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    <h1>Projects</h1>
    <p class="intro">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.</p>
    <p class="intro">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 <a href="roadmap.html">roadmap</a>.</p>
    <section id="semiparametric-efficiency-theory" class="project">
    <h2>1. Semiparametric Efficiency Theory</h2>
    <p class="section-label">Description.</p>
    <p>This project formalizes foundational results in semiparametric efficiency theory, especially the asymptotic theory underlying efficient estimation in statistical models.</p>
    <p class="section-label">Milestones.</p>
    <ul>
    <li>Contiguity</li>
    <li>Local asymptotic normality, or LAN</li>
    <li>Hájek-Le Cam Local Asymptotic Minimax Theorem</li>
    <li>Convolution theorem</li>
    <li>Argmax Theorem</li>
    </ul>
    <p class="section-label">Maintainer.</p>
    <p>Rajarshi Mukherjee; Aaron Lin</p>
    <p><strong>Roadmap.</strong> <a href="roadmap.html#sec-1-4">1.4 Semiparametric Efficiency Theories</a></p>
    </section>
    <section id="graphical-models" class="project">
    <h2>2. Graphical models</h2>
    <p>The project will formalize important results in graphical models.</p>
    <h3>Milestones achieved</h3>
    <p>None.</p>
    <h3>Current projects</h3>
    <ul>
    <li>Trek rule and Wright&#x27;s path analysis.</li>
    <li>Invariant connections under marginalization.</li>
    </ul>
    <h3>Potential future projects</h3>
    <p class="section-label">Graphs</p>
    <ul>
    <li>d/m-separation and the augmentation criterion.</li>
    <li>commutativity of intervention and marginalization for SWIGs.</li>
    </ul>
    <p class="section-label">Linear SEMs</p>
    <ul>
    <li>m-separation implies conditional independence in cyclic Gaussian linear SEMs (Spirtes, Koster).</li>
    <li>trek-separation criterion for linear SEMs (Sullivant, Talaska, Draisma).</li>
    </ul>
    <p class="section-label">Statistical models</p>
    <ul>
    <li>Undirected graphs: Hammersley-Clifford theorem.</li>
    <li>Relations between different models in subclasses of ADMGs.</li>
    <li>Markov equivalence class for DAGs.</li>
    </ul>
    <h3>Maintainer</h3>
    <p>Qingyuan Zhao</p>
    <p><strong>Roadmap.</strong> <a href="roadmap.html#sec-1-12">1.12 Causal Identification Theories</a> (To be updated.)</p>
    </section>
    <section id="decision-theory-and-statistical-experiments" class="project">
    <h2>3. Decision Theory and Statistical Experiments</h2>
    <p class="section-label">Description.</p>
    <p>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.</p>
    <p class="section-label">Milestones.</p>
    <ul>
    <li>Convergence of Statistical Experiments</li>
    <li>Sufficiency, Completion, and Ancillarity of Sigma Fields</li>
    <li>Minimax theorem</li>
    <li>Complete Class Theorem</li>
    </ul>
    <p class="section-label">Maintainer.</p>
    <p>Zixiao Wang</p>
    <p><strong>Roadmap.</strong> <a href="roadmap.html#sec-1-1">1.1 Fundamentals of Decision Theory</a>; <a href="roadmap.html#sec-1-2">1.2 Comparison of Experiments</a></p>
    </section>
    <section id="empirical-process-foundations" class="project">
    <h2>4. Empirical Process Foundations</h2>
    <p class="section-label">Description.</p>
    <p>This project develops the foundations of empirical process theory needed for asymptotic statistics.</p>
    <p class="section-label">Milestones.</p>
    <ul>
    <li>Maximal inequalities</li>
    <li>Glivenko-Cantelli lemma</li>
    <li>Donsker&#x27;s theorem</li>
    </ul>
    <p class="section-label">Maintainer.</p>
    <p>Debarghya Mukherjee</p>
    <p><strong>Roadmap.</strong> <a href="roadmap.html#sec-1-13">1.13 Core Probabilistic Toolbox</a></p>
    </section>
    <section id="propose-a-project" class="project">
    <h2>Propose a Project</h2>
    <p>If you would like to propose a new project, please contact Rajarshi Mukherjee at <a href="mailto:ram521@mail.harvard.edu">ram521@mail.harvard.edu</a>.</p>
    </section>
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