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Degree plans (Thesis vs. Non-Thesis)

Students may complete the program of “Master of Science in Statistics and Data Science” by
choosing one of two possible degree plans:

• The Master’s Thesis Degree Plan (Thesis Plan), or
• The Comprehensive Exam Plan (Non-Thesis Plan).

To complete their master’s degree via the Thesis Plan, students must complete at least 30 credits
of acceptable graduate courses, which must include:

• at least 6 thesis credits (by enrolling in the thesis course STAT 797), and
• at least 12 non-thesis credits of 700-level courses, and
• at least 21 credits through on-campus courses at the university. For transfer credits, please consult the Graduate Director.

To complete their master’s degree via the Non-Thesis Plan, students must pass the
comprehensive exam and complete at least 32 credits of acceptable graduate courses, which
must include:

• at least 18 non-thesis credits of 700-level courses.
• at least 23 credits through on-campus courses at the university. For transfer credits, please consult the Graduate Director.
• 1 credit of the Comprehensive Exam course Math 795 (Stat 795 coming in Fall 2020).

Degree requirements

To graduate, students must successfully complete the following six courses:
STAT 645 - Introduction to Statistical Computing (3 units, offered every fall semester)
STAT 661 - A First Course in Probability (3 units, offered every semester)
STAT 667 - Statistical Theory (3 units, offered every semester)
STAT 755 - Multivariate Data Analysis (3 units, offered every spring semester)
STAT 757 - Applied Regression Analysis (3 units, offered every fall semester)
STAT 760 - Statistical Learning (3 units, offered every spring semester)
In addition to the required courses, students following the

• Thesis Plan, must complete 6 elective and 6 thesis credits;
• Non –thesis Plan, must complete 12 elective and 1 comprehensive exam credits;

An internship may be included in the plan of study, subject to availability and approval of the
Graduate Director.

Electives

For elective credits to count towards degree requirements, all these credits must be approved by

• the student’s Graduate Committee (Section 4) if the student formed the Graduate Committee, or
• by the Graduate Director, if the student did not form the Graduate Committee yet;

Appropriate courses outside the Department of Mathematics and Statistics may be approved,
depending on the student’s research interests.

The Master’s thesis

Students who choose the Thesis Plan must write a master’s thesis to complete the program. This process starts with the student choosing a Thesis Advisor (Advisor), a choice typically made during the student’s first year in the program. The Advisor is a graduate faculty member of the Department of Mathematics and Statistics who works in a research area of interest to the student. To initiate the Student-Advisor collaboration, the student should approach the faculty member and ask her/him if she/he is willing to serve as the student’s Advisor. The student and Advisor jointly choose members of the student’s Graduate Committee (Section 4).

Once an Advisor has been identified, she/he will guide the student through the thesis writing process. This may involve preparatory work such as reading books and/or research papers, computer programming, intense calculations, etc.
While working on the thesis, the student needs to be enrolled in the thesis course STAT 797, completing a total of 6 credits. These are typically broken up as 3 credits during the student’s 3rd semester and 3 during the student’s 4th semester(though the student could choose to take all 6 credits in the 4th semester, for example).

The Advisor will instruct the student about the content and format of the thesis. A Master’s Thesis, unlike a Ph.D. Thesis is not expected to contain original content but should demonstrate the student’s mastery of an area of statistics and data science. Upon completion, the student will defend her/his thesis by giving a public presentation, followed by a period of questions by the student’s Graduate Committee members.

Scheduling of the defense

MS thesis defense is a public event. It is the student’s responsibility to contact her/his Graduate Committee and the Graduate Director (all that sign the Notice of Completion) regarding their availability. It is strongly advised that the student schedules defense no later than 1 month before the planned defense date. It is also the student’s responsibility to reserve an appropriate room for her/his defense. Defense announcements should be sent to the Mathematics and Statistics office for further dissemination.

The Comprehensive exam

Students who choose the Non-Thesis Plan must complete the Comprehensive Exam. This exam is offered once every semester, close to the end of the semester. The exact date for the exam is announced by the Graduate Director in a timely fashion.

General information

The exam is to evaluate students' fundamental knowledge of probability and statistics. The topics for the exam are a union of the major topics from the Probability (STAT 661) and Mathematical Statistics (STAT 667) courses.

Study guidelines

To study for the exam, we recommend taking both Probability (STAT 661) and the Statistics Theory (STAT 667) classes; practicing by doing problems assigned as homework and more problems from the course textbooks; doing relevant problems from the actuarial exams; studying proofs of theorems in the texts. Students are expected to know all definitions and theorems with proofs. We stress that the exam is not based on any particular book. It is an exam based on knowledge of fundamental topics in probability and mathematical statistics. Some texts you may find helpful include:

Main reference

Larsen, R. J. and Marx, M. L. “An Introduction to Mathematical Statistics and Its Applications”, 5th edition, Prentice-Hall.

