Twin Cities campus

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Twin Cities Campus

Statistics Minor

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.catalogs.umn.edu/grad/programs/g164.html
  • Program Type: Graduate minor related to major
  • Requirements for this program are current for Fall 2021
  • Length of program in credits (master's): 9
  • Length of program in credits (doctoral): 14
  • This program does not require summer semesters for timely completion.
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 both theoretical and applied statistics.
Program Delivery
  • via classroom (the majority of instruction is face-to-face)
Prerequisites for Admission
Special Application Requirements:
Students interested in the minor are strongly encouraged to confer with their major field advisor and director of graduate studies, and the Statistics director of graduate studies regarding feasibility and requirements.
International applicants must submit score(s) from one of the following tests:
  • TOEFL
    • Internet Based - Total Score: 79
Key to test abbreviations (TOEFL).
For an online application or for more information about graduate education admissions, see the General Information section of this website.
Program Requirements
Use of 4xxx courses toward program requirements is permitted under certain conditions with adviser approval.
Courses offered on both the A-F and S/N grading basis must be taken A-F, with a minimum grade of B- earned for each, unless otherwise approved by the Statistics director of graduate studies. Doctoral students cannot apply 4-level courses or STAT 5021 to the minor. The minimum cumulative GPA for minor field coursework is 2.80.
Coursework (9 to 14 credits)
Master’s students select 9 credits, and doctoral students select 14 credits from the following in consultation with their advisor and the Statistics director of graduate studies.
STAT 4051 - Statistical Machine Learning I (4.0 cr)
STAT 4052 - Statistical Machine Learning II (4.0 cr)
STAT 4101 - Theory of Statistics I (4.0 cr)
STAT 4102 - Theory of Statistics II (4.0 cr)
STAT 5021 - Statistical Analysis (4.0 cr)
STAT 5101 - Theory of Statistics I (4.0 cr)
STAT 5102 - Theory of Statistics II (4.0 cr)
STAT 5201 - Sampling Methodology in Finite Populations (3.0 cr)
STAT 5302 - Applied Regression Analysis (4.0 cr)
STAT 5303 - Designing Experiments (4.0 cr)
STAT 5401 - Applied Multivariate Methods (3.0 cr)
STAT 5421 - Analysis of Categorical Data (3.0 cr)
STAT 5511 - Time Series Analysis (3.0 cr)
STAT 5601 - Nonparametric Methods (3.0 cr)
STAT 5701 - Statistical Computing (3.0 cr)
STAT 5931 - Topics in Statistics (3.0 cr)
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 8056 - Statistical Learning and Data Mining (3.0 cr)
STAT 8101 - Theory of Statistics 1 (3.0 cr)
STAT 8102 - Theory of Statistics 2 (3.0 cr)
STAT 8111 - Mathematical Statistics I (3.0 cr)
STAT 8112 - Mathematical Statistics II (3.0 cr)
STAT 8201 {Inactive} (3.0 cr)
STAT 8311 - Linear Models (3.0 cr)
STAT 8312 - Linear and Nonlinear Regression (3.0 cr)
STAT 8313 {Inactive} (3.0 cr)
STAT 8321 - Regression Graphics (3.0 cr)
STAT 8401 - Topics in Multivariate Methods (3.0 cr)
STAT 8411 - Multivariate Analysis (3.0 cr)
STAT 8421 - Theory of Categorical Data Analysis (3.0 cr)
STAT 8501 - Introduction to Stochastic Processes with Applications (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)
Program Sub-plans
Students are required to complete one of the following sub-plans.
Students may not complete the program with more than one sub-plan.
Masters
Doctoral
  
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· College of Liberal Arts

View future requirement(s):
· Fall 2022

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STAT 4051 - Statistical Machine Learning I
Credits: 4.0 [max 4.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall & Spring
This is the first semester of the Applied Statistics sequence for majors seeking a BA or BS in statistics. The course introduces a wide variety of applied statistical methods, methodology for identifying types of problems and selecting appropriate methods for data analysis, to correctly interpret results, and to provide hands-on experience with real-life data analysis. The course covers basic concepts of single factor analysis of variance (ANOVA) with fixed and random effects, factorial designs, analysis of covariance (ANCOVA), repeated measures analysis with mixed effect models, principal component analysis (PCA) and multidimensional scaling, robust estimation and regression methods, and rank tests. Numerous datasets will be analyzed and interpreted, using the open-source statistical software R and Rstudio. prerequisites: (STAT 3701 or STAT 3301) and (STAT 4101 or STAT 5101 or MATH 5651)
STAT 4052 - Statistical Machine Learning II
Credits: 4.0 [max 4.0]
Grading Basis: A-F only
Typically offered: Every Fall & Spring
This is the second semester of the core Applied Statistics sequence for majors seeking a BA or BS in statistics. Both Stat 4051 and Stat 4052 are required in the major. The course introduces a wide variety of applied statistical methods, methodology for identifying types of problems and selecting appropriate methods for data analysis, to correctly interpret results, and to provide hands-on experience with real-life data analysis. The course covers basic concepts of classification, both classical methods of linear classification rules as well as modern computer-intensive methods of classification trees, and the estimation of classification errors by splitting data into training and validation data sets; non-linear parametric regression; nonparametric regression including kernel estimates; categorical data analysis; logistic and Poisson regression; and adjustments for missing data. Numerous datasets will be analyzed and interpreted, using the open-source statistical software R and Rstudio. prerequisites: STAT 4051 and (STAT 4102 or STAT 5102)
STAT 4101 - Theory of Statistics I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Random variables/distributions. Generating functions. Standard distribution families. Data summaries. Sampling distributions. Likelihood/sufficiency. prereq: Math 1272 or Math 1372 or Math 1572H
STAT 4102 - Theory of Statistics II
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Estimation. Significance tests. Distribution free methods. Power. Application to regression and to analysis of variance/count data. prereq: STAT 4101
STAT 5021 - Statistical Analysis
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Intensive introduction to statistical methods for graduate students needing statistics as a research technique. prereq: college algebra or instr consent; credit will not be granted if credit has been received for STAT 3011
STAT 5101 - Theory of Statistics I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Logical development of probability, basic issues in statistics. Probability spaces. Random variables, their distributions and expected values. Law of large numbers, central limit theorem, generating functions, multivariate normal distribution. prereq: (MATH 2263 or MATH 2374 or MATH 2573H), (MATH 2142 or CSCI 2033 or MATH 2373 or MATH 2243)
STAT 5102 - Theory of Statistics II
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Sampling, sufficiency, estimation, test of hypotheses, size/power. Categorical data. Contingency tables. Linear models. Decision theory. prereq: [5101 or Math 5651 or instr consent]
STAT 5201 - Sampling Methodology in Finite Populations
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Simple random, systematic, stratified, unequal probability sampling. Ratio, model based estimation. Single stage, multistage, adaptive cluster sampling. Spatial sampling. prereq: 3022 or 3032 or 3301 or 4102 or 5021 or 5102 or instr consent
STAT 5302 - Applied Regression Analysis
Credits: 4.0 [max 4.0]
Typically offered: Every Fall, Spring & Summer
Simple, multiple, and polynomial regression. Estimation, testing, prediction. Use of graphics in regression. Stepwise and other numerical methods. Weighted least squares, nonlinear models, response surfaces. Experimental research/applications. prereq: 3032 or 3022 or 4102 or 5021 or 5102 or instr consent Please note this course generally does not count in the Statistical Practice BA or Statistical Science BS degrees. Please consult with a department advisor with questions.
STAT 5303 - Designing Experiments
Credits: 4.0 [max 4.0]
Typically offered: Every Fall, Spring & Summer
Analysis of variance. Multiple comparisons. Variance-stabilizing transformations. Contrasts. Construction/analysis of complete/incomplete block designs. Fractional factorial designs. Confounding split plots. Response surface design. prereq: 3022 or 3032 or 3301 or 4102 or 5021 or 5102 or instr consent
STAT 5401 - Applied Multivariate Methods
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall
