Edinburgh Research Explorer

Gaussian Regression and Optimal Finite Dimensional Linear Models

Research output: Working paper

Related Edinburgh Organisations

Documents

Original languageEnglish
Number of pages20
Publication statusPublished - 1997

Abstract

The problem of regression under Gaussian assumptions is treated generally. The relationship between Bayesian prediction, regularization and smoothing is elucidated. The ideal regression is the posterior mean and its computation scales as O(n3), where nis the sample size. We show that the optimal m-dimensional linear model under a given prior is spanned by the first meigenfunctions of a covariance operator, which is a trace-class operator. This is an infinite dimensional analogue of principal component analysis. The importance of Hilbert space methods to practical statistics is also discussed.

Download statistics

No data available

ID: 23424762