Dr. Corcoran's research is focused on fast and accurate Markov chain Monte Carlo (MCMC) algorithms with applications to problems in high-dimensional Bayesian network inference, target tracking, statistical mechanics, high-energy physics, and rarefied gas dynamics. Most recently, she has been involved in target tracking via data fusion, perfect sampling for Bayesian principal components analysis, the development of perfect simulation algorithms for chemical kinetic networks, and new statistical methods for edge detection in images.
keywords
Monte Carlo algorithms, multi-target tracking, Bayesian network recovery, edge detection in image processing, particle filtering , chemical reaction networks, data fusion
APPM 4560 - Markov Processes, Queues, and Monte Carlo Simulations
Primary Instructor
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Spring 2019 / Spring 2020 / Spring 2021 / Spring 2022 / Spring 2023
Brief review of conditional probability and expectation followed by a study of Markov chains, both discrete and continuous time, including Poisson point processes. Queuing theory, terminology and single queue systems are studied with some introduction to networks of queues. Uses Monte Carlo simulation of random variables throughout the semester to gain insight into the processes under study. Same as APPM 5560 and STAT 4100.
APPM 4720 - Open Topics in Applied Mathematics
Primary Instructor
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Spring 2018
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 5560 - Markov Processes, Queues, and Monte Carlo Simulations
Primary Instructor
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Spring 2019 / Spring 2020 / Spring 2021 / Spring 2022 / Spring 2023
Brief review of conditional probability and expectation followed by a study of Markov chains, both discrete and continuous time, including Poisson point processes. Queuing theory, terminology and single queue systems are studied with some introduction to networks of queues. Uses Monte Carlo simulation of random variables throughout the semester to gain insight into the processes under study. Same as APPM 4560, STAT 4100 and STAT 5100.
APPM 5720 - Open Topics in Applied Mathematics
Primary Instructor
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Spring 2018 / Fall 2018
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.
APPM 6560 - Measure-Theoretic Probability
Primary Instructor
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Fall 2020
Introduces a series of fundamental concepts and results in probability theory, using rigorous measure-theoretic language. Provides a solid foundation for further studies and research in probability, stochastic processes, statistics, and data science. Recommended prerequisites: Undergraduate analysis at the level of APPM 4440.
APPM 6950 - Master's Thesis
Primary Instructor
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Fall 2019 / Spring 2020 / Fall 2021 / Spring 2022
May be repeated up to 6 total credit hours.
APPM 7400 - Topics in Applied Mathematics
Primary Instructor
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Fall 2018
Provides a vehicle for the development and presentation of new topics with the potential of being incorporated into the core courses in applied mathematics. May be repeated up to 6 total credit hours.
DTSA 5002 - Statistical Inference for Estimation in Data Science
Primary Instructor
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Summer 2021 / Fall 2021 / Spring 2022 / Summer 2022 / Fall 2022 / Spring 2023 / Summer 2023 / Fall 2023 / Spring 2024 / Summer 2024 / Fall 2024
Introduction to statistical inference, sampling distributions, and confidence intervals. Learn how to define and construct good estimators, method of moments estimation, maximum likelihood estimation, and methods of constructing confidence intervals that will extend to more general settings.
DTSA 5003 - Hypothesis Testing for Data Science
Primary Instructor
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Fall 2021 / Spring 2022 / Summer 2022 / Fall 2022 / Spring 2023 / Summer 2023 / Fall 2023 / Spring 2024 / Summer 2024 / Fall 2024
This course will focus on theory and implementation of hypothesis testing, especially as it relates to applications in data science. Students will learn to use hypothesis tests to make informed decisions from data. Special attention will be given to the general logic of hypothesis testing, error and error rates, power, simulation, and the correct computation and interpretation of p-values. Attention will also be given to the misuse of testing concepts, especially p-values, and the ethical implications of such misuse.
MATH 4520 - Introduction to Mathematical Statistics
Primary Instructor
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Fall 2019 / Fall 2021
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.
MATH 5520 - Introduction to Mathematical Statistics
Primary Instructor
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Fall 2019 / Fall 2021
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 STAT 5520.
STAT 4100 - Markov Processes, Queues, and Monte Carlo Simulations
Primary Instructor
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Spring 2020 / Spring 2021 / Spring 2022 / Spring 2023
Brief review of conditional probability and expectation followed by a study of Markov chains, both discrete and continuous time, including Poisson point processes. Queuing theory, terminology and single queue systems are studied with some introduction to networks of queues. Uses Monte Carlo simulation of random variables throughout the semester to gain insight into the processes under study. Same as APPM 4560 and APPM 5560.
STAT 4520 - Introduction to Mathematical Statistics
Primary Instructor
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Fall 2019 / Fall 2021
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 5100 - Markov Processes, Queues, and Monte Carlo Simulations
Primary Instructor
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Spring 2020 / Spring 2021 / Spring 2022 / Spring 2023
Brief review of conditional probability and expectation followed by a study of Markov chains, both discrete and continuous time, including Poisson point processes. Queuing theory, terminology and single queue systems are studied with some introduction to networks of queues. Uses Monte Carlo simulation of random variables throughout the semester to gain insight into the processes under study. Recommended prerequisite: previous coursework equivalent to that of APPM 3570 or STAT 3100 or MATH 4510, with a minimum grade of C-. Same as APPM 4560, STAT 4100 and APPM 5560.
STAT 5520 - Introduction to Mathematical Statistics
Primary Instructor
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Fall 2019 / Fall 2021
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 5530 - Mathematical Statistics
Primary Instructor
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Fall 2019 / Fall 2020 / Fall 2021 / Fall 2022
Covers the theory of estimation, confidence intervals, hypothesis testing, and decision theory. In particular, it covers the material of APPM 5520 in greater depth, especially the topics of optimality and asymptotic approximation. Additional topics include M-estimation, minimax tests, the EM algorithm, and an introduction to Bayesian estimation and empirical likelihood techniques. Recommended Prerequisite is a one-semester calculus-based probability course such as MATH 4510 or APPM 3570. Degree credit not granted for this course and STAT 5520 or MATH 5520 or STAT 4520 or MATH 4520.
