Overview

Introductory statistics often ends just as modern statistical work begins. This short course introduces several ideas that become important in advanced study without attempting to provide a complete graduate sequence.

Learners encounter regularization, resampling, Bayesian updating, causal inference and high-dimensional estimation through carefully chosen examples. Each topic is presented as a response to a specific weakness of simpler methods.

The purpose is orientation: learners should finish with a map of advanced statistical thinking and enough technical context to decide what to study next.

Learning objectives

By the end of the course, learners should be able to:

• explain why regularization can improve out-of-sample performance;
• use resampling to study estimator uncertainty and model stability;
• interpret Bayesian updating as a coherent framework for combining prior information and evidence;
• distinguish prediction from causal identification;
• recognize challenges created by high-dimensional data;
• identify which advanced statistical tools are appropriate for different analytical problems.

Intended participants and prerequisites

Course structure

The course is organised into six units. Each unit combines concise explanation, worked examples and short analytical exercises.

Unit	Subject	Principal questions
1	Regularization	Why can deliberately biased estimates predict better?
2	Resampling	How can repeated sampling ideas measure stability and uncertainty?
3	Bayesian inference	How are prior information and new evidence combined?
4	Causal inference	What additional assumptions are required to move from association to effect?
5	High-dimensional statistics	What changes when the number of variables becomes large?
6	Choosing a method	How should the structure of a question determine the statistical tool?

Teaching and assessment

Teaching is delivered through concise lectures, technical notes, worked examples and guided exercises. AI-supported interaction may be used to explain concepts, generate additional practice and challenge a learner's reasoning, but assessment remains based on the learner's demonstrated understanding.

Component	Purpose	Weight
Short exercises	Check understanding of the principal concepts	40%
Applied investigation	Use the course framework on a new problem or dataset	30%
Final assessment	Integrated reasoning across the course	30%

A certificate of completion is issued only when the required assessments have been completed at the stated standard. Participation alone does not constitute completion.

Faculty

Materials and technical requirements

Learning environment

Learners need a current web browser and access to the Gordon learning platform. Where a course uses code, spreadsheets, datasets or external readings, the relevant requirements are identified inside the unit.

Course materials

Required readings, datasets and practice materials are identified within each unit. Public courses are designed so that required core materials can be accessed without a separate tuition charge.