D.A. Wooff
Bayes linear sufficiency in non-exchangeable multivariate multiple regressions
Wooff, D.A.
Authors
Abstract
We consider sufficiency for Bayes linear revision for multivariate multiple regression problems, and in particular where we have a sequence of multivariate observations at different matrix design points, but with common parameter vector. Such sequences are not usually exchangeable. However, we show that there is a sequence of transformed observations which is exchangeable and we demonstrate that their mean is sufficient both for Bayes linear revision of the parameter vector and for prediction of future observations. We link these ideas to making revisions of belief over replicated structure such as graphical templates of model relationships. We show that the sufficiencies lead to natural residual collections and thence to sequential diagnostic assessments. We show how each finite regression problem corresponds to a parallel implied infinite exchangeable sequence which may be exploited to solve the sample-size design problem. Bayes linear methods are based on limited specifications of belief, usually means, variances, and covariances. As such, the methodology is well suited to highdimensional regression problems where a full Bayesian analysis is difficult or impossible, but where a linear Bayes approach offers a pragmatic way to combine judgements with data in order to produce posterior summaries.
Citation
Wooff, D. (2014). Bayes linear sufficiency in non-exchangeable multivariate multiple regressions. Bayesian Analysis, 9(1), 77-96. https://doi.org/10.1214/13-ba847
Journal Article Type | Article |
---|---|
Online Publication Date | Feb 24, 2014 |
Publication Date | Mar 1, 2014 |
Deposit Date | Jun 14, 2012 |
Publicly Available Date | Jun 3, 2014 |
Journal | Bayesian Analysis |
Print ISSN | 1936-0975 |
Electronic ISSN | 1931-6690 |
Publisher | International Society for Bayesian Analysis (ISBA) |
Peer Reviewed | Peer Reviewed |
Volume | 9 |
Issue | 1 |
Pages | 77-96 |
DOI | https://doi.org/10.1214/13-ba847 |
Keywords | Bayes linear, Sufficient, Multivariate multiple regression, Approximate Bayesian, Residual space, Diagnostics, Sequential, Sample-size design. |
Publisher URL | http://ba.stat.cmu.edu/ |
Files
Published Journal Article
(173 Kb)
PDF
Copyright Statement
First published in the journal Bayesian analysis, published by the International Society for Bayesian Analysis.
You might also like
Statistical management of pay-per-click processes for search engines
(2016)
Book Chapter
Modelling Uncertainty in Pore Pressure Using Dynamic Bayesian Networks
(2015)
Conference Proceeding
Multiwell Deconvolution
(2014)
Journal Article
Downloadable Citations
About Durham Research Online (DRO)
Administrator e-mail: dro.admin@durham.ac.uk
This application uses the following open-source libraries:
SheetJS Community Edition
Apache License Version 2.0 (http://www.apache.org/licenses/)
PDF.js
Apache License Version 2.0 (http://www.apache.org/licenses/)
Font Awesome
SIL OFL 1.1 (http://scripts.sil.org/OFL)
MIT License (http://opensource.org/licenses/mit-license.html)
CC BY 3.0 ( http://creativecommons.org/licenses/by/3.0/)
Powered by Worktribe © 2024
Advanced Search