Course Description

This interdisciplinary course introduces the mathematical concepts required to interpret results and subsequently draw conclusions from data in an applied manner. The course presents different techniques for applied statistical inference and data analysis, including their implementation in Python, such as parameter and distribution estimators, hypothesis testing, Bayesian inference, and likelihood.

More informally, this 3-credit, undergraduate-level course covers probability and statistics topics required for data scientists to analyze and interpret data. The course will involve theoretical topics and some programming assignments. The course is targeted primarily for junior and senior undergraduate students who are comfortable with concepts relating to probability and are comfortable with basic programming. Undergraduates from Computer Science, Applied Mathematics and Statistics, and Electrical and Computer Engineering would be well suited for taking this class. Topics covered include Probability Theory, Random Variables, Stochastic Processes, Statistical Inference, Hypothesis Testing, and Regression. For more details, refer to the syllabus below.

The class is in-person, and is expected to be interactive and students are encouraged to participate in class discussions.

Grading will be on a curve, and will be based primarily on assignments and exams. For more details, refer to the section on grading below.

Prerequisites: C or higher in CSE 214; AMS 310; CSE or DAS major. See Bulletin for definitive information. Comfort in probability theory and proficiency with Python (since programming assignments tasks will be in Python) will be helpful.

Learning Objectives:An understanding of core concepts of probability theory and standard statistical techniques. An understanding of random variables, distributions, and hypothesis testing. An ability to apply quantitative research methods (correlation and regression), and modern techniques of optimization and machine learning such as clustering and prediction.

Syllabus & Schedule

Date	Topic	Readings	Notes
Aug 26 (Tu) [Lec 01]	Course introduction, class logistics
Aug 28 (Th) [Lec 02]	Probability review - 1 Basics: sample space, outcomes, probability Events: mutually exclusive, independent Calculating probability: sets, counting, tree diagram	AoS 1.1 - 1.5 MHB 3.1 - 3.4	assignment 1 out, due Sep 8th
Sep 02 (Tu) [Lec 03]	Probability review - 2 Conditional probability Law of total probability Bayes' theorem	AoS 1.6, 1.7 MHB 3.3 - 3.6
Sep 04 (Th) [Lec 04]	Random variables - 1 Mean, Moments, Variance pmf, pdf, cdf Bernoulli(p) Indicator RV Binomial(n, p) Geometric(p)	AoS 2.1 - 2.3, 3.1 - 3.4 MHB 3.7 - 3.9	Python scripts: draw_Bernoulli, draw_Binomial, draw_Geometric
Sep 09 (Tu) [Lec 05]	Random variables - 2 Uniform(a, b) Exponential(λ) Normal(μ, σ2), and its several properties	AoS 2.4, 3.1 - 3.4 MHB 3.7 - 3.9, 3.14.1	Python scripts: draw_Uniform, draw_Exponential, draw_Normal assignment 2 out, due Sept 22
Sep 11 (Th) [Lec 06]	Random variables - 3 Joint probability distribution Linearity and product of expectation Linearity of variance	AoS 2.5 - 2.7 MHB 3.10, 3.13
Sep 16 (Tu) [Lec 07]	Probability inequalities Weak Law of Large Numbers Central Limit Theorem	AoS 4.1 - 4.2, 5.3 - 5.4 MHB 3.14.2, 5.2
Sep 18 (Th) [Lec 08]	Python review		Optional
Sep 23 (Tu) [Lec 09]	Non-parametric inference - 1 Basics of inference Empirical PMF Sample mean bias, se, MSE	AoS 6.1, 6.2, 6.3.1	assignment 3 out, due Oct 3
Sep 25 (Th) [Lec 10]	Non-parametric inference - 2 Empirical Distribution Function (or eCDF) Statistical Functionals Plug-in estimator	AoS 6.3.1, 7.1 - 7.2	Python scripts: sampleUniform, sampleExponential, sampleNormal, eCDF
Sep 30 (Tu) [Lec 11]	Non-parametric inference - 3 Percentiles, quantiles Outlier detection, Tukey's rule Normal-based confidence intervals	AoS 6.3.2, 7.1
Oct 02 (Th) [Lec 12]	Parametric inference - 1 Basics of parametric inference Method of Moments Estimator (MME) Properties of MME	AoS 6.3.1 - 6.3.2, 9.1 - 9.2
Oct 07 (Tu) [Lec 13]	Mid-term 1 review
Oct 09 (Th)	Mid-term 1
Oct 14 (Tu)	Fall Break		No class
Oct 16 (Th) [Lec 14]	Parametric inference - 2 Likelihood Maximum Likelihood Estimator (MLE) Properties of MLE	AoS 9.3 - 9.4, 9.6	assignment 4 out, due Oct 31
Oct 21 (Tu) [Lec 15]	Hypothesis testing - 1 Basics of hypothesis testing The Wald test	AoS 10 - 10.1 DSD 5.3 - 5.3.1
Oct 23 (Th) [Lec 16]	Hypothesis testing - 2 Type I and Type II errors The Wald test	AoS 10 - 10.1 DSD 5.3.1
Oct 28 (Tu) [Lec 17]	Hypothesis testing - 3 The Wald test Z-test	AoS 10.10.2 DSD 5.3.2
Oct 30 (Th) [Lec 18]	Hypothesis testing - 4 Z-test t-test	AoS 10.10.2 DSD 5.3.2	assignment 5 out, due Nov 12
Nov 04 (Tu) [Lec 19]	Hypothesis testing - 5 Kolmogorov-Smirnov test (KS test)	AoS 15.4 DSD 5.3.3
Nov 06 (Th) [Lec 20]	Statistics in Medicine		Guest lecture by Dr. Shrivastava
Nov 11 (Tu) [Lec 21]	Hypothesis testing - 6 p-values Permutation test	AoS 10.2, 10.5 DSD 5.5
Nov 13 (Th) [Lec 22]	Hypothesis testing - 7 Pearson correlation coefficient Chi-square test for independence	AoS 3.3, 10.3 - 10.4 DSD 2.3	assignment 6 out, due Dec 1
Nov 18 (Tu) [Lec 23]	Hypothesis testing - 8 Chi-square test for independence	AoS 3.3, 10.3 - 10.4 DSD 2.3
Nov 20 (Th) [Lec 24]	Regression - 1 Basics of Regression Simple Linear Regression	AoS 13.1, 13.3 - 13.4 DSD 9.1
Nov 25 (Tu) [Lec 25]	Regression - 2 Ordinary Least Squares Multiple Linear Regression	AoS 13.5 DSD 9.1
Nov 27 (Th)	Thanksgiving break		No class
Dec 02 (Tu) [Lec 26]	Mid-term 2 review
Dec 04 (Th)	No class		No class
Dec 16 (Tu)	Mid-term 2	At 11:15am	11:15am-12:45pm

