About 18.650 - Fundamentals of Statistics

Welcome to the Spring 2025 offering of Course 18's largest and most popular statistics class! We are planning to cover a lot of statistical ground, so buckle up! In fact, our textbook is titled "All of Statistics" (hereafter referred to as "the book"). This is a bit of an overstatement, but it will feel like it.

This course will allow you to quickly get a broad overview of the breadth of topics where statistical ideas may be applied. This is a theoretical course with a strong emphasis on how and why statistical methods are valid. In particular, following the course will require some mathematical maturity (see the Prerequisites section below).

Announcements are all on Canvas (this webpage). Discussions are encouraged on the dedicated Piazza Forum.

Class Learning Objectives

This class offers a fast-paced tour of many statistical concepts, ranging from estimation to hypothesis testing and regression (both parametric and nonparametric). We will also cover some more advanced topics where statistical methods shine, and that are usually excluded from introductory statistics classes (such as causal inference, classification, survival analysis, etc.).

While the main goal is for students to have a broad overview of the statistical landscape, an underlying objective is to foster general principles for the development of efficient statistical methods. At the end of this class, you will be able to:

• From a real-life situation, formulate a statistical problem in mathematical terms
• Understand the role of mathematics in the design and analysis of statistical methods
• Select appropriate statistical methods
• Understand the implications and limitations of various methods
• Crush a hedge fund interview (at least the statistics part)

Prerequisites

You are expected to have taken an introductory class on probability and have some basics of linear algebra. Note: there are many "probability + statistics" classes (e.g., 18.05), but this class focuses only on statistics and assumes a good background in probability.

More specifically, the prerequisites are:

• Calculus I (GIR)
• Probability at the level of 18.600 or 6.041 (In a nutshell, the first three chapters of the book)
• Notions of linear algebra (vectors, matrices, orthogonality, inner products, etc.)

To test your probability knowledge, the first problem set is a review of important concepts that will be used throughout the semester. If you struggle to complete this problem set, you should spend some time studying the first three chapters of the book.

Lectures

Lectures are: Monday, Wednesday, Friday 1-2pm, in 2-190.

The goal of the lectures will be to highlight statistics concepts from the book and illustrate how they fit together. Given the pace of lectures,  many details will be left out of lecture and will have to be studied from the book, recitations, and lecture notes. 

The class videos will be recorded and made available on Canvas, but please understand that unforeseen technical incidents can occur. The recordings are intended as a supplementary resource rather than a substitute for attending the live lectures. Your presence in class is highly encouraged.

Schedule

Lecture	Date	Topics	Chapter
1	Mon Feb 3	Overview	Other
2	Wed Feb 5	Summary statistics	Other
3	Fri Feb 7	Convergence + Delta method	5
4	Mon Feb 10	Common distributions / Gaussian distribution	2/3
5	Wed Feb 12	Multivariate distributions, Covariance, Joint/Conditional distribution	2/14
6	Fri Feb 14	Multivariate Gaussians, CLT, Delta	5/14
No class	Mon Feb 17	PRESIDENT'S DAY
7	Tues Feb 18	Models and point estimation	6
8	Wed Feb 19	Asymptotic normality and confidence intervals	6
9	Fri Feb 21	MLE	9
	Mon Feb 24	Review
	Wed Feb 26	Test 1
10	Fri Feb 28	MLE Properties	9
11	Mon Mar 3	Mixtures	9
12	Wed Mar 5	EM Algorithm	9
13	Fri Mar 7	Method of Moments; Bootstrap basics	8
14	Mon Mar 10	Bootstrap	8
15	Wed Mar 12	Hypothesis testing definitions	6/10
16	Fri Mar 14	Wald test	10
17	Mon Mar 17	p values	10
	Wed Mar 19	Review
	Fri Mar 21	TEST 2
No class	Mon Mar 24	SPRING BREAK
No class	Wed Mar 26	SPRING BREAK
No class	Fri Mar 28	SPRING BREAK
18	Mon Mar 31	Chi-squared test	10
19	Wed Apr 2	Nonparametric tests	10
20	Fri Apr 4	Multiple hypothesis testing	10
21	Mon Apr 7	Bayesian statistics basics	11
22	Wed Apr 9	Bayesian statistics calculations	11
23	Fri Apr 11	Linear regression 1	13
24	Mon Apr 14	Linear regression 2	13
25	Wed Apr 16	Logistic regression	13
26	Fri Apr 18	Model selection	13
No class	Mon Apr 21	PATRIOTS' DAY
	Wed Apr 23	Review
	Fri Apr 25	Test 3
27	Mon Apr 28	Survival analysis	other
28	Wed Apr 30	Causal Inference	16
29	Fri May 2	Nonparametric curve estimation 1	20
30	Mon May 5	Nonparametric curve estimation 2	20
31	Wed May 7	Survey sampling	Other
32	Fri May 9	Classification	22
33	Mon May 12	Data visualization: MDS, SNE, t-SNE, UMAP	22

Office hours

Office hours are an important part of the class. This page is a good description of how to best use office hours to improve your performance in the class.

Anya: Mondays, 2-3pm in 2-255.

Exceptions:

• 2/10 OH is in 2-242. 
• Week of 2/17: OH happens on 2/18
• Week of 2/24: no OH
• Week of 4/21: OH happens on 4/23

Rui: Wednesdays 4-6pm in E51-385

Jiachun: Thursdays 5-7pm in 2-139

Hongyu: Tuesdays 2-4pm in 34-304

Exceptions:

• The 2/18 office hour will be from 4-6pm rather than 2-4pm

Edward: Tuesdays 4-6pm in 2-142

Gracie: Fridays 11-noon in 2-142

Isabella: Mondays 4-5pm and Fridays 4-5pm in 2-142

Exceptions:

• Week of 2/17: No Monday OH, and Friday OH will be 4-6pm.
• Week of 4/21: No Monday OH, and Friday OH will be 5-6pm.

