Course Description

This advanced-level statistics course, offered by MITx, is a comprehensive exploration of the fundamental principles that underpin modern data science, machine learning, and artificial intelligence. It aims to provide students with a deep, mathematically grounded understanding of statistical concepts and their practical applications in turning data into valuable insights and informed decisions.

What Students Will Learn

• Construct and evaluate estimators using methods such as moment estimation and maximum likelihood
• Develop skills in quantifying uncertainty through confidence intervals and hypothesis testing
• Learn to select appropriate models using goodness-of-fit tests
• Master predictive modeling techniques, including linear, nonlinear, and generalized linear models
• Gain proficiency in dimension reduction techniques, particularly principal component analysis (PCA)
• Understand the mathematical foundations of statistical principles in data science and machine learning
• Acquire the ability to visualize and interpret high-dimensional data

Prerequisites

• Completion of 6.431x (Probability - The Science of Uncertainty and Data) or an equivalent probability theory course
• Strong foundation in college-level single and multi-variable calculus
• Proficiency in working with vectors and matrices
• Basic understanding of statistical concepts and data analysis

Course Topics

• Construction of estimators and analysis of their asymptotic performance
• Parametric modeling and model selection techniques
• Variable selection in linear regression
• Nonlinear phenomena modeling
• High-dimensional data visualization methods
• Advanced statistical inference and hypothesis testing
• Goodness-of-fit tests for model evaluation
• Dimension reduction techniques, focusing on PCA
• Mathematical principles linking various statistical methods
• Real-world applications of statistical concepts in data science and AI

Who This Course Is For

• Advanced undergraduate or graduate students in statistics, data science, or related fields
• Professionals seeking to deepen their understanding of statistical principles in machine learning and AI
• Researchers looking to expand their statistical knowledge beyond basic methods
• Aspiring data scientists aiming to build a strong theoretical foundation
• Anyone interested in pursuing the MITx MicroMasters Program in Statistics and Data Science

Real-World Applications

• Developing more accurate predictive models in various industries
• Improving decision-making processes through advanced statistical analysis
• Enhancing machine learning algorithms with a deeper understanding of underlying statistical principles
• Conducting more robust research in fields relying on data analysis
• Advancing artificial intelligence applications with mathematically grounded statistical knowledge
• Solving complex data-driven problems in business, science, and technology
• Innovating new statistical methods and techniques for emerging data challenges