Projects
We welcome researchers from all areas to propose projects of many kinds, including computer science projects, dataset-building efforts, automatic theorem proving tools, and research on human-AI collaboration. This is a space to experiment with what research, education, and related enterprises may look like in the future.
At the moment, many listed projects focus on sub-areas of statistics and help evolve the library. These projects connect concrete formalization work with the broader Statlib roadmap.
1. Semiparametric Efficiency Theory
Description.
This project formalizes foundational results in semiparametric efficiency theory, especially the asymptotic theory underlying efficient estimation in statistical models.
Milestones.
- Contiguity
- Local asymptotic normality, or LAN
- Hájek-Le Cam Local Asymptotic Minimax Theorem
- Convolution theorem
- Argmax Theorem
Maintainer.
Rajarshi Mukherjee; Aaron Lin
2. Graphical models
The project will formalize important results in graphical models.
Milestones achieved
None.
Current projects
- Trek rule and Wright's path analysis.
- Invariant connections under marginalization.
Potential future projects
Graphs
- d/m-separation and the augmentation criterion.
- commutativity of intervention and marginalization for SWIGs.
Linear SEMs
- m-separation implies conditional independence in cyclic Gaussian linear SEMs (Spirtes, Koster).
- trek-separation criterion for linear SEMs (Sullivant, Talaska, Draisma).
Statistical models
- Undirected graphs: Hammersley-Clifford theorem.
- Relations between different models in subclasses of ADMGs.
- Markov equivalence class for DAGs.
Maintainer
Qingyuan Zhao
Roadmap. 1.12 Causal Identification Theories (To be updated.)
3. Decision Theory and Statistical Experiments
Description.
This project studies the formalization of statistical experiments, their comparisons, and convergence, along with other decision-theoretic foundations such as the minimax theorem and complete class theorem.
Milestones.
- Convergence of Statistical Experiments
- Sufficiency, Completion, and Ancillarity of Sigma Fields
- Minimax theorem
- Complete Class Theorem
Maintainer.
Zixiao Wang
Roadmap. 1.1 Fundamentals of Decision Theory; 1.2 Comparison of Experiments
4. Empirical Process Foundations
Description.
This project develops the foundations of empirical process theory needed for asymptotic statistics.
Milestones.
- Maximal inequalities
- Glivenko-Cantelli lemma
- Donsker's theorem
Maintainer.
Debarghya Mukherjee
Roadmap. 1.13 Core Probabilistic Toolbox
Propose a Project
If you would like to propose a new project, please contact Rajarshi Mukherjee at ram521@mail.harvard.edu.