The Department of Statistics offers graduate programs leading to a Master's degree in Applied Statistics and a Ph.D. degree in Statistics. The Master's degree is intended to prepare a student for a career as a professional statistician working in business, government or industry, while the Ph.D. degree allows for the additional possibility of an academic career. We also offer a Master's degree in Statistics as an embedded degree for PhD students at the University of Michigan, both in our own department and in other programs.

### Ph.D. Program

These requirements apply to students admitted in Fall 2014 or later. Students admitted in Fall 2011 or earlier should see the old requirements. Students admitted in Fall 2012 and 2013 should contact the Graduate Chair about their individual transition plan.

The Ph.D. in Statistics is flexible and allows students to pursue a variety of directions, ranging from statistical methodology and interdisciplinary research to theoretical statistics and probability theory. Students typically start the Ph.D. program by taking courses and gradually transition to research that will ultimately lead to their dissertation, the most important component of the Ph.D. program. The major requirements of the Ph.D. program are coursework, qualifying exams, advancement to candidacy, and dissertation, discussed in detail below.

### Required Courses

The core PhD curriculum consists of four course sequences, offered annually:

**Applied Statistics**— Stats 600 and 601**Theoretical Statistics**—**Probability**—- Computational Methods for Statistics —

Stats 600, 601, 610, 611, 620, and 621 are semester-long courses, and Stats 607 I and II, 608 I and II are half-semester modules. Any combination of two half-semester modules in the 607/608 sequence is equivalent to one course. All doctoral students must take at least 6 out of 8 required courses, with at least one course selected from each of the four sequences. A B+ average or higher in the six selected courses is required.

In addition, all students are required to complete two professional development seminar courses:

- Stats 810, which covers research ethics and introduction to research tools. Must be taken in the first semester in the program.
- Stats 811, which focuses on technical writing and presentation skills. Must be completed no later than by the end of the third year in the program.

### First Year Course Placement

Our Ph.D. program admits students with diverse academic backgrounds. A mandatory screening test is given to all new Ph.D. students at the start of the first year to determine the most appropriate individual study program for each student. The Graduate Chair will advise the students on course selection based on their screening test results and academic records. Some students complete all the required courses and exams by the end of their first year, while others take additional preparatory courses and postpone some of the required courses to their second year.

### Qualifying Exams

Doctoral students are required to pass two qualifying exams.

- Comprehensive theory exam. This exam covers probability and theoretical statistics at the level of a graduate textbook such as "Statistical Inference" by Casella and Berger, used by Stats 510/511 and Biostats 601/602 courses. It also includes selected theoretical topics from the applied sequence (Stats 600/601). The comprehensive exam is offered twice a year, in late August and in late May. Students with advanced preparation may take this exam at the start of their first year. Two attempts are allowed, and the attempt at the start of the first year does not count towards this maximum of two. All students need to pass this exam within 12 months of enrolling in the program unless an exception is approved by the Graduate Chair.
- Applied statistics exam. This exam tests modeling and data analysis skills and is roughly based on Stats 600/601. It is given as a 3-day take-home exam once a year in late May. Two attempts are allowed. All students need to pass this exam within two years of enrolling in the program unless an exception is approved by the Graduate Chair.

**Advancing to Candidacy**

Students who have passed the qualifying exams are expected to find a faculty advisor and start research leading to their dissertation proposal. The Graduate Chair and the faculty mentor assigned to each first year student can assist with finding a faculty advisor. Students are expected to submit a dissertation proposal and advance to candidacy within three semesters from passing the qualifying exams. Requirements for advancing to candidacy are:

**At least 18 credit hours of graduate course work,**including at least 6 out of the required 8 core courses and Stats 810. A B+ average in the selected 6 core courses is required. Stats 808/809/818/819 (Department Seminar), Stats 990 (Dissertation Research) and similar non-graded courses do not count towards the credit requirement.**At least 4 credit hours of cognates,**which are 400- and higher-level courses from outside the Statistics department. All cognate course selections must be approved by the Graduate Chair.**Writing a dissertation proposal and passing the oral preliminary exam**which consists of presenting the proposal to the student's preliminary thesis committee.

A dissertation proposal should identify an interesting research problem, provide motivation for studying it, review the relevant literature, and propose an approach for solving the problem. The written proposal is given to the preliminary thesis committee ahead of time and then presented in the oral preliminary exam. The preliminary thesis committee is chaired by the faculty advisor and must include at least two more regular faculty members from Statistics. It may also include up to two additional members who can come from other departments or universities. The preliminary thesis committee may continue to serve as the doctoral thesis committee, but this is not required.

