Linear Prediction

Abstract

This book investigates prediction of a spatially varying quantity based on observations of that quantity at some set of locations. Although the notion of prediction sometimes suggests the assessment of something that has not yet happened, here I take it to mean the assessment of any random quantity that is presently not known exactly. This work focuses on quantities that vary continuously in space and for which observations are made without error, although Sections 3.7, 4.2, 4.3, 6.6 and 6.8 do address some issues regarding measurement errors. Our goals are to obtain accurate predictions and to obtain reasonable assessments of the uncertainty in these predictions. The approach to prediction I take is to consider the spatially varying quantity to be a realization of a real-valued random field, that is, a family of random variables whose index set is ${\mathbb{R}^d}$.