ar1_processes#

Series: lecture-python-intro
File: lectures/ar1_processes.md
Audit date: 2026-08-26
Corpus snapshot: a12d17c0ef
Categories audited: writing, math, code, figures, references, links, admonitions (JAX out of scope)
Overall score: 7.9 / 10
Priority: LOW

Score breakdown#

Category	Score	One-line note
Writing	6/10	`qe-writing-001` ×3; `qe-writing-009` (proposed) ×1; `qe-writing-005` ×1, +3 more.
Math	7.5/10	`qe-math-010` (proposed) ×2.
Code	6/10	`qe-code-002` ×21; `qe-code-001` ×3.
JAX	out of scope	JAX rules target `lecture-jax`.
Figures	7/10	`qe-fig-005` ×6; `qe-fig-008` ×9; `qe-fig-001` ×1.
References	9/10	`qe-ref-001` ×1.
Links	10/10	no mechanical violations detected.
Admonitions	10/10	no mechanical violations detected.

Issues#

Critical#

None found.

High severity#

[qe-code-002] — Use Unicode symbols for Greek letters in code. Count: 21. Lines: 166, 180, 182, 210, 211, 213, 216, 230, 265, 267, …. Example: spelled-out mu.
[qe-fig-005] — Descriptive figure names for cross-referencing. Count: 6. Lines: 171, 209, 228, 263, 407, 623. Example: code-cell figure without mystnb figure metadata.
[qe-fig-008] — Use lw=2 for line charts. Count: 9. Lines: 182, 215, 436, 437, 530, 531, 633, 634, 635. Example: plot() without lw=.
[qe-math-010 (proposed)] — Blackboard \mathbb{P}, \mathbb{E}, \mathbb{V} with braces. Count: 2. Lines: 372. Example: missing braces: \mathbb E.

Medium severity#

[qe-code-001] (reviewer) — Follow PEP8 unless closer to mathematical notation. Count: 3. Lines: 46, 186, 540. Example: line 46 #set default figure size has no space after the hash; line 186 ax.legend(bbox_to_anchor=[1.05,1],loc=2,borderaxespad=1) omits the space after every comma; line 540 parameter_pairs= (2, 2), ... has a space after = but not before.
[qe-writing-001] — Use one sentence per paragraph. Count: 3. Lines: 465, 488, 568. Example: 2 sentences in one paragraph.

Low severity#

[qe-fig-001] — Do not set figure size unless necessary. Count: 1. Lines: 46. Example: style override.
[qe-ref-001] — Use correct citation style. Count: 1. Lines: 335. Example: {cite} in narrative flow: ‘by {cite}’.
[qe-writing-003] (reviewer) — Maintain logical flow. Count: 1. Lines: 447. Example: exercise ar1p_ex2 (lines 447-490) asks the reader to build a kernel density estimator and test it on three beta distributions; nothing connects it to AR(1) processes, and its real purpose - supplying the KDE class that exercise ar1p_ex3 needs at line 628 - is never stated.
[qe-writing-005] (reviewer) — Use bold for definitions, italic for emphasis. Count: 1. Lines: 288. Example: line 288 is a definition sentence - ‘A stationary distribution is a distribution that is a “fixed point” of the update rule’ - with the defined term left unbolded, four lines before the same lecture correctly bolds stationary at line 292.
[qe-writing-007] (reviewer) — Use visual elements to enhance understanding. Count: 1. Lines: 310. Example: the Ergodicity section (lines 310-359) asserts that time-series averages converge to expectations under the stationary distribution and never plots it, although the neighbouring stability claims each get a figure (lines 171, 209, 228, 263).
[qe-writing-008] — Remove excessive whitespace between words. Count: 1. Lines: 369. Example: 2 spaces.
[qe-writing-009 (proposed)] — Write “IID” — not “i.i.d.” or “iid”. Count: 1. Lines: 561. Example: iid.

Strengths#

Every labelled display equation is actually used: can_ar1, ar1_ma, dyn_tm, mu_sig_star and ar1_ergo are each cited later with {eq}, so no label is dead weight.
The stability argument is built visually in four steps - the ten-period density sequence at line 171, the forty-period sequence at line 209, the same sequence from a different initial condition at line 228, then the analytical limit psi-star overlaid on it at line 263.
Side remarks are parked in parenthetical one-line paragraphs (lines 74-75, 150, 203, 303-304) rather than being spliced into the main argument.
All three exercises use gated {exercise} / {solution-start} … {solution-end} syntax with :class: dropdown, so solutions are hidden by default.

Recommended actions#

Rename the spelled-out Greek variables in the first half of the lecture - mu, mu_star, std_star at lines 166, 180-184, 211-217, 267-268 - to the Unicode forms already used in the second half at lines 604-635 (mu, psi); the lecture currently spells the same quantity two different ways (qe-code-002, 12 occurrences).
Fix the dropped terms in the backward-iteration display: line 97 should read a^3 X_{t-3} + a^2 b + a^2 c W_{t-2} + a b + a c W_{t-1} + b + c W_t - the a b and a c W_{t-1} terms produced by the previous substitution are missing.
Add mystnb figure metadata (mystnb: figure: name/caption) to the seven plotting cells at lines 171, 209, 228, 263, 407, 523 and 623 so the figures are nameable and cross-referenceable (qe-fig-005, 7 occurrences).
Set lw=2 on the nine ax.plot calls at lines 182, 215, 436, 437, 530, 531, 633, 634 and 635 (qe-fig-008, 9 occurrences).
Bold the defined term at line 288 and give the Ergodicity section (line 310) a figure showing a running time average converging to mu-star, so the one unillustrated claim in the lecture is illustrated like the rest.
Fix the PEP8 spacing at lines 46, 186 and 540, and make the plot labels at lines 633-635 raw strings (label=r"$\psi_t$") - as written the backslash is an invalid escape sequence.
Sweep the remaining single-instance mechanical items: brace \mathbb E at line 372 (qe-math-010 (proposed)), iid to IID at line 561 (qe-writing-009 (proposed)), the mid-narrative {cite} at line 335 (qe-ref-001), the double space at line 369 (qe-writing-008), the figsize override at line 46 (qe-fig-001), and split the two-sentence paragraphs at lines 465, 488 and 568 (qe-writing-001).