Notes

The weekly inferential spine

The notes are the backbone of the course. There is one note per week, and reading the current week’s note before class — and again after — is the single most reliable way to keep up. Every note follows the same shape, so once you learn to read one, you can read them all.

How to read a week

Each weekly note is built from the same parts, in the same order. Knowing the anatomy lets you skim for what you need and study with intent:

  • The week question. A single inferential question that the week exists to answer. Hold it in mind as you read; everything else is in service of it.
  • Concept development. The core ideas, built up in a few short sections from intuition toward a precise inferential statement. This is the part to read slowly — and where the conditioning, the assumptions, and the claim are made explicit.
  • Worked examples. Each idea is worked on the recurring reading-fluency study (a synthetic campus reading-intervention study) — the method is set up, the computation is shown, and the result is interpreted in sentences — plus one transfer example in a fresh context, so you see the idea move.
  • A common mistake. The inferential error students most often make on this topic — a confused conditioning statement, a misread interval, a mistaken p-value — named plainly so you can watch for it in your own work.
  • Ungraded self-checks. A few low-stakes practice prompts to test yourself. These are self-check only — no points, no submission.
  • Reading pointer. Where to read more: the relevant MIT OCW 18.05 reading (and, for the simulation and resampling weeks, ModernDive; for lighter review, Introduction to Modern Statistics), with the reminder that these notes are the course’s own synthesis.
  • Formula-verification status. An honest note that the formulas and numbers on the page are drafted and synthetic, pending review — this is a draft course site.
  • Looking ahead. A sentence or two connecting this week to the next, so the inferential arc stays visible.

Keep the notation glossary and the inference reference open alongside the notes.

The four parts

The fifteen weeks fall into four parts. Each part has a job, and the weeks within it build on one another.

Part I — The inferential problem. What inference is, how sampling variability behaves, how we measure an estimate’s variability, and how we judge an estimator.

  1. Week 1 — What statistical inference is
  2. Week 2 — Sampling distributions & simulation
  3. Week 3 — Estimators & standard errors
  4. Week 4 — Bias, variance & MSE

Part II — Likelihood & classical inference. Comparing parameter values by likelihood, finding the MLE, and building confidence intervals and hypothesis tests.

  1. Week 5 — Likelihood
  2. Week 6 — Maximum likelihood estimation
  3. Week 7 — Confidence intervals (midterm)
  4. Week 8 — Hypothesis tests & p-values
  5. Week 9 — Error rates, power & decisions

Part III — Simulation-based inference. Estimating uncertainty by resampling, and testing by relabeling under a null.

  1. Week 10 — Bootstrap inference
  2. Week 11 — Randomization & permutation tests

Part IV — Bayesian inference & synthesis. The Bayesian lens, a comparison of all four frameworks, a project workshop, and a closing synthesis.

  1. Week 12 — Bayesian inference
  2. Week 13 — Comparing inferential frameworks
  3. Week 14 — Inference project workshop
  4. Week 15 — Final review & synthesis

Public vs. graded

These notes and the practice in them are public and ungraded — study material only. No graded prompts, answer keys, rubrics, point values, or due dates appear on this site. Graded inference checkpoints, quizzes, homework, inference labs, the midterm, the project, and the final live in Blackboard (the LMS), which is authoritative for due dates, submissions, and grades. If this page and Blackboard ever disagree, follow Blackboard.