Dr. Dukic' research is focused on Bayesian statistical modeling and statistical computing, with applications to ecology, medicine, and business. Her research has resulted in novel methods for meta analysis, diagnostic testing accuracy assessment, survival modeling, biomarker modeling, risk and loss reserve modeling, and spread of epidemics (flu, smallpox, meningitis, and MRSA), and weather impact on infectious diseases and pests.
APPM 4570 - Statistical Methods
Primary Instructor
-
Fall 2018
Covers basic statistical concepts with accompanying introduction to the R programming language. Topics include discrete and continuous probability laws, random variables, expectation and variance, central limit theorem, testing hypothesis and confidence intervals, linear regression analysis, simulations for validation of statistical methods and applications of methods in R. Same as APPM 5570.
APPM 4590 - Statistical Modeling
Primary Instructor
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Spring 2018 / Spring 2019
Introduces methods, theory and applications of statistical models, from linear models (simple and multiple linear regression), to hierarchical linear models. Topics such as estimation, residual diagnostics, goodness of fit, transformations, and various strategies for variable selection and model comparison will be discussed in depth. Examples and exercises will be demonstrated using statistical software. Same as APPM 5590.
APPM 4720 - Open Topics in Applied Mathematics
Primary Instructor
-
Spring 2019
Provides a vehicle for the development and presentation of new topics that may be incorporated into the core courses in applied mathematics. Department enforced prerequisite: variable, depending on the topic, see instructor. May be repeated up to 15 total credit hours. Same as APPM 5720.
APPM 5570 - Statistical Methods
Primary Instructor
-
Fall 2018
Covers basic statistical concepts with accompanying introduction to the R programming language. Topics include discrete and continuous probability laws, random variables, expectation and variance, central limit theorem, testing hypothesis and confidence intervals, linear regression analysis, simulations for validation of statistical methods and applications of methods in R. Same as APPM 4570.
APPM 5590 - Statistical Modeling
Primary Instructor
-
Spring 2018 / Spring 2019
Introduces methods, theory and applications of statistical models, from linear models (simple and multiple linear regression), to hierarchical linear models. Topics such as estimation, residual diagnostics, goodness of fit, transformations, and various strategies for variable selection and model comparison will be discussed in depth. Examples and exercises will be demonstrated using statistical software. Department enforced prerequisite: APPM 4570 or APPM 4520 or MATH 4520 or instructor consent required. Same as APPM 4590.
APPM 5720 - Open Topics in Applied Mathematics
Primary Instructor
-
Spring 2019
Provides a vehicle for the development and presentation of new topics that may be incorporated into the core courses in applied mathematics. Department enforced prerequisite: variable, depending on the topic, see instructor. May be repeated up to 6 total credit hours. Same as APPM 4720.
STAT 4000 - Statistical Methods and Application I
Primary Instructor
-
Fall 2018 / Fall 2019 / Fall 2020 / Fall 2021 / Spring 2023
Introduces exploratory data analysis, probability theory, statistical inference, and data modeling. Topics include discrete and continuous probability distributions, expectation, laws of large numbers, central limit theorem, statistical parameter estimation, hypothesis testing, and regression analysis. Considerable emphasis on applications in the R programming language. Same as STAT 5000.
STAT 4400 - Advanced Statistical Modeling
Primary Instructor
-
Spring 2020
Introduces methods, theory and applications of modern statistical models, from linear to hierarchical linear models, to generalized hierarchical linear models, including hierarchical logistic and hierarchical count regression models. Topics such as estimation, residual diagnostics, goodness of fit, transformations, and various strategies for variable selection and model comparison will be discussed in depth. Examples will be demonstrated using statistical programming language R. Same as STAT 5400.
STAT 4610 - Statistical Learning
Primary Instructor
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Fall 2022 / Spring 2023
Consists of applications and methods of statistical learning. Reviews multiple linear regression and then covers classification, regularization, splines, tree-based methods, support vector machines, unsupervised learning and Gaussian process regression. Same as STAT 5610.
STAT 4630 - Computational Bayesian Statistics
Primary Instructor
-
Spring 2020
Introduces Bayesian statistics, normal and non-normal approximation to likelihood and posteriors, the EM algorithm, data augmentation, and Markov Chain Monte Carlo (MCMC) methods. Additionally, introduces more advanced MCMC algorithms and requires significant statistical computing. Examples from a variety of areas, including biostatistics, environmental sciences, and engineering, will be given throughout the course. Recommended prerequisite: prior programming experience. Same as STAT 5630.
STAT 5000 - Statistical Methods and Application I
Primary Instructor
-
Fall 2018 / Fall 2019 / Fall 2020 / Spring 2023
Introduces exploratory data analysis, probability theory, statistical inference, and data modeling. Topics include discrete and continuous probability distributions, expectation, laws of large numbers, central limit theorem, statistical parameter estimation, hypothesis testing, and regression analysis. Considerable emphasis on applications in the R programming language. Recommended prerequisites of APPM 1360 or MATH 2300 or equivalent. Same as STAT 4000.
STAT 5400 - Advanced Statistical Modeling
Primary Instructor
-
Spring 2020
Introduces methods, theory and applications of modern statistical models, from linear to hierarchical linear models, to generalized hierarchical linear models, including hierarchical logistic and hierarchical count regression models. Topics such as estimation, residual diagnostics, goodness of fit, transformations, and various strategies for variable selection and model comparison will be discussed in depth. Examples will be demonstrated using statistical programming language R. Recommended prerequisite: previous coursework equivalent to one of STAT 3400 or STAT 4010 or STAT 5010 and one of STAT 4520 or STAT 5520 or STAT 5530; all with a minimum grade of C-. Same as STAT 4400.
STAT 5610 - Statistical Learning
Primary Instructor
-
Fall 2022 / Spring 2023
Consists of applications and methods of statistical learning. Reviews multiple linear regression and then covers classification, regularization, splines, tree-based methods, support vector machines, unsupervised learning and Gaussian process regression. Recommended prerequisite: previous coursework equivalent to that of STAT 3400 or STAT 4010 or STAT 5010; minimum C- grade for all. Same as STAT 4610.
STAT 5630 - Computational Bayesian Statistics
Primary Instructor
-
Spring 2020
Introduces Bayesian statistics, normal and non-normal approximation to likelihood and posteriors, the EM algorithm, data augmentation, and Markov Chain Monte Carlo (MCMC) methods. Additionally, introduces more advanced MCMC algorithms and requires significant statistical computing. Examples from a variety of areas, including biostatistics, environmental sciences, and engineering, will be given throughout the course. Recommended prerequisite: prior programming and basic statistical modeling experience is required. Same as STAT 4630.