Additional references

• DeGroot, M.H. and Schervish, M.J. “Probability and Statistics”, Addison Wesley, 3rd edition, 2002.
• Bean, M.A. “Probability: The Science of Uncertainty with Applications to Investments, Insurance and Engineering”, American Mathematical Society, 2009.
  

Exam Syllabus

1. The formal language of probability: Random experiment, set theory, sample space, counting, and combinatorial methods, probability of union of events, conditional probability, multiplication rule, independent events, the law of total probability, and Bayes' theorem.
2. Univariate and multivariate random variables and probability distributions: Discrete, continuous, and mixed distributions; cumulative distribution function; probability density function; probability mass function; quantile function and percentile; marginal and conditional distributions; independence; functions of random variables and random vectors; linear transformations; sums, products, and quotients of random variables; minima and maxima of random variables; order statistics; mixtures and compound distributions and their applications;  probability integral transform theorem and random variate generation; Monte-Carlo methods.
3. Measures of expectation, variation and risk, expected value, geometric mean, median, mean squared and mean absolute error, variance and standard deviation, moments and moment generating function, survival and hazard functions, covariance and correlation, conditional expectation and variance.
4. Special discrete and continuous distributions and their applications: Bernoulli, binomial, Poisson, hypergeometric, multinomial, negative binomial, geometric, exponential, gamma, Weibull, beta, uniform, Pareto, univariate and multivariate normal, lognormal distributions.
5. Convergence of probability distributions: Convergence in distribution, convergence in probability, and almost sure convergence; Markov and Chebyshev inequalities; the law of large numbers and the central limit theorem; normal approximation to binomial; delta method.
   
6. Sampling distributions related to the normal distribution: The sample mean and its properties; chi-square, student-t, and F distributions; joint distribution of the sample mean and variance.
7. Estimation: The method of moments; maximum likelihood estimation and its properties; efficiency, consistency, sufficiency, and unbiasedness; small and large sample confidence intervals; information inequality; loss and risk functions; uniformly minimum variance unbiased (UMVU) estimation; Bayesian estimation.
8. Testing hypotheses: Mathematical setup and terminology; power and sample size calculations; p-values; likelihood ratio tests, one and two-sample z-test and t-test; F-test; Kolmogorov-Smirnov test; chi-square tests of goodness-of-fit; contingency tables and tests for homogeneity.
9. Linear models: The method of least squares, linear regression, statistical inference under linear regression model.

The Comprehensive Exam is 6 hours long and is broken up into a 3-hour morning session (typically 9 am - 12 noon) and a 3-hour afternoon session (1 pm-4 pm). Students will be allowed a maximum of two attempts at passing the Comprehensive Exam. If the first written attempt is not successful, the student may ask for an opportunity of an oral exam to be scheduled as soon as practical (usually within 2 weeks) the same semester. If the student does not pass the oral exam, s/he will have a second chance to take the written test the following semester, as scheduled. There is no opportunity for an oral exam after the second written Comprehensive Exam. During the semester the student takes the exam, s/he must be enrolled in MATH 795 (from Fall 2020 STAT 795) – the Comprehensive Exam course.

Graduate school academic requirements

Good Standing

Each graduate course must be completed with a grade of "C" or better for the credit to be acceptable toward an advanced degree.

In addition, students must maintain good standing with an overall cumulative graduate credit GPA of at least 3.0 on a scale of 4.0. Students must have a minimum GPA of 3.0 in order to meet graduation eligibility. All graduate students must maintain a cumulative graduate GPA of 3.0. If their GPA drops below 3.0, they are either placed on probation or dismissed. Undergraduate courses will not count towards graduate GPA.

Probation

If the student’s cumulative grade-point total is between 2.31 and 2.99, the student is placed on probation. The student must then raise her/his cumulative graduate GPA to 3.0 by the end of the following semester or the student will be dismissed from graduate standing. Thesis, dissertation, S/U graded credits, and transfer credits have no impact on a student’s GPA.

Dismissal

If the graduate grade-point total is 2.30 or lower, the student is dismissed from graduate standing, or if the graduate GPA remains below 3.0 for two (2) consecutive semesters, the student is dismissed from graduate standing.

Dismissed students are no longer in a graduate program but may take graduate-level courses as a Grad Special. Students wishing to complete their degree must obtain approval to take graduate-level courses, raise their graduate GPA to at least 3.0, and then re-apply to a graduate program. Any courses taken to raise their GPA will be included in the graduate special/ transfer credit limitation (12 credits for master’s degrees).