ASTAM Review Notes Skill

Syllabus topic codes (for filenames and progress)

Map every request to one primary topic T1–T6 (SOA ASTAM syllabus areas and approximate weights):

If the user’s input fits multiple topics, pick the dominant one for the filename; mention secondary tags in the note body (YAML frontmatter or a short “Also relates to” line).

Practice analytics — dashboard + JSON ledger (English dashboard)

Maintain a simple numeric ledger and an English rollup note so progress is visible without a separate web app:

When to update (agent — required):

1. Type = problems: Append problemSets (id, recordedAt, topic, title, format, vaultNote, pointsPossible, optional subparts / largeQuestions, optional subBranchIds e.g. ["t2-a","t2-b"]). Bump lastUpdated; refresh At a glance and Problem sets.
2. Type = mistakes / grading: Append gradedSessions (plus optional subBranchBreakdown, subBranchScoringMode, questionBranchMap). Sub-branches may overlap: if one large question tests multiple outcomes, credit its full earned/possible to each listed branch (non_exclusive_by_question); then branch possible sums can exceed the session’s pointsPossible — state this in the dashboard. Recompute topicTotals (session points, exclusive) and subBranchTotals from subBranchBreakdown. Refresh the dashboard tables. Legacy sessions with empty subBranchBreakdown only affect topic rollup.
3. Syllabus change: If SOA rewrites outcomes, edit syllabusBranches in the JSON and realign dashboard labels from 2026-spring-exam-astam-syllabus.md (or the current syllabus file).

Keep JSON and dashboard consistent in the same edit batch. Do not leave the dashboard stale after changing the ledger.

Atomic update checklist (agent — same task, same save):

1. Edit ASTAM-Practice-Data.json (problemSets and/or gradedSessions, totals).
2. Immediately update ASTAM-Practice-Dashboard.md tables / “At a glance” so every number shown has a JSON source.
3. If you only change one file by mistake, re-open the pair and fix before ending the turn.

Optional later: a small script could render dashboard rows from JSON; until then, the checklist prevents drift.

Syllabus subpart mapping (authoring → Mistakes → ledger)

Goal: Every scorable subpart should map to t#-a / t#-b / … (ids in ASTAM-Practice-Data.json → syllabusBranches) so that 错题 / 得分 can be pasted into gradedSessions without re-reading the whole stem.

Rules for the agent when Type = problems:

1. Do not put syllabus codes in the visible stem (no “(T3b)” in the text the student sees).
2. Do record the mapping in a machine-friendly, low-noise way. Preferred (Obsidian preview hides it): an HTML comment immediately after each subpart heading or prompt line, e.g. <!-- astam: t3-b -->. Alternative: a single block at the end of the Problems note, e.g. <!-- astam-syllabus-map: {"Q1":{"(a)":"t3-a","(b)":"t3-b"}} --> (JSON inside the comment).
   • Anti-forget template: When drafting a new sheet, insert a placeholder immediately after every scorable subpart prompt, e.g. <!-- astam: t?-? -->, then replace ? once ASTAM-Practice-Data.json branch ids are chosen. Optional vault habit: an Obsidian template/snippet that pastes <!-- astam: --> so the cursor lands between the colons.
3. When the user later asks for Mistakes or you append gradedSessions, copy branchId from that map into mistakeSubparts (and/or questionBranchMap for formal MCQ), then recompute topicTotals and subBranchTotals (or subBranchBreakdown per session). Overlap: if one subpart truly tests multiple outcomes, use the same non-exclusive pattern as T2 MCQ (subBranchScoringMode, multiple branches).

gradedSessions shape (for humans + agents): See ASTAM-Practice-Data.json (in user's vault) keys _gradedSessionShapeGuide (field glossary) for structure examples.

When Type = mistakes: Prefer listing each wrong/graded subpart with ref + branchId in JSON so the dashboard branch rows stay reproducible.

Agent responsibilities (on Dashboard study-plan section):

1. Whenever you create or rename a syllabus-related note in the user's vault, update the Dashboard's T1–T6 index and weekly rows with [[wikilinks]].
2. If the user reports review progress, set the matching 完成 checkboxes to [x] in the Dashboard weekly tables.
3. Bump the 最后更新 line at the end of the study-plan section.

Note: When a topic has several practice sheets in syllabus / study order, use a numeric segment after T# so the file explorer sorts them: T5-1-bayesian-credibility-Problems.md, T5-2-buhlmann-straub-Problems.md, T5-3-empirical-bayes-Problems.md (same pattern for T2–T4 multi-sheet sets).

