Twin Cities campus

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Twin Cities Campus

Statistics Ph.D.

Statistics, School of
College of Liberal Arts
Link to a list of faculty for this program.
Contact Information
School of Statistics, 313 Ford Hall, 224 Church Street SE, Minneapolis, MN 55455 (612-625-8046; fax: 612-624-8868)
Email: info@stat.umn.edu
Website: http://www.stat.umn.edu
  • Program Type: Doctorate
  • Requirements for this program are current for Fall 2024
  • Length of program in credits: 73
  • This program does not require summer semesters for timely completion.
  • Degree: Doctor of Philosophy
Along with the program-specific requirements listed below, please read the General Information section of this website for requirements that apply to all major fields.
The School of Statistics is the primary venue at the University for research, teaching, and dissemination of the theory, methodology, and applications of statistical procedures. Students may specialize in any area of statistics. The core program for all students has strong components of theoretical, computational, and applied statistics.
Program Delivery
  • via classroom (the majority of instruction is face-to-face)
Prerequisites for Admission
International applicants must submit score(s) from one of the following tests:
  • TOEFL
    • Internet Based - Total Score: 79
    • Internet Based - Writing Score: 21
    • Internet Based - Reading Score: 19
    • Paper Based - Total Score: 550
  • IELTS
    • Total Score: 6.5
  • MELAB
    • Final score: 80
Key to test abbreviations (TOEFL, IELTS, MELAB).
For an online application or for more information about graduate education admissions, see the General Information section of this website.
Program Requirements
40 credits are required in the major.
9 credits are required outside the major.
24 thesis credits are required.
This program may be completed with a minor.
Use of 4xxx courses towards program requirements is not permitted.
A minimum GPA of 3.00 is required for students to remain in good standing.
At least 2 semesters must be completed before filing a Degree Program Form.
A maximum of 6.0 units of S/N graded courses can apply to these requirements.
Core Courses (28 credits)
Take the following courses. Take STAT 8913 for a total of 4 credits.
STAT 8051 - Advanced Regression Techniques: linear, nonlinear and nonparametric methods (3.0 cr)
STAT 8052 - Applied Statistical Methods 2: Design of Experiments and Mixed -Effects Modeling (3.0 cr)
STAT 8053 - Applied Statistical Methods 3: Multivariate Analysis and Advanced Regression (3.0 cr)
STAT 8054 - Statistical Methods 4: Advanced Statistical Computing (3.0 cr)
STAT 8111 - Mathematical Statistics I (3.0 cr)
STAT 8112 - Mathematical Statistics II (3.0 cr)
STAT 8311 - Linear Models (3.0 cr)
STAT 8801 - Statistical Consulting (3.0 cr)
STAT 8913 - Literature Seminar (1.0 cr)
Electives (12 credits)
Select 12 credits from the following in consultation with the advisor. Other coursework can be applied to this requirement with approval of the advisor and director of graduate studies.
PUBH 7420 - Clinical Trials: Design, Implementation, and Analysis (3.0 cr)
PUBH 7450 - Survival Analysis (3.0 cr)
PUBH 8442 - Bayesian Decision Theory and Data Analysis (3.0 cr)
PUBH 8472 - Spatial Biostatistics (3.0 cr)
STAT 8056 - Statistical Learning and Data Mining (3.0 cr)
STAT 8511 - Time Series Analysis (3.0 cr)
STAT 8931 - Advanced Topics in Statistics (3.0 cr)
STAT 8932 - Advanced Topics in Statistics (3.0 cr)
Outside Coursework (9 credits)
Required Math Courses (6 credits)
Take the following courses. Comparable courses can be substituted with approval of the advisor and director of graduate studies.
MATH 8651 - Theory of Probability Including Measure Theory (3.0 cr)
MATH 8652 - Theory of Probability Including Measure Theory (3.0 cr)
Additional Courses (3 credits)
Select 3 credits in consultation with the advisor and director of graduate studies to complete the 9-credit minimum.
CSCI 5525 - Machine Learning: Analysis and Methods (3.0 cr)
IE 8521 - Optimization (4.0 cr)
MATH 5075 - Mathematics of Options, Futures, and Derivative Securities I (4.0 cr)
MATH 5076 - Mathematics of Options, Futures, and Derivative Securities II (4.0 cr)
MATH 8659 - Stochastic Processes (3.0 cr)
POL 8124 - Game Theory (3.0 cr)
Thesis Credits
Take 24 doctoral thesis credits.