Resources

• Recommended text: (AoS) "All of Statistics : A Concise Course in Statistical Inference" by Larry Wasserman (Springer publication).
• Students are strongly suggested to purchase a copy of this book.
• Recommended text: (MHB) "Performance Modeling and Design of Computer Systems: Queueing Theory in Action" by Mor Harchol-Balter (Cambridge University Press)
• Suggested for probability review and stochastic processes.
• There is copy placed on reserve in the library. The instructor also has a few personal copies that you can borrow.
• Recommended text: (DSD) "The Data Science Design Manual" by (our very own) Steven Skiena (Springer publication).
• Suggested for data science topics in the second half of the course.


• Others:
• S.M. Ross, Introduction to Probability Models, Academic Press
• S.M. Ross, Stochastic Processes, Wiley

Grading (tentative)

• Assignments: 40%
• 6 assignments during the semester. Expect 5-7 questions per assignment, including some programming questions (especially after mid-term 1).
• Collaboration is allowed (max group size 4). You are free to form your own groups, and group membership can change between assignments.
• Submit one softcopy solution per group, typed or handwritten, but should be legible.
• Assignments are due at 11:59pm on the due date, via Brightspace. No late submissions allowed.


• Exams: 60%
• Two in-person exams.
• Mid-term 1: 25%.
• Mid-term 2: 35%.
• Easier than the assignments and no long derivations or programming questions.


• Attendance: 0%
• Attendance is not required but strongly encouraged.
• Lectures will not be recorded.
• Exam questions are often based on class discussions, so attendance is helpful!



• Important:
• Academic dishonesty will immediately result in an F and the student will be referred to the Academic Judiciary. See below section on Academic Integrity.
• Grading will be on a curve.
• Assignment of grades by the instructor will be final; no regrading requests will be entertained.
• There is a University policy on grading, as well as a set of grading guidelines agreed upon by the CS faculty. The instructor is obligated to uphold these policies.
  No exceptions will be made for any student and no special circumstances will be entertained.

Academic Integrity Statement

Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Faculty is required to report any suspected instances of academic dishonesty to the Academic Judiciary. Faculty in the Health Sciences Center (School of Health Professions, Nursing, Social Welfare, Dental Medicine) and School of Medicine are required to follow their school-specific procedures. For more comprehensive information on academic integrity, including categories of academic dishonesty please refer to the academic judiciary website at http://www.stonybrook.edu/commcms/academic_integrity/index.html.

Critical Incident Management

Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of Student Conduct and Community Standards any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn. Faculty in the HSC Schools and the School of Medicine are required to follow their school-specific procedures. Further information about most academic matters can be found in the Undergraduate Bulletin, the Undergraduate Class Schedule, and the Faculty-Employee Handbook.

Student Accessibility Support Center Statement

If you have a physical, psychological, medical, or learning disability that may impact your course work, please contact the Student Accessibility Support Center, Stony Brook Union Suite 107, (631) 632-6748, or at sasc@stonybrook.edu. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential.