This repository contains my lecture notes and solved exercises from Casella-Berger: Statistical Inference (Chapters 6-9), along with supporting materials from MIT 18.650: Statistics for Applications and UMich STATS 511: Statistical Inference. The focus is on point estimation, hypothesis testing, and interval estimation, which are fundamental to Machine Learning, AI, and Robotics.
- Principles of Data Reduction: Sufficiency, Minimal Sufficiency, Ancillary Statistics, Complete Statistics, and the Likelihood Principle.
- Point Estimation: Methods of Moments, Maximum Likelihood Estimators, Bayes Estimators, The EM Algorithm, Methods of Evaluating Estimators, and Fisher Information.
- Hypothesis Testing: Neyman-Pearson Lemma, Likelihood Ratio Tests, and Decision Theory.
- Interval Estimation: Confidence Intervals, Bayesian Credible Intervals, and Large Sample Approximations.
- Lecture Notes: Summaries of theoretical concepts with detailed explanations.
- Problem Sets: Solutions to exercises from Casella-Berger, reinforcing understanding through problem-solving.
- Supplementary Resources: Notes from UMich STATS 511 and MIT 18.650 for additional perspectives.
This repository is dedicated to building a strong foundation in Statistical Inference, which is essential for Statistical Machine Learning, Computational Statistics, and Probabilistic Robotics. The concepts covered here are fundamental for Monte Carlo Methods, Bayesian Filtering, and Smoothing, which are widely applied in State Estimation, Control Systems, and Robotics.
By mastering these principles, I aim to bridge the gap between theory and practical implementation in robotics and autonomous systems, ensuring a rigorous mathematical understanding for designing probabilistic models, filtering techniques, and decision-making algorithms.
Whenever possible, I aim to document my work in LaTeX for clarity and professional presentation.
I am focused on building strong mathematical and statistical foundations to support my work in Robotics, AI, and State Estimation.
Feel free to connect with me:
- Email: [email protected]
- LinkedIn: www.linkedin.com/in/sai-sampath-kedari