Before registering, the student must submit an outline of the proposed work for approval by the supervisor and the chair of the Department. Advanced study in a specialized field under the supervision of a member of the department staff. May be repeated for credit.
Prerequisites: the instructors permission. Individual research and tutorial in archaeology for advanced graduate students.
Guided reading and research on a topic or in a field chosen by the student in consultation with a member of the faculty.
The biostatistical field is changing with new directions emerging constantly. Doing research in these new directions, which often involve large data and complex designs, requires advanced probability and statistics tools. The purpose of this new course is to collect these important probability methods and present them in a way that is friendly to a biostatistics audience. This course is designed for PhD students in Biostatistics. Its primary objective is to help the students achieve a solid understanding of these probability methods and develop strong analytical skills that are necessary for conducting methodological research in modern biostatistics. At the completion of this course, the students will a) have a working knowledge in Law of Large Numbers, Central Limit Theorems, martingale theory, Brownian motions, weak convergence, empirical process, and Markov chain theory; b) be able to understand the biostatistical literature that involves such methods; c) be able to do proofs that call for such knowledge.
Prerequisites: the instructors permission. Individual research in all divisions of anthropology and in allied fields for advanced graduate students
Prerequisites: the instructors permission. Individual research in all divisions of anthropology and in allied fields for advanced graduate students
This course offers a general introduction to essential materials in advanced statistical theory for doctoral students in biostatistics. The course is designed to prepare doctoral students in biostatistics for their written theory qualifying exam. Students in this course will learn theory of estimation, confidence sets and hypothesis testing. Specific topics include a quick review of measure-theoretic probability theory, concepts of sufficiency and completeness, unbiased estimation (UMVUE), least squares principle, likelihood estimation, a variety of estimators and their asymptotic properties, confidence sets, the Neyman-Pearson lemma and uniformly most powerful tests. If time permits, the likelihood ratio test, score test and Wald test, and sequential analysis will be covered.
The course is designed for entering doctoral students and provides a rigorous introduction to the fundamental theory of optimization. It examines optimization theory in continuous, deterministic settings, including optimization in Euclidean as well as in more general, infinite-dimensional vector spaces. The course emphasizes unifying themes (such as optimality conditions, Lagrange multipliers, convexity, duality) that are common to all of these areas of mathematical optimization. Applications across a range of problem areas serve to illustrate and motivate the theory that is developed. Additionally, review sessions explaining how to solve complex optimization problems using CVX and Python are offered.
The aim of this course is to provide students a systematic training in key topics in modern supervised statistical learning and data mining. For the most part, the focus will remain on a theoretically sound understanding of the methods (learning algorithms) and their applications in complex data analysis, rather than proving technical theorems. Applications of the statistical learning and data mining tools in biomedical and health sciences will be highlighted.
This is an advanced course for first-year Ph.D. students in Biostatistics. The aim is to provide a solid foundation of the theory behind linear models and generalized linear models. More emphasis will be placed on concepts and theory with mathematical rigor. Topics covered including linear regression models, logistic regression models, generalized linear regression models and methods for the analysis contingency tables.
Students get together to discuss the paper which will be presented at the IEOR-DRO seminar. One group of students (~2 students) presents. A faculty member is present to guide and facilitate the discussion. Students are evaluated on their effort in leading one of the discussions and participating in the other discussions
Formerly known as FINCB9323.
This course serves as an introduction to econometrics and statistical inference at the graduate level. Topics will include asymptotic inference, linear regression, an introduction to causal inference, general model estimation techniques, and discrete choice models. The intent is to thoroughly understand basic econometric models and tools necessary for empirical research.
Formerly known as FINCB9324.
This course serves as an introduction to econometrics and statistical inference at the graduate level. Topics will include mathematical statistics, estimation methods for linear and non-linear models, statistical methods for making inferences, and an introduction to causal inference. The intent is to thoroughly understand basic econometric models and statistical tools necessary for empirical research.
This course is a medium-level introduction to Python and its applications in finance, especially "backtesting." If you need a complete introduction, please follow the online "CBS Python Level 1," a prerequisite to this course that I assume all of you have taken.
When a finance practitioner discovers a new investment strategy (or "alpha signal"), they backtest it: they look at historical data, buy and sell at the posted prices according to the strategy, and then compute the portfolio's return. Back-testing is an essential procedure for both industry (traders back-test a strategy before deployment) and academia (research papers in finance that propose a new profitability factor usually contain a back-test and a measure of profitability).
Then introduce doc tests, unit tests, and object-oriented programming. Along the way, students will also develop a solid mastery of Python, which may be useful for interviewing for summer internships.
