, so this is drift rather than a missing convention.

Medium severity#

  • [qe-code-001] (reviewer) — Follow PEP8 unless closer to mathematical notation. Count: 3. Lines: 889, 899, 906. Example: three one-line docstrings are written as padded single-quoted strings rather than triple-quoted (PEP 257, referenced by PEP 8): "Simulate n_paths draws of μ_{t+1} = ζ μ_t + α w_{t+1} from μ_0 = 0." (889), and likewise 899 and 906. The other three docstrings in the lecture (690-693, 698-701, 1178-1184) use triple quotes, so the file is inconsistent with itself; the same three functions are copied into lq_robust_bewley.md, where they have the same problem. No other PEP8 deviation was found - no long lines, no trailing whitespace, and the arithmetic spacing is correct throughout.

  • [qe-fig-003] — No matplotlib embedded titles. Count: 2. Lines: 834, 840. Example: .set_title.

  • [qe-writing-002] (reviewer) — Keep writing clear, concise, and valuable. Count: 4. Lines: 227, 318, 599, 1124. Example: line 227 is a 70-word semicolon chain that defines ten symbols in a single sentence (\(^*\), \(c\), \(s\), \(h\), \(k\), \(i\), \(d\), \(b\), \(\gamma\), \(w^*\), \(v^*\)) - the lecture uses bulleted lists for exactly this job at 74-78 and 148-152, so the list form is available and preferred; line 318 packs the special case, two identities and a marginal-propensity result into 50 words; line 599 runs to 48 words with two subordinated ‘as in locus’ clauses; and line 1124 in the exercise solution leaves a working step in the text - ‘\(\hat\beta - 1 = -\delta + u/\delta \cdot \beta/\beta\), more directly \(\hat\beta-1+u = (u-\delta^2)/\delta\)’ - where the first expression multiplies by \(\beta/\beta\) and is then abandoned.

Low severity#

  • [qe-fig-001] — Do not set figure size unless necessary. Count: 1. Lines: 823. Example: figsize=.

  • [qe-writing-003] (reviewer) — Maintain logical flow. Count: 1. Lines: 154. Example: the note at 147-155 tells the reader that ‘{doc}`robust_permanent_income` writes the same object as \(\theta^2\)’, where the object is \(\alpha^2\) - but \(\theta\) is not introduced until line 229, where it is the penalty parameter of the robust Bellman equation, related to \(\sigma\) by \(\sigma = -\theta^{-1}\) at 236. So \(\theta\) carries two unrelated meanings in the lecture and the reader meets the second one first. This matters more than usual here because the lecture opens with a note (74-78) devoted to freeing up symbols so that \(\sigma\) can be the robustness parameter.

  • [qe-writing-007] (reviewer) — Use visual elements to enhance understanding. Count: 1. Lines: 717. Example: the collision of the two Riccati roots is the subject of a {note} (650-656) and of the whole of exercise 2 (1101-1150), and it is never drawn. It appears only as a four-row printed table of root pairs (717-724) and, in the exercise, as a printed string of ‘+’ and ‘-’ characters (1145). A plot of the two roots of {eq}`eq:rcs-riccati` against \(\sigma\) over \((\underline\sigma, 0]\), with the branch point marked, would show the double root, the sign flip and the breakdown point in one frame - and this is a lecture with four well-captioned figures elsewhere, so the omission stands out.

Strengths#

  • The lecture opens by declaring exactly the three notational departures it makes from its two prerequisites - \(v_{t+1}\) for the distortion, \(\eta_i\) instead of \(\sigma_i\) so that \(\sigma\) is free, and \(a_t\) for net assets instead of \(b_t\) for debt (74-78) - which is the single most useful thing a third lecture in a sequence can do.

  • The organising role of \(\alpha^2\) is stated and then honoured: the note at 147-155 lists the three different things the same scalar measures across the three lectures, and every subsequent result - the locus {eq}`eq:rcs-oe`, the persistence {eq}`eq:rcs-zeta`, the breakdown point {eq}`eq:rcs-breakdown` and the spectrum {eq}`eq:rcs-spectrum` - depends on \(\sigma\) only through \(\sigma\alpha^2\).

  • The two observational-equivalence theorems are not left as a confusing pair: 579-599 explains that they hold different agents fixed, works through what each one implies for the drift of expected consumption, and states plainly that the economics is the same in both.

  • The closed-form solution earns its keep three times over: the discriminant of {eq}`eq:rcs-riccati` is shown to be a perfect square (632-644), which yields both roots exactly, explains why a distance-based numerical root selector silently switches branches (650-656), and locates the breakdown point as the point where the two roots coincide (674-678).

  • The breakdown point and the detection error probability are presented as two different kinds of bound - a hard mathematical limit and a soft statistical one - and the lecture then reports how they actually interact in this calibration, including the caveat that their near-coincidence at \(T = 40\) ‘is a property of this calibration and of \(T = 40\), not a theorem’ (984).

  • Probability events are written the way the proposed qe-math-014 (proposed) asks, with braces: \(\mathbb{P}\{\text{prefer approximating} \mid \text{worst-case is true}\}\) (869-870).