Syllabus (public companion)
Orientation and course shape — Blackboard is authoritative for graded specifics
This public page is an orientation companion to the syllabus, not the operational syllabus itself. It describes the shape of the course in qualitative terms. It carries no numeric grade weights, no due dates, and no submission rules. For everything that counts toward your grade — exact weights, deadlines, policies, and submissions — Blackboard (the LMS) is authoritative. If this page and Blackboard ever disagree, follow Blackboard.
Course description
Statistical Inference treats inference as the disciplined process of learning from data under uncertainty. We observe a sample but want to say something responsible about a larger process, population, parameter, or claim. The course builds the reasoning and the tools for that: sampling distributions and simulation, estimators and standard errors, bias and variance, likelihood and maximum likelihood estimation, confidence intervals, hypothesis tests and p-values, error rates and power, the bootstrap, randomization and permutation tests, Bayesian updating, and the connection from inference to decisions. The course is deliberately pluralistic — frequentist, likelihood-based, simulation-based, and Bayesian — with the emphasis always on what each method conditions on, what it claims, what it assumes, and how its conclusions should be communicated.
Who it is for
This course assumes a prior probability course and a prior introductory statistics course, or comparable preparation: you should be comfortable with random variables, expectation, variance, common distributions, conditional probability, the normal distribution, and basic statistical summaries. It uses algebra, summation, functions, derivatives, and basic integrals, and asks you to read mathematical notation carefully and say what it means in words. Prior R experience is helpful but not required — simulation and computational examples are scaffolded. The main expectation is willingness to work carefully through examples, run and read code, and explain inferential conclusions in words.
Learning outcomes
By the end of the course, a successful student will be able to:
- Explain the inferential problem and distinguish parameters, statistics, estimators, estimates, standard errors, and sampling distributions.
- Use simulation to approximate a sampling distribution and reason about sampling variability.
- Evaluate estimators using bias, variance, mean squared error, consistency, and practical interpretability.
- Use likelihood to compare parameter values, and compute and interpret maximum likelihood estimates.
- Construct and interpret confidence intervals without treating them as probability statements about a fixed parameter.
- Conduct and interpret hypothesis tests — test statistics, p-values, significance levels, Type I and Type II error, and power — and explain common misinterpretations.
- Use bootstrap methods, and randomization/permutation tests, to estimate uncertainty and weigh evidence under a null model.
- Explain the structure of Bayesian inference (prior, likelihood, posterior, posterior prediction) and compare frequentist, likelihood-based, simulation-based, and Bayesian statements.
- Use simple loss functions or decision rules to connect inference to action.
- Communicate inferential conclusions carefully — assumptions, uncertainty, limitations, and consequences.
Weekly rhythm
This is a lecture/activity course meeting three days a week, and each day has a settled role:
- Monday — inferential concept + checkpoint. We introduce a major inferential idea, work definitions and examples, and close with a short checkpoint.
- Wednesday — derivation, computation, or simulation. We work technical examples, derive key results, or use simulation to investigate sampling variability and uncertainty.
- Friday — quiz / inference case. A short quiz on recent material, then an applied inference case — a method comparison, or a critique of an inferential conclusion.
This rhythm is the plan; the authoritative weekly schedule, including any shifts, lives in Blackboard.
Assessment shape (indicative — not a contract)
The table below conveys the relative emphasis of each graded category in qualitative terms only. It is not a grading contract: it carries no percentages and no point values, and the actual weights live in Blackboard.
| Category | Rough emphasis |
|---|---|
| Inference checkpoints | small |
| Weekly quizzes | small |
| Homework | the largest single category |
| Inference labs | small–moderate |
| Midterm | moderate |
| Project | small–moderate |
| Final | moderate |
Read this as a picture of where the weight sits: regular homework is the backbone of the grade, the two exams carry moderate weight, the labs and project sit in the middle, and the smaller pieces — checkpoints and quizzes — add up around them. For the exact weighting, consult Blackboard.
Software and reproducibility
We use R (through RStudio or Posit Cloud) and Quarto to simulate, resample, and report inference. Computation supports the reasoning rather than replacing it: you read, edit, and run code; interpret output; and write short written conclusions. Every analysis is written so it can be reproduced — a single Quarto file, a fixed random seed, and recorded session information — so the same code yields the same result. Setup instructions are on the R · Quarto setup page.
AI use (summary)
Generative AI tools may be used as a study and workflow aid — to explain a concept a second way, generate practice problems, help debug your own simulation code, or walk through a similar example. They may not produce work you submit as your own, complete your homework or project explanations, fabricate calculations, or replace your responsibility to understand the reasoning, and they are prohibited on quizzes and exams unless explicitly allowed.
Because inference is highly sensitive to assumptions and conditioning, AI output must be checked carefully — many wrong inferential explanations come from confusing a parameter with a statistic, treating a confidence interval as a posterior probability, assuming independence without justification, or misreading a p-value. Whenever you use AI on a graded written assignment, lab, or project component, include a brief AI Use Note with three labeled lines:
| Field | What to record |
|---|---|
| Tool | which assistant you used (with approximate date or version) |
| Purpose | what you used it for |
| Verification | how you checked, tested, revised, or validated the output |
Verification is the load-bearing line: recompute a result, check assumptions, run a simulation, compare to class notes, verify the conditioning statement, or rewrite the explanation in your own words after checking it. You are responsible for every line of code and every sentence of interpretation you submit. The full policy lives in Blackboard.
Materials
You will need:
- MIT OpenCourseWare 18.05, Introduction to Probability and Statistics — the free primary course materials, CC BY-NC-SA 4.0, at ocw.mit.edu.
- Statistical Inference via Data Science: A ModernDive into R and the Tidyverse, 2nd ed. (Ismay, Kim & Valdivia) — a free supplement, CC BY-NC-SA 4.0, at moderndive.com/v2, used for simulation-based inference and reproducible R workflows.
- Introduction to Modern Statistics, 2nd ed. (Çetinkaya-Rundel & Hardin) — a free optional review source, CC BY-SA 3.0, at openintro-ims.netlify.app.
- R, RStudio or Posit Cloud, and Quarto — for the inference labs and reproducible reports.
- Blackboard (the LMS) — for all graded work, dates, and announcements.
- A non-graphing scientific calculator for in-class quizzes; most computation is done in R.
Not used in this course: Cengage, WebAssign, MyLab, or any paid homework platform.
Where things live
Keep the two homes of the course straight:
- Blackboard (the LMS) is the operational home: graded inference checkpoints, quizzes, homework, inference labs, the midterm, the project, the final, all due dates, all submissions, and all grades. It is authoritative.
- This public site is the public notes home: weekly notes, labs as study material, resources, and orientation pages. It is ungraded.
This companion exists to orient you. Whenever a graded specific is at stake — a weight, a deadline, a policy — go to Blackboard, which is authoritative.