At the oral preliminary exam, the committee will ask questions about the proposal and the relevant background and either elect to accept the proposal as both substantial and feasible, or ask for specific revisions, or decline the proposal. The unanimous approval of the proposal by the committee is necessary for the student to advance to candidacy.

### Additional Course Requirements

Students must take at least three additional PhD level semester-long courses or equivalent in half-semester modules. This requirement can be fullfilled with additional courses from the core sequences, advanced PhD courses, or topics courses. Stats 810, 811, and 750 (independent reading) do not count towards this requirement. While these additional courses are not required for advancement to candidacy, it is expected that students take at least some of them before advancing to candidacy. Taking courses after advancement to candidacy may require careful planning as candidates are allowed to take only one course per semester without an increase in tuition.

In addition, all PhD students are expected to register for Stats 808/809/818/819 (Department Seminar) every semester and attend the seminar regularly. Candidates registered for another course do not have to register for the department seminar, but are still expected to attend.

Exceptions to the above requirements and credit for graduate work completed elsewhere may be granted by the Graduate Chair.

### Annual Progress Reports

All candidates are required to give a short presentation on their research progress once a year. These talks are normally scheduled during the student seminar.

### Dissertation and Defense

Each doctoral student is expected to write a dissertation that makes a substantial and original contribution to statistics or a closely related field. This is the most important element of the doctoral program. After advancing to candidacy, students are expected to focus on their thesis research under the supervision of the thesis advisor and the doctoral committee. The doctoral committee must include at least three regular faculty members from Statistics and at least one regular faculty member from another department (a cognate member). The written dissertation is submitted to the committee for evaluation and presented in an oral defense open to the public.

### Rackham Requirements

The Rackham Graduate School imposes some additional requirements concerning residency, fees, and time limits. Students are expected to know and comply with these requirements.

### Applied Master's Program

*Please note that this Program was updated for students admitted beginning Fall 2011 and supersedes previous versions.*

The Master's program in Applied Statistics prepares graduates for careers as applied statisticians in industry, government, consulting firms, and research organizations. Course requirements include at least 10 courses for a total of 30 credit hours. While requirements include basic courses in probability and theoretical statistics, the emphasis is on statistical modeling and data analysis. A wide variety of elective courses are offered in the Department of Statistics and in other departments, including Biostatistics, Computer Science, Economics, Industrial & Operations Engineering, Mathematics, School of Information, Sociology, and the Survey Research Center. Most students take two years (4 semesters) to complete the degree, although it is possible to do it in 3 semesters. Students cumulative GPA must be 3.00 (B) or better to stay in good standing.

### Prerequisites

It is strongly recommended that prospective students have a good background in calculus and linear algebra and have taken one course in probability and one in theoretical statistics. Students who have not taken these prerequisite courses are generally required to take them in the first year of graduate study, with no credit toward the requirements for the degree.

### Courses

The following core, elective, and cognate courses are required of all students.

**Students must take each of the following core courses:**

**STATS 500**— Applied Statistics**STATS 503**— Applied Multivariate Analysis**STATS 504**— Statistical Consulting**STATS 510**— Probability**STATS 511**— Theoretical Statistics

**Students must take a minimum of three of the following elective courses:**

**Either STATS 430 ,**Applied Probability OR**STATS 526**, Discrete State Stochastic Processes (for more advanced students)**Either STATS 406**, Introduction to Statistical Computing OR**STATS 607/608**, Statistical Computing (for more advanced students) OR**BIOSTAT 615**, Statistical Computing**Either STATS 414,**Introduction to Bayesian Data Analysis**BIOSTAT 682,**Applied Bayesian Inference**STATS 509**— Statistics for Financial Data**STATS 531**— Analysis of Time Series**Either STATS 535**, Reliability OR**BIOSTAT 675**, Survival Time Analysis**MATH/STATS 547**— Probabilistic Modeling in Bioinformatics**STATS 560**— Introduction to Nonparametric Statistics**STATS 570**— Design of Experiments**STATS 580**— Methods and Theory of Sample Design**BIOSTAT 675**— Survival Analysis**BIOSTAT 695**— Analysis of Categorical Data**BIOSTAT 696**— Spatial Statistics- Any approved 600- or above statistics courses.

