Develop a deep understanding of the principles that underpin statistical inference: estimation, hypothesis testing and prediction. 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.
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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.
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)