File naming (syllabus-friendly, sortable)

Prefer ASCII-friendly names so folders sort by topic then subtype:

T{n}[-{k}]-{ShortTopicSlug}-{Kind}.md

• n: 1–6 per table above.
• k (optional): Review-order index when multiple sheets cover the same T# in syllabus sequence (e.g. 1 = first outcome block, 2 = next). Example: T4-1-parametric-mle-ci-Problems.md, T4-2-delta-bayesian-Problems.md, T4-3-model-selection-gof-Problems.md.
• ShortTopicSlug: short English kebab-case hint (e.g. severity, aggregate-recursion, coverage-deductible, parametric-selection, buhlmann, pricing-reserving). For subsections, extend the slug (e.g. aggregate-ii-recursion).
• Kind: one of Summary, Problems, Solutions, Mistakes.

Examples: T2-1-aggregate-iii-Problems-MCQ.md, T4-2-delta-bayesian-Problems.md, T5-3-empirical-bayes-Problems.md, T5-2-buhlmann-Summary.md.

Problems naming (MCQ vs WA): Use the same …-Problems.md for both default (checkbox MCQ) and 非选择题 (WA). Do not add a -MCQ segment to the filename (e.g. not …-Problems-MCQ.md). If you need two sheets for the same topic (one MCQ, one WA), distinguish with ShortTopicSlug (e.g. aggregate-iii vs aggregate-iii-wa). Optional separate answer file: …-Problems-Key.md; mistake log: …-Problems-Mistakes.md.

Legacy files with spaces, …-Problems-MCQ.md, or older T2 Aggregate II … names may remain; for new notes, use this pattern. When creating or heavily editing a legacy file, add an HTML comment at the top (after YAML if any), e.g. <!-- canonical: T2-aggregate-iii-Problems.md (MCQ) -->, so agents know the preferred rename target without breaking existing [[wikilinks]] until the user renames.

Each note should include near the top (after optional YAML):

• ASTAM topic: T# — [English syllabus name]
• Reference to relevant sources (ASM lessons, Past Exams, etc.) when applicable.

Answer key (…-Problems-Key.md) — isolation + when to create

Goal: The student can practice without seeing letters or worked MCQ answers; grading has a stable reference so the agent does not re-derive everything from scratch.

Placement (pick one — user may state a preference):

1. Preferred — separate file: T#-…-Problems-Key.md sits beside T#-…-Problems.md. The Problems note links it only in header/footer, e.g. After attempt: [[…-Problems-Key]]. No answer letters appear in the Problems file.
2. Single-note option (e.g. “Key 都放在最后”): If the user asks for one file, structure strictly as:
   • Top → middle: only stems, options (MCQ), study-guide highlights, syllabus-map comment — zero spoilers.
   • Bottom: a single terminal block separated by --- and a visible spoiler heading, e.g. ## Answer key (spoilers — after attempt only), optionally preceded by <!-- astam:stop-reading-for-practice -->. All correct letters, short rationale, and post-answer Knowledge highlights go below that heading only — never interleaved after each question in the scroll path used during timed practice.

Workflow norms (lowers “无 Key 批改成本”):

• After a Type = problems delivery, the student can say “生成 Key” in the same chat or the next message; opening the Key file is after attempt.
• On Type = mistakes / grading, prefer an existing …-Problems-Key.md when present; only re-solve from stems if Key is missing.

User parameters (mini protocol)

When the user omits parameters, infer reasonable defaults and state them in a one-line preamble.

Vault user norm (when Type=problems): Default to 选择题 — each scorable subpart is single-best-answer with exactly five options A–E (- [ ] **A.** … - [ ] **E.**). Use 非选择题 (constructed response, no A–E) only when the user explicitly requests it (e.g. 非选择题, 大题, written answer, WA, format: wa, constructed-response). If the user only says 出题 / practice / MCQ is unspecified, treat as MCQ.

Default when the user says 出题 / practice problems (Type=problems):

• Emit only the stem markdown: T#-{slug}-Problems.md (see naming above). Default answers: no: the Problems file contains no worked solutions and no correct letters (MCQ). Do not create …-Problems-Key.md unless the user explicitly asks (e.g. 答案、Key、详解、对答案、批改用 key).
• Format: unless the explicit 非选择题 / wa request applies, each subpart is single-best-answer MCQ with exactly five options A–E and Obsidian - [ ] / - [x] checkboxes.
• Exception — 非选择题 (explicit only): omit options; strict ASTAM constructed-response style with exam-like multi-level structure (see Content rules).

Content rules (short)

• Math (Obsidian-friendly — default for all new/edited ASTAM notes):

  • Inline: In stems, solutions, lists, and tables, use $...$ for every short formula or symbol. Never use $$ inside running text, bullets, or cells.
  • Display: Use $$...$$ only as a standalone paragraph (blank lines before and after).
  • Multi-line in one block: wrap in $$\begin{aligned}...\end{aligned}$$ (or gathered / cases as needed); use & at the start of each line or &= so lines align like printed notes — do not rely on raw \\ alone.
  • Preview: block left-aligned (optional): centered display is MathJax default; for flush-left blocks enable snippet astam-math-display-left.css in your Obsidian vault CSS snippets.
  • Avoid HTML entities inside math formulas.