There will be no office hours and no recitations during the first week of class.

Recitations

When signing up for the class, you should be assigned to a recitation. These are integral parts of the course and will help improve your problem solving skills. Recitations are taught by Teaching Assistants.

Section 1	Thursdays 10am-11am	4-270
Section 2	Thursdays 3pm-4pm	4-153
Section 3	Thursdays 4pm-5pm	4-153

There will be no office hours and no recitations during the first week of class.

Reading

The textbook is an essential part of the class. It's actually quite reasonably priced compared to other statistics textbooks (starts around $40 for a new copy). It is also available for free on SpringerLink (access via the library) as a PDF. 

Larry Wasserman. All of Statistics. Springer, 2004

Grading

Homework	40%	Four Psets to be turned in via gradescope.
Midterms	30%	3 in-class tests (see dates below)
Final exam	30%	TBA

We will be dropping the lowest of your three midterm grades, so that each of your two highest midterm grades will count for 15% of your total grade. 

Additional credit: You may get additional points on your final exam by answering other student's questions on Piazza. For every 10 endorsed answers, you will receive one additional point on your final exam (The final grade will be capped at 100).

Homework:

There are four problem sets during the semester, which will help you master the material. They will also feature questions taken from recent hedge-fund interviews to help you place these questions in the context of the class.

You are encouraged to work with other students on the homework problems, but verbatim copying of homework is absolutely forbidden. Please indicate on your homework with whom you worked.

As a rule of thumb, you should be able to explain your reasoning during a meeting. Therefore each student must ultimately produce his or her own homework to be handed in for grading. You should also explain as much as possible of your reasoning when solving a problem. You should certainly ask the instructor or the TA for help with the homework problems, but only after you have earnestly attempted to solve them on your own. Any questions regarding homework grades should first be addressed to the TA; if they cannot be satisfactorily resolved with the TA, then feel free to discuss them with the instructor.

Use Piazza to find partners.

Homework is due on Gradescope by 11:59 of the due date, Eastern Time.

Pset 1: Wednesday, February 19

Pset 2: Friday, March 14

Pset 3: Monday, April 14

Pset 4: Wednesday, May 7

Late homework policy

You are allowed a total of 4 late days throughout the semester. However, you can only use 2 late days per pset. If you turn in a pset more than 2 days after it is due, you will receive a grade of zero. 

Late days are counted in whole days. For example, Pset 1 is due on a Wednesday. If you turn it in any time on Thursday, then you have used up 1 late day. 

Manage these days carefully as late submissions outside of this policy will not be accepted even with emergencies. Extraordinary conditions such as long-term illness will be assessed on a case-by-case basis.

Exams

There will be four timed exams: three in-class midterm exams and one final exam.

The in-class exams will last for the duration of the lecture (starting at 1:05, ending at 1:55). They will be held in Walker 50-340.

Midterm dates

Test 1: Wednesday, February 26

Test 2: Friday, March 21

Test 3: Friday, April 25

Exam make-up policy

• You always have the option of missing one of the midterm exams without taking a make-up, since your overall midterm exam grade is determined based on your highest two of three scores. If you would like to skip an exam for any reason, there is no need to contact me about this. 
• If you cannot attend a midterm or the final exam due to a justified conflict, then you may request a make-up exam. 
• If you would like to take a make-up exam due to a foreseen conflict (e.g. MIT athletic event), please contact me by email or Piazza. I may ask that you send me documentation of the conflict.
• If you would like to take a make-up exam due to an unforeseen conflict (e.g. sickness or family emergencies), please contact S3 if you are an undergrad, or GradSupport if you are a grad student, and have them reach out to me.
• Travel (e.g. leaving early for spring break)  generally does not count as a justified conflict.  

Piazza discussion forum

 We have set up a discussion forum on Piazza at this link: piazza.com/mit/spring2025/18650

Discussion forum overview

The course provides an online discussion forum for you to communicate with the course team and other students.  Please see the guidelines below for more information on how to use these embedded discussions.

How to use Piazza

You can ask anonymous questions to the rest of the class (see below for some syntactic guidelines) and you are encouraged to interact through Piazza rather than emails to instructors whenever possible.
Students are expected to answer questions and not just ask them (see the Grading section above for additional credit). The teaching staff will endorse good answer to give them more visibility. 

Discussion forum guidelines

The discussion forum is the main way for you to communicate with the course team and other students. Here are some guidelines to help you successfully navigate and interact on the Piazza forum:

• Use discussion while working through the material. You should discuss anything related to a lecture or a part of the book.

• Use latex formatting when writing equations ($$ tags)

• Use informative topic titles and tags. To make it easier to identify relevant discussion topics, please use informative titles and folders when creating a new discussion topic. We suggest using titles or tags that are as informative as possible.

• Be very specific. Provide as much information as possible about what you need help for: Which part of what problem or material? Why do you not understand the question? Do you need help understanding a particular concept? What have you tried doing so far? Use a descriptive title to your post. This will attract the attention of other learners having the same issue.

• Academic integrity. We encourage collaboration and help, but please do not ask for nor post problem solutions.

• Upvote good posts. This applies to questions and answers. Click on the green plus button so that good posts can be found more easily. 

• Feel free to ask or answer anonymously.

• Search before asking. The forum can become hard to use if there are too many threads, and good discussions happen when people participate in the same thread. Before asking a question, use the search feature by clicking on the magnifying glass on the left-hand side.

• Write clearly. Avoid ALL CAPS, abbrv of wrds (abbreviating words), and excessive punctuation!!!!