Term Paper STAT 775,
Fall 2021

Summary

For the final project, you are to to write a term paper in mathematical typesetting software. You can use any software you prefer, but the report is required to be produced in a clean, easy-to-read document with the required document structure below. Figures should be captioned, with clear and easy-to-interpret labels and graphics. The final report must be uploaded in a PDF format to Webcampus. The report should be written in 12 point font, have 1.0 or 1.5 line-spacing and be approximately 5 - 10 pages long, not including references or the appendix of code in the page count.

You are expected to use resources from outside of this course to investigate a topic of your choice and to summarize this topic according to the assignment objectives and rubric. The goal of the assignment will be to read at least one paper of your choice in order to discuss the role of data assimilation in the application, or to discuss the novelty of a technique demonstrated in the work and how it provides novel tools for estimation problems. Suggested topics are:

• A paper related to your own research – if you are working on an application, you may discuss a paper in which data assimilation techniques have been used in your own research context and what advantages and disadvantages this approach may have.
• Data assimilation and machine learning – discuss how the Bayesian formalism for data assimilation extends to general machine learning models and hybrid models including both data assimilation and machine learning techniques.
• Adaptive inflation or localization techniques – discuss different techniques that can be utilized in order to “automatically tune” hyper-parameters in the estimation scheme, from the perspective of, e.g., Bayesian heirarchical models or moment matching techinques.
• Adaptive (quasi-)Newton algorithms – discuss how, e.g., linesearch techniques or the Levenberg-Marquardt algorithm / trust region approaches differ from the standard Netwon-based optimization.
• Expectation maximization – discuss how EM has been used to create, e.g., Gaussian mixture models estimating model and observation error statistics in the classical Kalman filter and / or in ensemble Kalman estimators.
• Multiple data assimilation – discuss the technique of multiple data assimilation and how this relates to tempering in statistical physics and / or a weak-constraint cost function.
• Reduced precision numerics – discuss the consequences of reducing the precision of numerics on the data assimilation and uncertainty quantification problem. What are the trade-offs and the rationale for reducing precision?
• Stochastic model reduction – discuss how stochastic reduction of multi-scale physics affects the data assimilation and uncertainty quantification problem.

Your report needs to identify an example where this technique is used in a research or replication paper. Examples from blogs are acceptable for works referenced and may help with discussing code implementations, but you will need to draw your particular example from a scholarly source.

Document structure

Category	Expected results	Total points
Section 1: Introduction	Introduce your topic, the motivation of the work, and discuss how this work fits in within our framework of analysis.	10 points
Section 2: Discuss the primary reference	Discuss where the example is drawn from and what the purpose was of this example, e.g., what questions were the authors trying to answer. Discuss what analysis was performed in this example in the source and why this technique was relevant.	10 points
Section 3: Discuss how the problem relates to your own research	Provide a proposal on how to utilize these techniques in a novel context. Discuss how other techniques have already been utilized in the field and discuss why the research proposal may provide some advantage over existing work.	10 points
Section 4: Conclusions and looking forward	Reflect on the course themes and how this scholarly work fits into the context of data assimilation and estimation theory. Discuss in what ways this investigation could be pursued further given more time.	10 points
Section 5: Works cited		Required
Section 6: Appendix of Python code as necessary		Required
Grand total	All of the above	40/40 points