All STATS courses 600-level or above can be used as elective courses, with the exception that students can not use 600, 601 as electives if they have taken STATS 500, 503, and that they can not use 610, 611 as electives if they have taken STATS 510 and STATS 511. For students who are enrolled prior to Fall, 2012, Biostat 601 and 602 can be used to replace STATS 510 and STATS 511.

**To obtain credits toward the degree requirement for cross-listed courses, students have to enroll under the STATS course number.**

**Students must take 4 credits of cognate courses:**

Cognates are courses from outside the Department of Statistics, and must be pre-approved by the program advisor.

### Cognate Suggestions

Students can use the flexibility in the choice of elective and cognate courses to align their program of study with their interests. Some suggestions of cognate courses by area are given below, along with electives that are most important to take if you are interested in that area. Students can take cognate courses from multiple areas, or choose other courses to serve as cognates. All cognate choices must be pre-approved by the program advisor.

#### Econometrics and Forecasting

Statistical techniques play an important role in predicting/forecasting various economic phenomena. To specialize in this area, students can take **STATS 509**, **STATS 531**, or both as an elective and take one or more of the following:

**ECON 501**— Microeconomic Theory**ECON 502**—Applied Macroeconomics**ECON 675**— Applied Econometrics

#### Financial Statistics

Modeling and analysis of financial data is another area that is attracting a lot of attention. Students interested in specializing in this area should take **STATS 509**, **STATS 531**, or both as an elective and take one or more of:

**MATH / IOE 506**— Stochastic Analysis for Finance II**IOE 552**— Financial Engineering I**FIN 513**— Financial Analysis**FIN 580**— Options and Futures in Corporate Decision Making

#### Industrial Statistics

Students can take elective courses offered by the Department of Industrial & Operations Engineering to develop expertise in the application of quality and reliability methods in industrial statistics. Suggested courses include **STATS 570** and **STATS 535** / **IOE 562** as electives and one or more of:

**IOE 466**— Statistical Process Control**IOE 515**— Stochastic Industrial Processes**IOE 541**— Inventory Analysis and Control**IOE 545**— Queuing Networks in Manufacturing**IOE 566**— Advanced Quality Control

#### Information Sciences

Advances in computing and measurement technologies have led to massive amounts of data being collected routinely. Statistical methods play a fundamental role in the collection, visualization, mining and analysis of large data sets. Students interested in this area can take **STATS 406** as elective and take one or more of:

**EECS 477**— Introduction to Algorithms**EECS 484**— Database Management Systems**EECS 485**— Web Database Information Systems**SI 531**— Human Interaction in Information Retrieval**SI 539**— Design of Complex Web Sites**SI 572**— Database Application Design**SI 601**— Data Manipulation

#### Survey Sampling

The use of sample surveys to obtain information on a myriad of subjects is becoming ever more popular. The demand for statisticians trained in this sub-area is extremely high. The University of Michigan has, in various departments and in the Institute for Social Research, the faculty talent to be able to offer one of the best specializations in the country. For this area, students can enroll in **STATS 580** as an elective and take one or more of:

**SOC 612**— Methods of Survey Sampling**SOC 613**— Advanced Methods of Survey Sampling**SOC 621**— Workshop on Sampling Techniques**SOC 711**— Questionnaire Design, Interviewing and Coding

See also other courses in survey sampling offered by the Department of Sociology and the Survey Methodology Program of the Institute for Social Research.

### Dual Master's Program

*Please note that this Program was updated for students admitted beginning Fall 2011 and supersedes previous versions.*

The regular Master's degree (Master of Arts in Statistics) is restricted to students who are already enrolled in a Ph.D. program at the University of Michigan in Ann Arbor. It is a dual degree earned while a student is working towards a Ph.D. in another field, aimed at students who do a significant amount of statistics as part of their thesis research. It is also awarded as an embedded degree to students working towards a Ph.D. in Statistics.

Students interested in a Master’s degree in Statistics who are not currently enrolled in a Ph.D. program at the University of Michigan, or whose Ph.D. thesis at Michigan does not involve a significant statistical component, should apply to the **Master’s Program in Applied Statistics**.

### Application

Applicants must have already been accepted by a Rackham Ph.D. program and should have a reasonable background in calculus, linear algebra, introductory probability, and introductory statistics.

