I modeled a multi-level distribution of three dimensional arrays using a Bayesian approach assuming a separable covariance structure that is the sum of a set of Kronecker products. The goal was to find patterns in the covariance of the survey participants’ responses across quality measures and years to enhance public reporting and quality monitoring.
keywords
hierarchical modeling, multivariate covariance estimation, vector autoregressive processes, small-area estimation, and Monte Carlo expectation maximization, quality measurement, financial econometrics, risk management, and high-dimensional statistical learning
Teaching
courses taught
APPM 1350 - Calculus 1 for Engineers
Primary Instructor
-
Fall 2020 / Spring 2022
Topics in analytical geometry and calculus including limits, rates of change of functions, derivatives and integrals of algebraic and transcendental functions, applications of differentiations and integration. Students who have already earned college credit for calculus 1 are eligible to enroll in this course if they want to solidify their knowledge base in calculus 1. For more information about the math placement referred to in the "Enrollment Requirements", contact your academic advisor. Degree credit not granted for this course and APPM 1345 or ECON 1088 or MATH 1081 or MATH 1300 or MATH 1310 or MATH 1330.
APPM 2360 - Introduction to Differential Equations with Linear Algebra
Primary Instructor
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Fall 2023 / Spring 2024
Introduces ordinary differential equations, systems of linear equations, matrices, determinants, vector spaces, linear transformations, and systems of linear differential equations. Credit not granted for this course and both MATH 2130 and MATH 3430.
APPM 3570 - Applied Probability
Primary Instructor
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Spring 2021 / Fall 2021 / Fall 2022 / Spring 2023
Studies axioms, counting formulas, conditional probability, independence, random variables, continuous and discrete distribution, expectation, joint distributions, moment generating functions, law of large numbers and the central limit theorem. Degree credit not granted for this course and ECEN 3810 or MATH 4510. Same as STAT 3100.
MATH 4520 - Introduction to Mathematical Statistics
Primary Instructor
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Fall 2021 / Fall 2022 / Fall 2023 / Fall 2024
Examines point and confidence interval estimation. Principles of maximum likelihood, sufficiency, and completeness: tests of simple and composite hypotheses, linear models, and multiple regression analysis if time permits. Analyzes various distribution-free methods. Same as MATH 5520 and STAT 4520 and STAT 5520.
STAT 3100 - Applied Probability
Primary Instructor
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Spring 2021 / Fall 2021 / Fall 2022 / Spring 2023
Studies axioms, counting formulas, conditional probability, independence, random variables, continuous and discrete distribution, expectation, joint distributions, moment generating functions, law of large numbers and the central limit theorem. Degree credit not granted for this course and ECEN 3810 or MATH 4510. Same as APPM 3570.
STAT 4400 - Advanced Statistical Modeling
Primary Instructor
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Spring 2022 / Spring 2023 / Spring 2024
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 4520 - Introduction to Mathematical Statistics
Primary Instructor
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Fall 2021 / Fall 2022 / Fall 2023 / Fall 2024
Examines point and confidence interval estimation. Principles of maximum likelihood, sufficiency, and completeness: tests of simple and composite hypotheses, linear models, and multiple regression analysis if time permits. Analyzes various distribution-free methods. Same as STAT 5520 and MATH 4520 and MATH 5520.
STAT 4610 - Statistical Learning
Primary Instructor
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Fall 2024
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 4680 - Statistics and Data Science Collaboration
Primary Instructor
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Fall 2020 / Spring 2021
Educates and trains students to become effective interdisciplinary collaborators by developing the communication and collaboration skills necessary to apply technical statistics and data science skills to help domain experts answer research or policy questions. Topics include structuring effective meetings and projects; communicating statistics to non-statisticians; using peer feedback, self-reflection and video analysis to improve collaboration skills; creating reproducible statistical workflows; working ethically. Same as STAT 5680.
STAT 5400 - Advanced Statistical Modeling
Primary Instructor
-
Spring 2022 / Spring 2023 / Spring 2024
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 5520 - Introduction to Mathematical Statistics
Primary Instructor
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Fall 2021 / Fall 2022 / Fall 2023 / Fall 2024
Examines point and confidence interval estimation. Principles of maximum likelihood, sufficiency, and completeness: tests of simple and composite hypotheses, linear models, and multiple regression analysis if time permits. Analyzes various distribution-free methods. Department enforced prerequisite: one semester calculus-based probability course, such as MATH 4510 or APPM 3570. Recommended prerequisite: previous coursework equivalent to APPM 3570 or STAT 3100 or MATH 4510; minimum grade of C- for all. Same as STAT 4520 and MATH 4520 and MATH 5520.
STAT 5610 - Statistical Learning
Primary Instructor
-
Fall 2024
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 5680 - Statistical Collaboration
Primary Instructor
-
Fall 2020 / Spring 2021
Educates and trains students to become effective interdisciplinary collaborators by developing the communication and collaboration skills necessary to apply technical statistics and data science skills to help domain experts answer research questions. Topics include structuring effective meetings and projects; communicating statistics to non-statisticians; using peer feedback, self-reflection and video analysis to improve collaboration skills; creating reproducible statistical workflows; working ethically. Recommended prerequisite: undergraduate statistics courses equivalent to STAT 4400 (minimum grade C-) or STAT 4010 (minimum grade C-) or Instructor's approval. Same as STAT 4680.
