A sparse matrix approach to Bayesian computation in large linear models

A sparse matrix approach to Bayesian computation in large linear models (2004)

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by Darren J Wilkinson , Stephen KH Yeung

Venue:	Comp. Statist. Data Anal
Citations:	4 - 2 self

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@ARTICLE{Wilkinson04asparse,
    author = {Darren J Wilkinson and Stephen KH Yeung},
    title = {A sparse matrix approach to Bayesian computation in large linear models},
    journal = {Comp. Statist. Data Anal},
    year = {2004},
    volume = {44},
    pages = {493--516}
}

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Abstract

This paper examines the problem of efficient Bayesian computation in the context of linear Gaussian Directed Acyclic Graph (DAG) models. Unobserved latent variables are grouped together in a block, and sparse matrix techniques for computation are explored. Conditional sampling and likelihood computations are shown to be straightforward using a sparse matrix approach, allowing MCMC algorithms with good mixing properties to be developed for problems with many thousands of latent variables. Keywords: Bayes linear models; block sampling; Gaussian models; linear systems; local computation; multivariate normal; precision matrix; sparse matrices; Markov Chain Monte Carlo (MCMC). # This is a University of Newcastle Statistics Preprint, STA01,2. Last updated: March 15, 2001. 1 Contents 1 Introduction 3 2 Model building 4 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Canonical parameterisation of the MVN . . . . . . . . . . . . . . . . . . ....

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