Bivariate and multivariate distributions. Multivariate normal distributions. Analysis of multivariate linear models. Repeated measures, growth curve, and profile analysis. Canonical correlation analysis. Principal components and factor analysis. Discrimination, classification, and clustering. pre-req: STAT 3032 or 3301 or 3022 or 4102 or 5021 or 5102 or instr consent Although not a formal prerequisite of this course, students are encouraged to have familiarity with linear algebra prior to enrolling. Please consult with a department advisor with questions.
STAT 5421 - Analysis of Categorical Data
Credits: 3.0 [max 3.0]
Typically offered: Every Fall & Spring
Varieties of categorical data, cross-classifications, contingency tables. Tests for independence. Combining 2x2 tables. Multidimensional tables/loglinear models. Maximum-likelihood estimation. Tests for goodness of fit. Logistic regression. Generalized linear/multinomial-response models. prereq: STAT 3022 or 3032 or 3301 or 5302 or 4051 or 8051 or 5102 or 4102
STAT 5511 - Time Series Analysis
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Characteristics of time series. Stationarity. Second-order descriptions, time-domain representation, ARIMA/GARCH models. Frequency domain representation. Univariate/multivariate time series analysis. Periodograms, non parametric spectral estimation. State-space models. prereq: STAT 4102 or STAT 5102
STAT 5601 - Nonparametric Methods
Credits: 3.0 [max 3.0]
Typically offered: Every Fall & Spring
Order statistics. Classical rank-based procedures (e.g., Wilcoxon, Kruskal-Wallis). Goodness of fit. Topics may include smoothing, bootstrap, and generalized linear models. prereq: Stat classes 3032 or 3022 or 4102 or 5021 or 5102 or instr consent
STAT 5701 - Statistical Computing
Credits: 3.0 [max 3.0]
Prerequisites: (Stat 5102 or Stat 8102) and (Stat 5302 or STAT 8051) or consent
Grading Basis: A-F or Aud
Typically offered: Every Fall
Statistical programming, function writing, graphics using high-level statistical computing languages. Data management, parallel computing, version control, simulation studies, power calculations. Using optimization to fit statistical models. Monte Carlo methods, reproducible research. prereq: (Stat 5102 or Stat 8102) and (Stat 5302 or STAT 8051) or consent
STAT 5931 - Topics in Statistics
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall
Topics vary according to student needs and available staff.
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 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 8101 - Theory of Statistics 1
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Review of linear algebra. Introduction to probability theory. Random variables, their transformations/expectations. Standard distributions, including multivariate Normal distribution. Probability inequalities. Convergence concepts, including laws of large numbers, Central Limit Theorem. delta method. Sampling distributions. prereq: Statistics grad major or instr consent
STAT 8102 - Theory of Statistics 2
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Statistical inference. Sufficiency. Likelihood-based methods. Point estimation. Confidence intervals. Neyman Pearson hypothesis testing theory. Introduction to theory of linear models. prereq: 8101, Statistics graduate major 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 8312 - Linear and Nonlinear Regression
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall
Nonlinear regression: asymptotic theory, Bates-Watts curvatures, super leverage, parameter plots, projected residuals, transform-both-sides methodology, Wald versus likelihood inference. Topics in linear and generalized linear models as they relate to nonlinearity issues, including diagnostics, semi-parametric models, and model assessment. prereq: 8311
STAT 8321 - Regression Graphics
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall
Foundations: dimension-reduction subspaces, Li-Duan Lemma, structural dimension. Inferring about central dimension-reduction subspaces by using 3D plots, graphical regression, inverse regression graphics, net-effect plots, principal Hessian directions, sliced inverse regression and predictor transformations. Graphics for model assessment. prereq: 8311
STAT 8401 - Topics in Multivariate Methods
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Bivariate and multivariate distributions. Multivariate normal distributions. Hotellings's T-squared, MANOVA, MANCOVA, and regression with multivariate dependent variable. Repeated measures, growth curve, and profile analysis. Canonical correlation analysis. Principle components and factor analysis. Discrimination, classification, clustering. prereq: 8311
STAT 8411 - Multivariate Analysis
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall & Spring
Multivariate normal distribution. Inference on the mean, covariance, and correlation and regression coefficients; related sampling distributions such as Hotelling's T-squared and Wishart distributions. Multivariate analysis of variance. Principal components and canonical correlation. Discriminant analysis. prereq: 8152
STAT 8421 - Theory of Categorical Data Analysis
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall
Categorical data, multidimensional cross-classified arrays, mixed categorical and continuous data. Loglinear, logit, and multinomial response models. Ordinal responses. Current research topics. prereq: 8062 or instr consent
STAT 8501 - Introduction to Stochastic Processes with Applications
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall
Markov chains in discrete and continuous time, renewal processes, Poisson process, Brownian motion, and other stochastic models encountered in applications. prereq: 5101 or 8101
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.