Introduction to Probability and Statistical Inference
This course provides a comprehensive introduction to the mathematical principles of probability and the theory and practice of statistical inference. The course develops a rigorous foundation for modeling uncertainty, analyzing random phenomena, and drawing reliable conclusions from data.
Beginning with the fundamentals of probability, students explore counting methods, conditional probability, Bayes' theorem, independence, random variables, and both discrete and continuous probability distributions. The course then introduces key concepts in mathematical statistics, including expectation, variance, covariance, the Law of Large Numbers, the Central Limit Theorem, and moment generating functions, providing the theoretical basis for modern statistical analysis.
Building on these foundations, the course covers the core methods of statistical inference, including parameter estimation, confidence intervals, hypothesis testing, maximum likelihood estimation, goodness-of-fit testing, and regression analysis. Students are also introduced to Bayesian inference, conjugate priors, maximum a posteriori estimation, and computational techniques such as Monte Carlo simulation and bootstrapping. Throughout the course, theoretical concepts are reinforced through practical examples and hands-on implementation using Python.
Upon successful completion of the course, students will be understand the mathematical foundations of probability, apply statistical methods to analyze real-world data, evaluate uncertainty and risk, and use both frequentist and Bayesian approaches to solve inference problems. The knowledge and skills developed in this course provide a strong foundation for advanced study in statistics, machine learning, data science, artificial intelligence, engineering, economics, and the natural sciences.
Beginning with the fundamentals of probability, students explore counting methods, conditional probability, Bayes' theorem, independence, random variables, and both discrete and continuous probability distributions. The course then introduces key concepts in mathematical statistics, including expectation, variance, covariance, the Law of Large Numbers, the Central Limit Theorem, and moment generating functions, providing the theoretical basis for modern statistical analysis.
Building on these foundations, the course covers the core methods of statistical inference, including parameter estimation, confidence intervals, hypothesis testing, maximum likelihood estimation, goodness-of-fit testing, and regression analysis. Students are also introduced to Bayesian inference, conjugate priors, maximum a posteriori estimation, and computational techniques such as Monte Carlo simulation and bootstrapping. Throughout the course, theoretical concepts are reinforced through practical examples and hands-on implementation using Python.
Upon successful completion of the course, students will be understand the mathematical foundations of probability, apply statistical methods to analyze real-world data, evaluate uncertainty and risk, and use both frequentist and Bayesian approaches to solve inference problems. The knowledge and skills developed in this course provide a strong foundation for advanced study in statistics, machine learning, data science, artificial intelligence, engineering, economics, and the natural sciences.
Lecturer
Date
21st September ~ 21st December, 2026
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Monday,Wednesday | 16:10 - 17:50 | A14-203 | Zoom 15 | 204 323 0165 | BIMSA |
Prerequisite
Differentiation and integration, Basic linear algebra, Elementary algebra and mathematical notation, Basic programming experience (preferably Python)
Audience
Undergraduate
, Advanced Undergraduate
Video Public
No
Notes Public
No
Language
English
Lecturer Intro
Jahed Abedi is a black hole physicist with a broad interest in gravitational physics, bridging both observational and theoretical domains. On the observational side, his work focuses on the search for gravitational wave (GW) echoes and Quasi-Normal Modes (QNMs) in LIGO/Virgo data, while his theoretical research delves into black hole perturbations, QNMs, and Quantum Field Theory (QFT) in curved space-time. Jahed was awarded the 2019 Buchalter Cosmology First Prize for one of his publications where he served as the lead author, reflecting the high impact of his research. He holds a Bachelor's degree in Electrical Engineering, as well as a Master's and PhD in Physics. His research seeks to answer several critical questions: How can a better pipeline be developed to test the Kerr nature of observed Binary Black Hole Mergers through black hole spectroscopy? With improved methods, can additional subdominant Quasi-Normal Modes (QNMs) be detected? Can these results validate previous searches or reveal deviations from General Relativity in GW data? What quantum effects might be expected from black holes, and if they exist, how significant are they? Can such effects be observed? Lastly, how can gravitational wave data confirm or rule out alternatives to classical black holes or their mimickers? Jahed's work continues to push the frontiers of black hole physics, and he remains open to collaborations and inquiries from those interested in his research.