In the second half, we will use this backtesting framework to measure the profitability of several strategies that use data science techniques, for example:
- Bollinger bands (using linear regression);
- valuation using multiples (using k-nearest neighbors);
- buy-hold-sell recommendations (using logistic regression and neural networks).
(If ethically allowed:) The instructor will apply each of these strategies in a live portfolio so we can see its performance in the real world week over week.
Algorithms and AI systems are increasingly deployed at scale in consequential social settings, e.g., online platforms, labor markets, healthcare systems, and educational institutions. The standard methods used to design and evaluate these algorithms were developed under assumptions of independent and identically distributed (i.i.d.) data, assumptions that are systematically violated when humans interact with each other and respond to the systems around them. Researchers working in these settings need to understand when these assumptions break down, what the resulting effects on system performance are, and how to design better systems.
This course examines the evaluation, deployment, and human response to algorithms in social systems where these i.i.d. assumptions fail. We study how interference between users, capacity constraints, and behavioral responses to algorithms undermine both classical machine learning methods and causal inference tools like A/B testing and RCTs — and for each failure mode, we examine recent methodological advances designed for these settings. Topics include experiment design under interference, recommendation systems and their downstream effects, human compliance and discretion in algorithmic decision-making, and the operational realities of deploying algorithms at scale. The course closes by applying this analytical lens to large language models, examining whether the same failure modes arise, and whether the same advances apply, as AI interventions scale across social systems. The class will draw on recent theory and methodological work in causal inference, operations research, and human-algorithm interaction to prepare students for research at this frontier.
This course is targeted at mathematically mature PhD students in operations research, statistics, computer science, economics, business, or quantitative fields interested in the intersection of algorithms and human behavior.
This seminar-style course will lead students through the process of writing a Master's Essay in the form of an NIH-style grant application (required for the MS/POR degree track). The essay is undertaken during the fall semester of the second year of study. At the end of the fall term, each student submits a written research proposal following NIH guidelines for either an R01 or K (career development) award. The emphasis in this course is on the quality of the proposed research. The following February, students make an oral presentation to the POR Advisory Board, summarizing the research proposal. Final grades are awarded after the presentations in February.
In this course, students will apply the concepts and methods introduced in Statistical Practices and Research for Interdisciplinary Science (SPRIS) I to a real research setting. Each student will be paired with a Biostatistics faculty member. The student will participate in one of the mentor’s collaborative projects to learn how to be an effective member of an interdisciplinary team. The relationship will mimic that between a medical resident and an attending physician.
The SPRIS II experience will vary depending on the assigned faculty member, but all students will gain exposure to preparing collaborative grant applications, designing research studies, analyzing real data, interpreting and presenting results, and writing manuscripts. Mentors will help to develop the student’s data intuition skills, ability to ask good research questions, and leadership qualities. Where necessary, students may replicate projects already completed by the faculty mentor to gain experience.
You may be asked to serve as research subjects in studies under direction of the faculty while enrolled in this course. Participation in voluntary.
Departmental colloquium in statistics.
This course will serve to provide an opportunity for Students who are Directing Concentrates to develop their thesis projects within a structured environment. The course may be taught in every week or alternating week formats. Students will be encouraged to submit ideas, treatments, scripts, rough cuts and fine cuts of their thesis films. The class is collaborative and serves as a base from which Directors can try out concepts and ideas, and receive input from fellow students as well as their thesis advisor.
Clinical and laboratory projects or field investigation related to nutrition, particularly in the area of growth and development.
This course offers an advanced exploration of a theme, tradition, or figure in 19th-century philosophy. Depending on the semester, the course may be organized around one central figure/text, or around a theme or tradition (for example, post-Kantian German idealism, 19th-century social and political philosophy, 19th-century philosophy of religion.)
All graduate students are required to attend the departmental colloquium as long as they are in residence. Advanced doctoral students may be excused after three years of residence. No degree credit is granted.
Overview:
The class will meet once monthly and will focus on the following:
1) Students’ thesis work - class will analyze, advise, give notes on, support, and discuss each person’s work over the year during the development, prep, production, post-production, and marketing periods of work for each thesis project.
2) Exploration of skills necessary to transition to working in the film industry after graduation. Topics include resume workshops, web site creation, film festival strategy, financing strategies, rights clearance, and press kit creation.
3) CU alums and other guest speakers will discuss their transitions from film school to working in the film industry, and will discuss their areas of expertise: TV producing, feature film producing, development, representation, networks and studios, teaching as a career, etc.