Learning Outcomes:
By the end of the course, students should be able to:
- identify which distribution is appropriate for certain types of data
- understand the purposes of inference and how to do it in practice
- estimate parameters and their associated uncertainty via likelihood methods, and interpret these values in the context of real-world problems.
- incorporate prior information into common statistical problems and obtain posterior probability distributions of parameters of interest.
Indicative Module Content:
Background of what is inference, recap on probability theory, random variables, common distributions for data.
Random vectors, independence, and conditional distributions.
Expectation, covariance, correlation.
Properties of random samples and asymptotics.
Frequentist statistical inference (method of moments, MLE, confidence intervals).
Uncertainty of estimates: parametric and non-parametric.
Numerical inferential algorithms.
Hypothesis testing.
Introduction to Bayesian inference.
Decision theory.