Stein's Method of functional central limit theorem
Lead Research Organisation:
University of Oxford
Department Name: Statistics
Abstract
Stein's method is a powerful tool for estimating distributional distances. It has been applied in multivariate, univariate and infinite-dimensional settings, including the Malliavin calculus. However it has been little used for functional approximations, except for some attempts of Barbour (1990) and Barbour and Janson (2009). We would like to develop this theory.
Examples of the problems we would like to apply it to include: processes of maxima of partial sums of random variables or the Wright-Fisher diffusions approximation.
The project falls within the EPSRC statistics and applied probability research area.
Examples of the problems we would like to apply it to include: processes of maxima of partial sums of random variables or the Wright-Fisher diffusions approximation.
The project falls within the EPSRC statistics and applied probability research area.
Organisations
People |
ORCID iD |
| G Reinert (Primary Supervisor) | |
| Mikolaj Kasprzak (Student) |
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/N509711/1 | 01/10/2016 | 30/09/2021 | |||
| 1654155 | Studentship | EP/N509711/1 | 01/10/2015 | 31/03/2019 | Mikolaj Kasprzak |
| Description | I have derived bounds on the distances between scaled sums of dependent random vectors and continuous Gaussian processes, together with examples. I have also extended the method of exchangeable pairs to the functional setting and bounded the distance between a process similar to the Moran model and a process similar to Wright-Fisher Diffusion. Together with collaborators, I also corrected a mistake in a paper by Andrew Barbour. I have created an exchangeable-pair framework for functional approximations. I have also contributed to two projects related to Bayesian Non-Parametrics and Machine Learning which concentrated on obtaining quality bounds in approximate inference. |
| Exploitation Route | My findings could be used by applied researchers working in population genetics and by theoretical researchers working in distributional approximation. They may also be applied by machine learning researchers and users interested in measuring the error they make when employing approximate Bayesian inference techniques. |
| Sectors | Digital/Communication/Information Technologies (including Software),Financial Services, and Management Consultancy,Other |