Description

553.430/630, Introduction to Statistics, covers the basic principles of statistical reasoning and data analysis. Emphasis is on both mathematical foundations and various techniques of application. Topics include classical parametric estimation, hypothesis testing, and multiple decision problems; linear models, analysis of variance, and regression; nonparametric and robust procedures; decision-theoretic and Bayesian methods. Please note: 553.630 consists of the same content, but (a) 630 exams may have additional questions, and (b) 630 is graded as a graduate (masters’ level) course.

Due to the COVID-19 transition to distance learning for Spring 2021, all lectures, sections, and office hours will be conducted online, via Zoom. All times below are Eastern Time. Please note that during the spring semester, there is a switch to Eastern Daylight Time (+1 hours) beginning on March 14, 2021. See links and further information below.

Prerequisites

553.420 (previous numbering: 550.420), Introduction to Probability.

Instructor

Avanti Athreya, [email protected]

Office: Whitehead 306-D

Instructor office hours:

1) Monday, 8:15 p.m. to 9:15 p.m.; Wednesday 8:15 p.m. to 9:15 p.m.

Office hours will begin on Wednesday, January 27, 2021.

Zoom link for Monday and Wednesday office hours:

https://wse.zoom.us/j/93704895916?pwd=Um1yYk94OWs3QThRZHdDNEFlSFpSUT09

and by appointment

Teaching Assistants

Wayne Hung, [email protected]

Amol Khanna, [email protected]

Ashwin Pasupathy, [email protected]

Nicholas Parente, [email protected]

Jason Rutberg, [email protected]

Sichong Zhang, [email protected]

Nicholas Parente, [email protected]

Heidi Zhang, [email protected]

Cherlin Zhu, [email protected]

Lecture and section times, teaching assistants, office hours, and associated Zoom meeting links:

(1) Course lecture: Monday and Wednesday, 1:30 p.m. to 2:45 p.m.

Zoom link for lecture:

https://wse.zoom.us/j/99734243626?pwd=dlRsaVlObUNBdU1ZNVJwN0lJaUhrUT09

For those who are unable to attend the live, synchronous Zoom lectures, recordings will be posted in the “Lecture videos” section of Blackboard.

(2) Section information, links, assignments, and TA office hours Section times are as follows: Th 9, 10:30, 12, 3, 4:30, and 6.

Section information, links, assignments, and TA office hours will be posted by 1/29/2021.

Any student can attend any TA’s office hours.

Textbook

Required: Mathematical Statistics and Data Analysis, by John A. Rice., 3rd edition. Note: the International Edition is also acceptable.

Useful additional material for R: Statistical Computing with R, by Maria L. Rizzo, 2008.

Online Resources

Please log in to Blackboard for all materials related to this course.

Course Objectives This is a first course in mathematical statistics. As such, after completing this course:

(1) Students will obtain an understanding of the mathematical foundations of commonly-used statistical methods, including estimation, hypothesis testing, analysis of variance, and regression.

(2) Students will be prepared for further work in statistical methodology at the upper undergraduate and beginning graduate-level.

(3) Students will gain experience with basic problem-solving and proof-writing.

(4) Students will gain familiarity with the statistical software R.

(5) Students will develop intuition for and appreciation of practical applications of underlying statistical theory.

Course Topics

• Overview of introductory probability. (Students are expected to be familiar with the following topics, which will be reviewed as warranted and as time permits.) Random variables, important discrete distributions (Bernoulli, binomial, Poisson) and continuous distributions (uniform, exponential, normal). Expectation, variance, and other moments. Cumulative distribution functions and densities. Joint distributions. Independence. Covariance and correlation. Conditional probability and conditional expectation. Laws of large numbers and the Central Limit Theorem. Delta method.

• Survey sampling. Simple random sampling, ratio estimation, stratified sampling.

• Parameter estimation. Method-of-moments estimators. Maximum likelihood estimators (MLEs). Large-sample theory for MLEs. Confidence intervals and testing. Bayes estimates. Sufficiency and efficiency. Fisher Information; Cram ´er-Rao lower bound.

• Hypothesis testing. Generalized likelihood ratio tests; Neyman-Pearson Lemma; confidence intervals and test duality.

• Two-sample testing. t-tests; time permitting, Wilcoxon-Mann-Whitney tests.

• Analysis of variance (ANOVA). One- and two-way layouts. Multiple comparisons.

• Regression. Simple linear regression; least-squares. Multiple regression.

• Computational methods. Simulation, bootstrap (parametric and nonparametric).

