Syllabus companion
Statistical Inference: Likelihood, Simulation, and Decisions (STAT 35103)
[!IMPORTANT] This page is a public orientation companion, not the operational syllabus. It summarizes, in plain language, what the course is and how it is shaped — it is not a contract. Blackboard (the LMS) is authoritative for the sealed syllabus, all due dates, submission rules, grading weights, and any graded content. If anything here and Blackboard ever disagree, follow Blackboard.
Course description
This course treats statistical inference as the disciplined process of learning from data under uncertainty. Across the term, the notes connect five things that inference always ties together: the data you actually have, the probability model you are willing to assume, the assumptions that model rests on, the uncertainty that remains after you have used the data, and the evidence that uncertainty gives you for a decision. The course is intentionally pluralistic: classical frequentist tools, simulation-based inference, likelihood-based reasoning, and introductory Bayesian inference are all taught side by side, and no single framework is presented as uniquely correct. By the end of the term the goal is to be able to look at the same question through more than one inferential lens and say, concretely, what each lens does and does not tell you.
Who it is for
This course assumes a prior probability course and a prior introductory statistics course, or comparable preparation. In particular, it assumes comfort with:
- Random variables, expectation, and variance.
- Common probability distributions (including the normal distribution).
- Conditional probability.
- Basic descriptive summaries of data (means, standard deviations, and the like).
It also uses ordinary undergraduate mathematics as a working tool: algebra, summation notation, functions, derivatives, and basic integrals appear throughout, mainly in the derivation weeks.
Learning outcomes
By the end of the course, you should be able to:
- Distinguish a population parameter from a sample statistic, and explain what it means for an estimator to have a sampling distribution.
- Use simulation to build intuition for sampling distributions, standard errors, and the behavior of estimators under repeated sampling.
- Evaluate an estimator’s bias, variance, and mean squared error, and explain the tradeoffs those quantities represent.
- Construct and interpret a likelihood function, and derive a maximum likelihood estimate for a simple model.
- Construct and correctly interpret confidence intervals, and state what a confidence interval does not mean.
- Conduct a hypothesis test, interpret a p-value correctly, and reason about Type I/Type II error rates and statistical power.
- Use bootstrap resampling and permutation/randomization tests as simulation-based alternatives to classical formulas.
- Set up a Bayesian prior, update it with data to obtain a posterior, and summarize that posterior.
- Compare frequentist, likelihood-based, simulation-based, and Bayesian approaches to the same inferential question, and articulate what each approach assumes and delivers.
Weekly rhythm
Each week (aside from a few review/workshop weeks noted on the schedule) follows the same three-day shape:
- Monday — an inferential concept is introduced, paired with a short in-class checkpoint.
- Wednesday — derivation, computation, and simulation: this is where the mathematics and the R demonstrations do the work of making Monday’s concept concrete.
- Friday — a short quiz plus an applied case, usually drawing on the course’s running MAC Study example.
Assessment shape (indicative — not a contract)
The table below describes the relative shape of the assessment plan in qualitative terms only. It is here so you know what kinds of graded work exist and roughly how much each contributes — it is not a grading contract. Exact weights, due dates, and submission rules live in Blackboard.
| Category | Indicative weight |
|---|---|
| Inference checkpoints | small |
| Weekly quizzes | small |
| Homework | largest single category |
| Inference labs | small |
| Midterm exam | moderate |
| Project | small to moderate |
| Final exam | moderate to large |
Software and reproducibility
The course uses R, RStudio/Posit Cloud, and Quarto. No paid homework platform (Cengage, WebAssign, MyLab, or similar) is used. Code shown in the notes and labs is base R — no specialized packages are required to follow along. Reproducibility is treated as a first-class habit: any simulation you run should set a fixed random seed (this course’s convention is set.seed(35103)) so that your results can be reproduced, by you or anyone else, on demand.
AI use (summary)
AI tools are permitted as a study aid — for example, to help you understand a concept, check your reasoning on ungraded practice, or clarify a derivation step. AI use is prohibited on quizzes and exams unless a specific exception is explicitly stated in Blackboard for that assessment. Whenever you do use an AI tool in your coursework, you are expected to record and verify that use with an AI Use Note, following this three-line shape:
| Field | What you record |
|---|---|
| Tool | Which AI tool you used |
| Purpose | What you used it for |
| Verification | How you checked the tool’s output was correct |
The Verification line is load-bearing: an AI Use Note without a real verification step does not satisfy the policy. You remain responsible for the correctness of anything you submit, regardless of which tools helped you produce it.
Materials
The course draws on three free, openly licensed sources, used at different intensities:
- MIT OpenCourseWare 18.05, Introduction to Probability and Statistics (CC BY-NC-SA 4.0) — the course’s primary spine, used selectively throughout the term. Free online at ocw.mit.edu.
- Statistical Inference via Data Science: A ModernDive into R and the Tidyverse, 2nd ed. (Ismay, Kim, Valdivia) (CC BY-NC-SA 4.0) — a genuinely used co-source, especially for simulation-based inference, hypothesis testing, bootstrapping, and randomization. Free at moderndive.com/v2.
- Introduction to Modern Statistics, 2nd ed. (Çetinkaya-Rundel & Hardin) (CC BY-SA 3.0) — an optional, lighter review source for introductory inference concepts, pointed to occasionally in the more foundational weeks. Free at openintro-ims.netlify.app.
No textbook purchase is required. In addition:
- Blackboard hosts the sealed syllabus, the schedule of graded work, submission links, and your grades — it is the operational home for the course.
- A non-graphing calculator is sufficient for this course; a graphing or programmable calculator is not required and is not needed for any assessment.
Where things live
Blackboard is operational and authoritative. It holds the sealed syllabus, due dates, submission rules, grading weights, quizzes, homework, labs, the midterm, the project, and the final exam.
This site is public notes, ungraded. It carries concept notes, derivations, labs-as-teaching-text, and reference resources for studying and self-checking — nothing on this site is graded, and nothing here should be treated as a substitute for what Blackboard says.
[!NOTE] Meeting time, room, and office hours shown elsewhere on this site (or left as placeholders) are not yet finalized and are pending confirmation. For the current, authoritative meeting time, room, and office hours, and for anything else where this page and Blackboard might disagree, Blackboard governs.
Public vs. graded
These notes, the examples, and the practice here 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, 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.