• Type = summary: mainly Chinese; key terms 中文 + English.

• Type = problems — references & scope: Ground stems in ASM ASTAM + Past Exams (especially Past Exams for difficulty and complexity). Cross-check ASTAM/Syllabus/ so the set covers the syllabus objectives for the requested topic slice — no gaps in exam scope for that slice. Attribution: for each large question (or clearly per set if one theme), add a short line such as Adapted from: ASM Lesson n §… and/or ASTAM Season Year Problem k style (chapter / lesson / exam sitting as applicable). If purely synthetic, state Original practice item (syllabus: T# …).

• Type = problems — ASTAM exam structure: Mirror released ASTAM layout: typically one major question with (a)(b)(c)… subparts; subparts may include nested (i)(ii) given items. Adjust part count to match density when possible; keep wording and every numeric and formula before shipping.

After determining path, proceed. Update your Dashboard study-plan section (if maintaining one) when adding new Mistakes files.

错因标签（Error type taxonomy） — shared by MCQ and WA

Every wrong or blank subpart in any Mistakes file must be labelled with exactly one of the following tags in §1 错题速查表 and §2/§2b 解析 header:

§3 定向补强 auto-trigger: only fire for concept, formula, or setup errors (≥2 subparts with the same branchId AND one of these three tags). Do not trigger for calc or misread — those require practice discipline, not concept review.

MCQ mistake log template (…-Problems-Mistakes.md) — required when grading MCQ

Use English ## headings only for the main sections. Four top-level sections (in order):

1. ## 1. Score and summary — 满分、得分、得分率、按题/按小问表、错题速查、🚩收藏速查（表内文字可中英混合）。

   • 错题速查表: wrong/blank subparts — columns: Subpart | 你的作答 | 正确答案 | 错因 tag (one of: concept / formula / setup / calc / misread) | 对应 branchId. The 错因 tag is the agent's best judgment based on the solution; the user may correct it.
   • 🚩 收藏速查表: list every flagged (- [x] 🚩) subpart — columns: Subpart | 是否也错 | 简短备注 (user fills later).

2. ## 2. Wrong / blank — questions, options, and solutions — For each large question that has ≥1 wrong or blank subpart:

   • Paste the full large-question stem (all "You are given" items) so the reader never needs to open the Problems file.
   • Paste each relevant subpart's prompt + all A–E options with legend at the start of §2:
     • Correct: green HTML + ✅ (optional「与你一致」).
     • User wrong: red + ❌.
     • Unanswered: ⚠️; still mark the correct option ✅.
   • Immediately under each subpart block, add #### Solutions — Question n (x) in 中英双语 (bilingual). Language rule for Mistakes §2 / §2b: body text uses Chinese for narrative flow, but every key concept, theorem name, formula label, and technical term must appear in both Chinese and English — e.g. "极大似然估计 (Maximum Likelihood Estimation)", "后验均值 (posterior mean)". English phrasing should be substantive, not just parenthetical glosses — include the English reasoning step or definition when it aids exam recall. All subparts in a displayed question get a solution note (not just the wrong ones): wrong / blank subparts need 【详析】 + 错因 tag; correct subparts get a brief 解题思路 + knowledge recap. 🚩-flagged subparts in this question also get 【🚩见§2b】 cross-reference — their full solution appears in §2b, not here.
   • After all subparts of that question, include a per-question Knowledge highlights blockquote (same format as Problems file but with answers now visible).

Self-contained principle: The Mistakes file should be readable on its own — the reader should not need to open …-Problems.md to see what a question asked. Every displayed question includes its full original stem (large-question givens + subpart prompts + options).

• Type = mistakes — language: 中英双语 (bilingual). Narrative in Chinese; all key concepts / terms / theorem names in Chinese + English (e.g. "贝叶斯估计 (Bayesian estimation)"). Formulas, definitions, and exam-critical distinctions should carry English phrasing substantial enough for direct exam use — not just a one-word gloss. MCQ 批改遵守本节顺序与「题后紧跟解析」版式。
• After emitting a new Mistakes file with scores: update ASTAM-Practice-Data.json + ASTAM-Practice-Dashboard.md per Practice analytics above.

WA mistake log template (…-Problems-Mistakes.md) — required when grading WA (非选择题)

WA subparts are partial-credit (no single correct letter). Use the same four-section structure as MCQ but adapted for written-answer grading.