Prospective applicants are encouraged to consult with the Department of Statistics prior to submitting an application. **Students are strongly discouraged from completing the course requirements and then applying to the program.** Note also that you must be enrolled in the program for one year and complete a writing component before the degree is awarded.

Applicants should submit a Dual Degree form to the Statistics Department Main Office (439 West Hall). A letter of recommendation from a Faculty or Graduate Advisor in the student’s home Ph.D. department is also required, along with an up-to-date CV and Statement of Purpose.

The Winter 2015 application deadline is December 1, 2014 and the Fall 2015 application deadline is April 30, 2015.

### Curriculum

The program requires a minimum of 24 credit hours of course work, including two cognate courses, and a writing component. Course selection **must **be pre-approved by the Program Advisor. Specifically, the requirements are:

**STATS 500 (Applied Statistics 1) and STATS 503 (Applied Multivariate Analysis).**More advanced students are encouraged to replace this sequence with STATS 600 (Linear Models) and STATS 601 (Analysis of Multivariate and Categorical Data) [*6 credit hours*]**BIOSTAT 601 (Probability) and BIOSTAT 602 (Biostatistical Inference).**More advanced students are encouraged to replace this sequence with STATS 610 (Statistical Inference) and STATS 611 (Large Sample Theory). [*at least 6 credit hours*]**At least two elective statistics courses from graduate-level courses**offered by the Department of Statistics or other approved courses (see list below). [*at least 6 credit hours*]**Two cognate courses from another department.**Consult the Program Advisor about acceptable cognate courses. [*at least 4 credit hours*]**A writing component**that demonstrates mastery of statistical methods in the design of data collection methods and/or modeling and analysis of data in the student's area of research. See more details below.

Students who have already taken courses that are equivalent to the required courses should discuss possible substitutions with the Program Advisor. Note that all students have to complete at least 24 credit hours in the program.

### List of Elective Courses

The following courses are acceptable as electives. Selected courses from outside the Department of Statistics may also be approved as electives; consult the Program Advisor.

**Either STATS 430**, Applied Probability OR**STATS 526**, Discrete State Stochastic Processes (for more advanced students)**Either STATS 406**, Introduction to Statistical Computing OR**BIOSTAT 615**, Statistical Computing**Either STATS 414,**Introduction to Bayesian Data Analysis**BIOSTAT 682,**Applied Bayesian Inference**STATS 509**— Statistics for Financial Data**STATS 531**— Analysis of Time Series**Either STATS 535**, Reliability OR**BIOSTAT 675**, Survival Time Analysis**MATH/STATS 547**—Probabilistic Modeling in Bioinformatics**STATS 560**—Introduction to Nonparametric Statistics**STATS 570**—Design of Experiments**STATS 580**—Methods and Theory of Sample Design**BIOSTAT 675**—Survival Analysis**Either BIOSTAT 695,**Analysis of Categorical Data OR**SOC 619**, Categorical Data Analysis.**BIOSTAT 696**— Spatial Statistics

All STATS courses 600-level or above can be used as elective courses, with the exception that students can not use 600, 601 as electives if they have taken STATS 500, 503, and that they can not use 610, 611 as electives if they have taken BIOSTAT 601 and 602.

To obtain credits toward the degree requirement for cross-listed courses, students have to enroll under the STATS course number.

### Writing Component

Since the dual degree is primarily designed for students who do a significant amount of statistics for their thesis research, the students in the program are required to have a Ph.D. thesis chapter, or a thesis-based research paper submitted for publication, which demonstrates mastery of statistical methods at the level of a Master's project. The writing component may focus on data collection (design of experiments, survey design), modeling and analysis of data, or both. It must be approved by a member of the student's Ph.D. committee with an appointment in the Statistics department. This committee member will need to sign a form approving the statistical writing component, typically at the time of the defense. The student must also provide a two-page summary of the writing component, to be submitted with the signed approval form, describing the scientific problem under investigation, its importance, and statistical methods used.

In the event that the student's thesis does not have a sufficient statistical component, this requirement may be replaced with two additional elective courses (at least 6 credit hours), making the total credit requirement equivalent to that of the Master's Program in Applied Statistics. Students are strongly advised to consult with the Statistics faculty member on their committee well in advance of the defense to determine the best course of action. Those who do not anticipate having a significant statistical component in their thesis should apply directly to the **Master's Program in Applied Statistics**.