Fundamentals of Statistics
Develop a deep understanding of the principles that underpin statistical inference: estimation, hypothesis testing and prediction. -- Part of the MITx MicroMasters program in Statistics and Data Science.
Course Information
Certificate Track
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About this Course
Statistics is the science of turning data into insights and ultimately decisions. Behind recent advances in machine learning, data science and artificial intelligence are fundamental statistical principles. The purpose of this class is to develop and understand these core ideas on firm mathematical grounds starting from the construction of estimators and tests, as well as an analysis of their asymptotic performance.
After developing basic tools to handle parametric models, we will explore how to answer more advanced questions, such as the following:
- How suitable is a given model for a particular dataset?
- How to select variables in linear regression?
- How to model nonlinear phenomena?
- How to visualize high-dimensional data?
Taking this class will allow you to expand your statistical knowledge to not only include a list of methods, but also the mathematical principles that link them together, equipping you with the tools you need to develop new ones.
This course is part of the MITx MicroMasters Program in Statistics and Data Science. Master the skills needed to be an informed and effective practitioner of data science. You will complete this course and three others from MITx, at a similar pace and level of rigor as an on-campus course at MIT, and then take a virtually-proctored exam to earn your MicroMasters, an academic credential that will demonstrate your proficiency in data science or accelerate your path towards an MIT PhD or a Master's at other universities. To learn more about this program, please visit https://micromasters.mit.edu/ds/.
What you'll learn
- Construct estimators using method of moments and maximum likelihood, and decide how to choose between them
- Quantify uncertainty using confidence intervals and hypothesis testing
- Choose between different models using goodness of fit test
- Make prediction using linear, nonlinear and generalized linear models
- Perform dimension reduction using principal component analysis (PCA)
Prerequisites
- Undergraduate probability theory
- Undergraduate level single and multi-variable calculus
- Vectors and matrices
Meet your instructors
Philippe Rigollet
Associate Professor
Philippe Rigollet is an associate professor in the Department of Mathematics at MIT. He works at the intersection of statistics, machine learning, and optimization, focusing primarily on the design and analysis of statistical methods for high-dimensional problems. He received a PhD in mathematical statistics from the University of Paris VI. He has held positions as a visiting assistant professor at the Georgia Institute of Technology and then as an assistant professor at Princeton University. He has received an NSF CAREER award, a Howard B. Wentz Jr. Junior Faculty Award at Princeton and the best paper award at the conference on learning theory COLT 2013.
