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- Stein's method
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Postgraduate research
- Info for new students
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- Michael Tallis PhD Research Travel Award
- Information about research theses
- Past research students
- Resources
- Entry requirements
- PhD projects
- Obtaining funding
- Application & fee information
Student services
- Help for postgraduate students
- Thesis guidelines
- School assessment policies
- Computing information
- Mathematics Drop-in Centre
- Consultation
- Statistics Consultation Service
- Academic advice
- Enrolment variation
- Changing tutorials
- Illness or misadventure
- Application form for existing casual tutors
- ARC grants Head of School sign off
- Computing facilities
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Abstract:
Distributional limit theorems such as the Central Limit Theorem are important in statistics and probabilistic combinatorics. These kinds of theorems are usually stated asymptotically, with a topological notion of distributional convergence called weak convergence. A shortcoming of these theorems is that they are not quantitative. That is, they give no understanding of the rate of convergence.
Stein's method is a technique for bounding the distance between distributions in a variety of metrics consistent with weak convergence. We will introduce the idea with a simple proof of a quantitative version of the central limit theorem. We then turn to a more involved problem in probabilistic combinatorics. To approach this problem we will use Stein's method in combination with the idea of an exchangeable pair.