STAT 8888 - Thesis Credit: Doctoral (1.0-24.0 cr)
 
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STAT 8051 - Advanced Regression Techniques: linear, nonlinear and nonparametric methods
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall
Linear/generalized linear models, modern regression methods including nonparametric regression, generalized additive models, splines/basis function methods, regularization, bootstrap/other resampling-based inference. prereq: Statistics grad or instr consent
STAT 8052 - Applied Statistical Methods 2: Design of Experiments and Mixed -Effects Modeling
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Spring
Design experiments/analyze data with fixed effects, random/mixed effects models. ANOVA for factorial designs. Contrasts, multiple comparisons, power/sample size, confounding, fractional factorials. Computer-generated designs. Response surfaces. Multi-level models. Generalized estimating equations (GEE) for longitudinal data with non-normal errors. prereq: 8051 or instr consent
STAT 8053 - Applied Statistical Methods 3: Multivariate Analysis and Advanced Regression
Credits: 3.0 [max 3.0]
Prerequisites: PhD student in stat or DGS permission and 8052
Grading Basis: A-F or Aud
Typically offered: Every Fall
Standard multivariate analysis. Multivariate linear model, classification, clustering, principal components, factor analysis, canonical correlation. Topics in advanced regression. prereq: PhD student in stat or DGS permission and 8052
STAT 8054 - Statistical Methods 4: Advanced Statistical Computing
Credits: 3.0 [max 3.0]
Prerequisites: STAT 8053 or #
Grading Basis: A-F or Aud
Typically offered: Every Spring
Optimization, numerical integration, Markov chain Monte Carlo, related topics. prereq: STAT 8053 or instr consent
STAT 8111 - Mathematical Statistics I
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Probability theory, basic inequalities, characteristic functions, and exchangeability. Multivariate normal distribution. Exponential family. Decision theory, admissibility, and Bayes rules. prereq: [5102 or 8102 or instr consent], [[Math 5615, Math 5616] or real analysis], matrix algebra
STAT 8112 - Mathematical Statistics II
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Statistical inference, estimation, and hypothesis testing. Convergence and relationship between convergence modes. Asymptotics of maximum likelihood estimators, distribution functions, quantiles. Delta method. prereq: 8111
STAT 8311 - Linear Models
Credits: 3.0 [max 4.0]
Typically offered: Every Fall
General linear model theory from a coordinate-free geometric approach. Distribution theory, ANOVA tables, testing, confidence statements, mixed models, covariance structures, variance components estimation. prereq: Linear algebra, 5102 or 8102 or instr consent
STAT 8801 - Statistical Consulting
Credits: 3.0 [max 3.0]
Prerequisites: STAT 8051 and STAT Grad Student or Instructor Consent
Grading Basis: S-N or Aud
Typically offered: Every Spring
Principles of effective consulting/problem-solving, meeting skills, reporting. Aspects of professional practice/behavior, ethics, continuing education. prereq: STAT 8051 and STAT Grad Student or Instructor Consent
STAT 8913 - Literature Seminar
Credits: 1.0 [max 4.0]
Grading Basis: S-N only
Typically offered: Every Fall & Spring
Students will read, present, discuss, and critique current literature/research. prereq: Statistics grad major or instr consent
PUBH 7420 - Clinical Trials: Design, Implementation, and Analysis
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Introduction to and methodology of randomized clinical trials. Design issues, sample size, operational details, interim monitoring, data analysis issues, overviews. prereq: 6451 or concurrent registration is required (or allowed) in 6451 or 7406 or instr consent
PUBH 7450 - Survival Analysis
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Statistical methodologies in analysis of survival data. Kaplan-Meier estimator, Cox's proportional hazards multiple regression model, time-dependent covariates, analysis of residuals, multiple failure outcomes. Typical biomedical applications, including clinical trials and person-years data. prereq: 7405, [STAT 5101 or STAT 8101]
PUBH 8442 - Bayesian Decision Theory and Data Analysis
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Theory/application of Bayesian methods. Bayesian methods compared with traditional, frequentist methods. prereq: [[7460 or experience with FORTRAN or with [C, S+]], Stat 5101, Stat 5102, Stat 8311, grad student in [biostatistics or statistics]] or instr consent
PUBH 8472 - Spatial Biostatistics
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall & Spring
Spatial data, spatial statistical models, and spatial inference on unknown parameters or unobserved spatial data. Nature of spatial data. Special analysis tools that help to analyze such data. Theory/applications. prereq: [[STAT 5101, STAT 5102] or [STAT 8101, STAT 8102]], some experience with S-plus; STAT 8311 recommended
STAT 8056 - Statistical Learning and Data Mining
Credits: 3.0 [max 3.0]
Grading Basis: OPT No Aud
Typically offered: Periodic Spring
STAT8056 covers a range of emerging topics in machine learning and data science, including high-dimensional analysis, recommender systems, undirected and directed graphical models, feed-forward networks, and unstructured data analysis. This course will introduce various statistical and computational techniques for prediction and inference. These techniques are directly applicable to many fields, such as business, engineering, and bioinformatics. This course requires the basic knowledge of machine learning and data mining (e.g., STAT8053).
