The course "Advanced Probability and Statistical Methods" provides a deep dive into advanced probability and statistical methods, essential for mastering data analysis in computer science. Covering joint distributions, expectation, statistical testing, and Markov chains, you'll explore key concepts and techniques that underpin modern data-driven decision-making. By engaging with real-world problems, you’ll learn to apply these methods effectively, gaining insights into the relationships between random variables and their applications in diverse fields.
Completing this course equips you with the skills to analyze complex data sets and make informed predictions, enhancing your proficiency in statistical reasoning and inference. Unique to this course is its blend of theoretical foundations and practical applications, ensuring that you can not only understand the principles but also implement them using tools like R. Whether you're pursuing a career in data science, machine learning, or any data-centric discipline, this course will empower you to tackle challenging statistical problems and drive meaningful insights from data.
Overview
Syllabus
- Course Introduction
- This course provides a comprehensive overview of probability theory and statistical inference, covering joint probability distributions, independence, and conditional distributions. Students will explore expected values, variances, and key statistical theorems, including the central limit theorem. Hypothesis testing, regression analysis, and stochastic processes such as Poisson processes and Markov chains will also be examined. Through practical applications and problem-solving, participants will gain essential skills in data analysis and interpretation.
- Joint Distributed Random Variables
- This module presents the joint distributions of multiple random variables, both discrete and continuous and introduces the concept of independence.
- Expectation
- This module focuses on the expectation of a random variable and joint random variable. Students will solve problems using the linearity of expectation and identify when its application is inappropriate. We will also explore variance, covariance, and correlation.
- Inequalities and Central Limit Theorem
- This module will apply several limit theorems to solve problems to include the central limit theorem, the Markov inequality, and the Chebyshev inequality. We will also prove Murphy’s Law.
- Statistical Testing
- This module develops student proficiency in probabilistic models to include Markov chains. Students will be introduced to problems involving surprise, uncertainty, and entropy.
- Markov Chain
- This module develops student proficiency in probabilistic models to include Markov chains. Students will be introduced to problems involving surprise, uncertainty, and entropy.
Taught by
Ian McCulloh and Tony Johnson
