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  <title>Statistical Inference Theory | Casella-Berger | UMich STATS 511 | MIT 18.650</title>
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    <h1>Statistical Inference Theory — Casella-Berger | UMich STATS 511 | MIT 18.650</h1>
    <p>This repository contains my <strong>lecture notes</strong> and <strong>solved exercises</strong> from <em>Casella & Berger: Statistical Inference (Chapters 6–9)</em>, along with supporting materials from <strong>MIT 18.650</strong> and <strong>UMich STATS 511</strong>. The focus is on <strong>point estimation, hypothesis testing, and interval estimation</strong> — the core pillars of modern <strong>Machine Learning, AI, and Robotics</strong>.</p>

    <h2>Key Topics Covered</h2>
    <ol>
      <li><strong>Principles of Data Reduction</strong>: Sufficiency, Minimal Sufficiency, Ancillary Statistics, Complete Statistics, and the Likelihood Principle.</li>
      <li><strong>Point Estimation</strong>: Methods of Moments, Maximum Likelihood, Bayes Estimators, EM Algorithm, Evaluating Estimators, and Fisher Information.</li>
      <li><strong>Hypothesis Testing</strong>: Neyman-Pearson Lemma, Likelihood Ratio Tests, and Decision Theory.</li>
      <li><strong>Interval Estimation</strong>: Confidence Intervals, Bayesian Credible Intervals, and Large Sample Approximations.</li>
    </ol>

    <h2>Repository Structure</h2>
    <ul>
      <li><strong>Lecture Notes</strong>: Summaries of theoretical concepts with detailed derivations.</li>
      <li><strong>Problem Sets</strong>: Solved exercises from <em>Casella-Berger</em> to reinforce concepts.</li>
      <li><strong>Supplementary Resources</strong>: Insights from <strong>UMich STATS 511</strong> and <strong>MIT 18.650</strong>.</li>
    </ul>

    <h2>Purpose</h2>
    <p>This work builds a <strong>rigorous foundation in Statistical Inference</strong> essential for <strong>Statistical Machine Learning, Computational Statistics, and Probabilistic Robotics</strong>. These concepts form the backbone of <strong>Monte Carlo Methods, Bayesian Filtering, and State Estimation</strong> — critical for modern control systems and AI-driven robots.</p>

    <p>By mastering these principles, I aim to unify <strong>theory and implementation</strong> in <strong>robotics and autonomous systems</strong>, developing probabilistic models and decision algorithms grounded in mathematical clarity.</p>

    <h2>About Me</h2>
    <p>I’m focused on building deep <strong>mathematical and statistical foundations</strong> for <strong>Robotics, AI, and State Estimation</strong>.</p>

    <p><strong>Contact:</strong><br>
      📧 <a href="mailto:sampath@umich.edu">sampath@umich.edu</a><br>
      🔗 <a href="https://www.linkedin.com/in/sai-sampath-kedari" target="_blank">LinkedIn Profile</a><br>
      🧠 <a href="https://github.com/SaiSampathKedari/Statistical-Inference-Theory" target="_blank">View GitHub Repository</a>
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      <p>© <span id="year"></span> Sai Sampath Kedari — Casella-Berger, MIT 18.650, UMich STATS 511 | Built for visibility, clarity, and rigorous math.</p>
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