Statistics for Applications
Course facts
- Payment: Free, no certificate
- Credits: Non Credit
- Learning style: Self-paced, start anytime
- Resources: Lecture Notes; Lecture Videos; Problem Sets
MIT OpenCourseWare details
- As taught in: Fall 2016
- Department: Mathematics
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The mathematics of statistical methods: maximum likelihood, hypothesis testing, regression, Bayesian statistics, PCA and generalized linear models.
Why does a statistical method work, and when does it fail? This course builds the mathematical foundations behind the methods used in applied statistics, in recorded lectures with notes: parametric inference, maximum likelihood and the method of moments, hypothesis testing and goodness of fit, regression, Bayesian statistics, principal component analysis and generalized linear models. The aim is to turn a real situation into a statistical problem, choose a method and understand its limits.
What You Will Achieve
- Formulate a real-life question as a statistical problem in mathematical terms
- Estimate parameters by maximum likelihood and the method of moments
- Design parametric hypothesis tests and goodness-of-fit tests
- Fit and interpret linear regression and generalized linear models
Program Overview
Statistical Inference
From a statistical model to estimates of its parameters.
- Introduction to statistics
- Parametric inference
- Maximum likelihood estimation
- The method of moments
Testing
Deciding between hypotheses with data.
- Parametric hypothesis testing
- Testing goodness of fit
Models and Methods
Regression, the Bayesian view and dimension reduction.
- Regression
- Bayesian statistics
- Principal component analysis
- Generalized linear models
Course Completion
Job Outlook
Mathematical statistics underpins data science, machine learning, biostatistics, econometrics, quantitative finance and experimental research.
Good for: Learners who want the mathematical theory behind the statistical methods they use or plan to use.
Keep in mind: The eleven problem sets have no published solutions, so you have to check your own work against the lecture notes and videos.
Bottom line: A rigorous recorded statistics course that explains why each method works and where its limits lie.
Frequently Asked Questions
Which statistical methods does the course cover?
Parametric inference, maximum likelihood, the method of moments, parametric hypothesis tests, goodness-of-fit tests, regression, Bayesian statistics, principal component analysis and generalized linear models.
Are solutions to the problem sets available?
No. The eleven problem sets are published without solutions, so they work best as practice that you check against the lecture notes and the videos.
Is the course mostly theory or applications?
Mostly theory: the goal is to understand the mathematics that makes statistical methods efficient, then use it to choose a method for a real situation and know its limitations.
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