STAT 8511 - Time Series Analysis
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall
Characteristics of time series. Stationarity. Second-order descriptions. Time-domain representation, ARIMA/GARCH models. Frequency domain representation, univariate/multivariate analysis. Periodograms, non-parametric spectral estimation, state space models. prereq: 5102 or 8111 or instr consent
STAT 8931 - Advanced Topics in Statistics
Credits: 3.0 [max 12.0]
Typically offered: Periodic Fall & Spring
Topics vary according to student needs/available staff.
STAT 8932 - Advanced Topics in Statistics
Credits: 3.0 [max 12.0]
Typically offered: Periodic Fall & Spring
Topics vary according to student needs/available staff.
MATH 8651 - Theory of Probability Including Measure Theory
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Probability spaces. Distributions/expectations of random variables. Basic theorems of Lebesque theory. Stochastic independence, sums of independent random variables, random walks, filtrations. Probability, moment generating functions, characteristic functions. Laws of large numbers. prereq: 5616 or instr consent
MATH 8652 - Theory of Probability Including Measure Theory
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Conditional distributions and expectations, convergence of sequences of distributions on real line and on Polish spaces, central limit theorem and related limit theorems, Brownian motion, martingales and introduction to other stochastic sequences. prereq: 8651 or instr consent
CSCI 5525 - Machine Learning: Analysis and Methods
Credits: 3.0 [max 3.0]
Typically offered: Fall Even Year
Models of learning. Supervised algorithms such as perceptrons, logistic regression, and large margin methods (SVMs, boosting). Hypothesis evaluation. Learning theory. Online algorithms such as winnow and weighted majority. Unsupervised algorithms, dimensionality reduction, spectral methods. Graphical models. prereq: Grad student or instr consent
IE 8521 - Optimization
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Theory and applications of linear and nonlinear optimization. Linear optimization: simplex method, convex analysis, interior point method, duality theory. Nonlinear optimization: interior point methods and first-order methods, convergence and complexity analysis. Applications in engineering, economics, and business problems. prereq: Familiarity with linear algebra and calculus.
MATH 5075 - Mathematics of Options, Futures, and Derivative Securities I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Mathematical background (e.g., partial differential equations, Fourier series, computational methods, Black-Scholes theory, numerical methods--including Monte Carlo simulation). Interest-rate derivative securities, exotic options, risk theory. First course of two-course sequence. prereq: Two yrs calculus, basic computer skills
MATH 5076 - Mathematics of Options, Futures, and Derivative Securities II
Credits: 4.0 [max 4.0]
Grading Basis: A-F or Aud
Typically offered: Every Spring
Mathematical background such as partial differential equations, Fourier series, computational methods, Black-Scholes theory, numerical methods (including Monte Carlo simulation), interest-rate derivative securities, exotic options, risk theory. prereq: 5075
MATH 8659 - Stochastic Processes
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
In-depth coverage of various stochastic processes and related concepts, such as Markov sequences and processes, renewal sequences, exchangeable sequences, stationary sequences, Poisson point processes, Levy processes, interacting particle systems, diffusions, and stochastic integrals. prereq: 8652 or instr consent
POL 8124 - Game Theory
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Application of noncooperative game theory in political science. Equilibrium concepts, bargaining, repeated games, games of incomplete information, signaling games, reputation, learning in games.
STAT 8888 - Thesis Credit: Doctoral
Credits: 1.0 -24.0 [max 100.0]
Grading Basis: No Grade
Typically offered: Every Fall & Spring
(No description) prereq: Max 18 cr per semester or summer; 24 cr required