Course Expectations & Grading

Course assessments and weights:

1) Three quizzes, posted and due within 24-hour period, each administered online, as a multiple-choice quiz on Blackboard, 20% each

2) Homework 20%

3) Final Exam administered online, posted during the stated final examination time and due within a sixhour period, as a multiple choice exam on Blackboard, 20%

For example, suppose that a students’ semester’s homework percentage is 85% (that is, the student received 85% of the possible homework points); quiz percentage on the first quiz is 80%, quiz percentage on the second quiz is 70%, and quiz percentage on the third quiz is 85%; and final exam percentage is 83%. Then this student’s final course percentage is calculated by taking the sum of the products of each of those percentages and the above weighting, as follows:

(0.85) × (0.2) + (0.80) × (0.2) + (0.70) × (0.20) + (0.85) × (0.20) + (0.83) × (0.20)

Grading: Homework should be submitted via Gradescope, which is accessible on Blackboard. Scores on homework and examinations will be released on Blackboard.

For both 430 and 630 students, a weighted final total based on the above weighting scheme will be computed for each students. Letter grades will be based on the weighted final total. The following grading rubric is approximate, and some adjustment to it, reflecting overall course difficulty, is typical.

• 90%–100% A; 87%–89% A-

• 85–86% B+; 80%–84% B; 77%–79% B-

• 74%–76% C+; 69%–73% C; 67%–68% C-

• 58%–66% D

• Below 57% F

Key Dates

(1) Quiz 1: TBD. The quiz will be released on Blackboard and due the following day. Students must upload their answers in Blackboard.

(2) Quiz 2: TBD. The quiz will be released on Blackboard and due the following day. Students must upload their answers in Blackboard.

(3) Quiz 3: TBD. The quiz will be released on Blackboard and due the following day.

(4) Final Exam: Date and time determined by the Registrar. The final exam will be released on Blackboard at the beginning of the scheduled examination time, and students must upload answers within a five-hour period.

Assignments & Readings

All reading and homework assignments, summaries of lectures, handouts, occasional lecture videos and solutions will be posted to Blackboard. Students are expected to complete the assigned reading from the text and other handouts, and to watch recommended lecture videos. 553.430/630 will focus on the material from Chapters 7–14 of the textbook. Students are assumed to be familiar with the material in Chapters 1–6 of the text; these chapters cover basic probability. Some of this material may be reviewed in lectures as needed and as time permits, but students are strongly encouraged to revisit this material on their own in order to prepare for the subsequent chapters. Homework will be assigned approximately weekly. Homework must be submitted via Gradescope.

Technology Access

In order to access course materials, you will need a computer, an internet connection, and for the final exam, access to a printer will be helpful (but is not required).

Ethics and class policies

The strength of the university depends on academic and personal integrity. In this course, students must be honest and truthful. Ethical violations include cheating on exams, plagiarism, reuse of assignments, improper use of the Internet and electronic devices, unauthorized collaboration, alteration of graded assignments, forgery and falsification, lying, facilitating academic dishonesty, and unfair competition.

More information about university misconduct policies can be found on the web at these sites: •

• Undergraduates: e-catalog.jhu.edu/undergrad-students/student-life-policies/

• Graduate students: e-catalog.jhu.edu/grad-students/graduate-specific-policies/

In addition, the specific course policies for this class are as follows:

• Homework will be assigned approximately each week and posted on Blackboard. Assignments must be submitted via Gradescope at the indicated time. Late homework will NOT be accepted. If you miss a homework deadline due to an unforeseen event, such as illness or a family emergency, your homework score for that particular assignment will be replaced by your average homework percentage on the remaining assignments. You are encouraged to work together on the homework, but the solutions you submit must be your own.

• NO MAKE-UP QUIZZES WILL BE GIVEN, REGARDLESS OF CIRCUMSTANCES. Accommodations for a missed quiz will be made ONLY if you have a documented and verifiable (i) university-sanctioned conflict on the day and time of the quiz or (ii) an illness or family emergency at the time of the quiz. You must also adhere to university-wide policies on academic honesty and student conduct.

• The final exam date is fixed and cannot be changed. No early finals will be given under any circumstances.

Students with Disabilities

Any student with a disability who may need accommodations in this class must obtain an accommodation letter from Student Disability Services, 101 Shaffer, (410) 516–4720, [email protected].

ABET Outcomes

• Ability to apply mathematics, science and engineering principles (a).

• Ability to design and conduct experiments, as well as to analyze and interpret data (b).

• Ability to function on interdisciplinary teams (d).

• Ability to identify, formulate and solve statistical problems as they arise in engineering (e).

• Understanding of professional and ethical responsibility (f).

• Ability to communicate effectively (g).

• Recognition of the need for, and an ability to engage in, life-long learning (i).