Scoring format (§1 scoring table):

Section rules:

1. ## 1. Score and summary — 满分、得分、得分率、上表（按大题汇总）、错题速查（含错因标签）。🚩 收藏速查表 (subpart | 是否也错 | 备注)。
2. ## 2. Wrong / blank — steps, marking, and solutions — For each large question with ≥1 wrong/partial subpart:
   • Paste the full large-question stem (all given items).
   • For each subpart — show in order:
     1. **Marking guide** — list expected steps and their point values (derive from Key if available; otherwise construct from first principles).
     2. **你的作答 vs 标准** — annotate where the approach diverged; assign partial credit per step if applicable.
     3. **错因 tag:** concept / formula / setup / calc / misread.
     4. **【详析】** — full bilingual explanation (same depth as MCQ §2 wrong subparts).
   • After all subparts, include a per-question Knowledge highlights blockquote.
   • Correct subparts get a brief 解题思路 note (no marking guide needed).
3. ## 2b. Bookmarked — review notes — Same rule as MCQ: every 🚩-flagged subpart appears here with full stem + derivation + Knowledge highlights, regardless of correctness.
4. ## 3. Key takeaways and further reading — Same §3 rules as MCQ (知识点表, 定向补强 auto-trigger, same error-tag thresholds).

Key differences from MCQ template: no A–E options; scoring is step-by-step; 错因 tagging is especially important for setup errors (student modeled the wrong quantity).

Knowledge highlights (required for Type = problems)

File division of responsibility:

• This section (SKILL.md): format rules, placement, when to add, language norms.

• reference-knowledge-highlights.md: mandatory block template, T1–T6 topic pitfall bank — read it before generating any T# problems to seed Core / 易错点 bullets.

• reference-astam-generation.md: math alignment examples and extended grading detail.

• Default (answers: no) — MCQ or WA: per large question on …-Problems.md — blockquote Knowledge highlights (study guide — no answers) (MCQ: no correct letters).

• MCQ + Key (user requested …-Problems-Key.md): repeat or expand highlights in the Key after brief rationale.

• WA + answers: yes: after each question’s solution in-file; when grading, highlights appear in Mistakes §2.

After every question (MCQ study guide, WA solution, or Key entry), the blockquote must include:

• First line: > **Knowledge highlights** — for default MCQ stems use > **Knowledge highlights (study guide — no answers)** so spoilers are avoided.
• Core: 1–3 bullets — formulas / steps directly tied to that question
• 易错点 / Common pitfalls: 1–2 bullets — typical exam confusions for that setup

If the user chooses answers: no answers, still add a short Knowledge highlights (study guide) blockquote under the question stem (no full solution). When grading (Type = mistakes), include full highlights in the Mistakes file §2 solutions.

Templates + pitfall bank by T1–T6: reference-knowledge-highlights.md — read it when generating problems so output stays consistent.

Optional: end multi-question files with a small Quick reference card table (see reference file).

Full detail and source list: reference-astam-generation.md.

End-of-task checklist

• Primary T# chosen and reflected in filename (for new files).
• Content grounded in syllabus + reference materials (Past Exams, ASM examples, formula sheets) where relevant.
• Type = problems: each question has Knowledge highlights per reference-knowledge-highlights.md (MCQ default = spoiler-free block on stem file).
• 出题 default: …-Problems.md stems only, answers: no (no solutions / no letters); Key only if requested. Filename uses Problems, not -MCQ.
• Past Exams + ASM examples consulted; syllabus scope for the slice covered; attribution lines present (ASM example ID + Past Exam sitting when adapted); [Hard] on ~1/5–1/4 of large questions (unless user overrides); remaining items Medium+.
• Complexity calibration passed: each large question has scenario unity (cross-subpart dependency); ≥2 non-formulaic subparts; ~1/3 of total subparts are comparison/judgment; draft depth checked against a named Past Exam question.
• New problems or graded Mistakes: ASTAM-Practice-Data.json + ASTAM-Practice-Dashboard.md updated in the same task.
• Type = problems: hidden <!-- astam: t#-x --> (or footer astam-syllabus-map) so Mistakes/ledger can attach branchId quickly.
• : every subpart has on its , subpart question text and first option (see canonical placement — no alternatives).

§2 includes correct subparts too: every subpart of a displayed question gets its solution/思路. Subparts that were both correct and un-flagged still appear (brief note is fine).

§2 density — default vs 精简 (minimal): Default = full stem + all options + all subpart solutions for every large question that has ≥1 wrong/blank subpart. If the user asks for 精简, 轻量, or minimal Mistakes, use compact §2:

• For large questions that are fully correct and have zero wrong/blank: a one-line summary only (e.g. "Q3: 全对 ✅") — no full restatement.
• For any large question with ≥1 wrong or blank subpart: keep full stem + all subparts for that question.
• ## 1, ## 2b, and ## 3 stay full quality.