Probability & Statistics

This course provides a comprehensive exploration of probability and statistics, with a strong emphasis on practical applications and data analysis. The course is divided into two main parts:

In the first part of the course, students will focus on understanding the principles of probability and their applications. Key topics include:

• Discrete Probability: Develop and utilize a random number generator to explore random networks.
• Conditional Probability: Apply Bayes' theorem in the context of Markov Chains.
• Continuous Probability: Study the central limit theorem and its application to Poisson processes.

In the second part of the course, the focus shifts to statistical analysis and data science. Key topics include:

• Estimation Techniques: Use linear regression to analyze chemical reaction networks.
• Predictive Modeling: Apply logistic regression to data classification tasks, such as distinguishing between images of cats and dogs, and explore neural networks.
• Decision Making: Conduct hypothesis tests and evaluate utility in scenarios like Pascal’s dilemma and evidence-based policy making.

Simulation and sampling methods are integral to this course, providing hands-on experience and deeper insights into the concepts discussed.

The primary objective of this course is to equip students with a solid understanding of both probability and statistics, enabling them to apply these concepts to real-world scenarios. 

By the end of the course, students will be able to:

• Comprehend and utilize discrete and continuous probability models.
• Apply conditional probability and Bayes' theorem in various contexts, including Markov Chains.
• Understand and apply the central limit theorem and Poisson processes.
• Conduct statistical analysis using estimation techniques such as linear regression.
• Develop predictive models using logistic regression and neural networks.
• Perform hypothesis testing and make informed decisions based on statistical data.
• Utilize simulation and sampling methods to enhance data analysis and interpretation skills.

In presence

This course employs a blended approach to ensure a thorough understanding of probability and statistics.

• Lectures: Weekly sessions covering theoretical concepts and foundational knowledge.
• Tutorials: Interactive weekly sessions for problem-solving and deeper engagement with the material.
• Projects: Two major projects applying theoretical concepts to real-world problems.
• Assessments: Midterm and final exams, along with project submissions, to evaluate understanding and application of course material.

Active participation in all components is essential for success. Simulation and sampling methods are integral throughout the course, providing practical data generation and analysis experience.

The course assessment includes a midterm exam, a final exam, and two major projects.