Bayesian ML Exam Survival Guide
Based on past papers: 2021 Part A/B, 2021 Resit, 2022, 2023
How to Use These Notes
Each file covers one exam question type. Every file has the same structure:
- Part 0 — What all the symbols mean (read this first)
- Part 1 — Core concepts in plain English
- Part 2 — Full step-by-step walkthrough of real exam questions
- Part 3 — Tricks & shortcuts (how to spot the right answer fast)
- Part 4 — Practice exercises (try these without looking at the answers)
- Answers — Hidden behind
<details>tags — click to reveal
Recommended Study Order
Study them in numerical order — each builds on the previous:
| # | File | Topic | Prerequisites |
|---|---|---|---|
| 1 | 01-bayes-rule-posterior | Bayes' Rule & Posterior Computation | None — start here |
| 2 | 02-beta-bernoulli-coin-toss | Beta-Bernoulli Coin Toss | Type 1 (Beta integral trick) |
| 3 | 03-gaussian-posterior-evidence | Gaussian Posterior & Evidence | Type 1 (Bayes' rule) |
| 4 | 04-model-evidence-averaging | Model Evidence & Averaging | Types 1–3 |
| 5 | 05-model-comparison-bayes-factor | Model Comparison & Bayes Factor | Types 1, 4 |
| 6 | 06-bayesian-classifier | Bayesian Classifier | Type 1, Type 3 |
| 7 | 07-ball-box-conditional | Ball/Box Conditional Probability | Type 1 (Bayes' rule practice) |
| 8 | 08-gmm-form | GMM Form (one-hot encoding) | None — pattern recognition |
| 9 | 09-vfe | Variational Free Energy | Types 1, 4 (evidence + posteriors) |
| 10 | 10-fep | Free Energy Principle | None — conceptual |
| 11 | 11-factor-analysis | Factor Analysis & Marginal | Type 3 (Gaussian marginals) |
| 12 | 12-recursive-filtering | Kalman / Recursive Filtering | Type 3 (Gaussian updates) |
| 13 | 13-log-likelihood-mle | Log-Likelihood & MLE | Type 8 (GMM form) |
| 14 | 14-gmm-vfe-fep-concepts | Mixed Concepts | Types 8, 9, 10 |
Difficulty & Surprise Factor
| # | Type | Difficulty | Surprise | Why |
|---|---|---|---|---|
| 8 | GMM Form | 10/100 | 5/100 | Pure pattern spotting. Literally same question across all exams |
| 1 | Bayes' Rule & Posterior | 15/100 | 20/100 | Fixed pipeline: multiply → normalize. Only the function changes |
| 2 | Beta-Bernoulli Coin | 20/100 | 30/100 | Count → add → formula. Watch: which outcome = 1 flips between exams |
| 3 | Gaussian Posterior | 20/100 | 25/100 | Plug numbers into 2 formulas. Different numbers, same skeleton |
| 11 | Factor Analysis | 20/100 | 20/100 | Joint and marginal are one-liners. Only W vs Λ notation changes |
| 9 | VFE | 25/100 | 20/100 | Same 3-4 questions recycled (upper bound, equality, KL). No variation |
| 5 | Bayes Factor | 25/100 | 20/100 | Evidence ratio × prior ratio. Same structure every time |
| 4 | Model Evidence | 25/100 | 25/100 | Two patterns only: Beta integral or Gaussian averaging. Predictable |
| 12 | Kalman / Filtering | 30/100 | 25/100 | 3-4 fixed questions. Formulas don't change |
| 7 | Ball/Box Conditional | 30/100 | 40/100 | Standard Bayes' rule, but two-draw/two-box variants add a wrinkle |
| 10 | FEP Concepts | 35/100 | 55/100 | No computation, but phrasing changes significantly each exam |
| 13 | Log-Likelihood & MLE | 40/100 | 35/100 | Same core questions. Inner vs outer product trap requires attention |
| 6 | Bayesian Classifier | 45/100 | 45/100 | Densities change each exam. Algebra for boundary shifts. Error limits need care |
| 14 | Mixed Concepts | 40/100 | 55/100 | True/false statements vary the most. Signal recovery appeared once, could return |
Free points (80+ score guaranteed): Types 8, 9, 11, 12 — pure pattern recognition. Where marks are lost: Types 6, 14 — densities change, concept questions test understanding, not recognition. Watch for traps: Type 2 (outcome=1 flips), Type 7 (two-draw variant differs), Type 10 (wrong answers get creatively reworded).
Quick Reference
- exam-cheatsheet.md — All formulas in one page, organized by type
- This file (
README.md) — Index and roadmap
Other Files in This Folder
| File | Description |
|---|---|
crash-course.md / .pdf |
Course crash course |
2021-part-a.md |
2021 Part A past paper |
2021-part-b.md |
2021 Part B past paper |
2021-resit.md |
2021 Resit past paper |
2022.md |
2022 past paper |
2023.md |
2023 past paper |
Study Strategy
Session 1-2: Types 1, 2, 3 → Foundation
Session 3-4: Types 4, 5, 6 → Gaussian algebra + model comparison
Session 5-6: Types 7, 8, 13 → Classification + GMM + MLE
Session 7-8: Types 11, 12 → Latent variables + Kalman
Session 9: Types 9, 10, 14 → VFE, FEP, concepts
Session 10: Full past paper under timed conditions
Per session: Read → Cover solution → Try yourself → Check → Redo wrong ones next day.