Prediction and design
type: Item
instance of: scholarly article
title: Prediction and design
zbMATH Open document ID: 0646.62080
author: Donald Ylvisaker
published in: The Annals of Statistics
publication date: 1987-01-01T00:00:00Z
review text: Let \(\{X_ t\), \(t\in T\}\) be a random process, and let S be a finite subset of T. Define \(E^ SX_ t=E(X_ t| X_ s\), \(s\in S)\). If for any t and S, \(E^ SX_ t=\sum p^ S_ t(s)X_ S\), where \(p^ S_ t(s)\geq 0\) and \(\sum p^ S_ t(s)\leq 1\), then \(\{X_ t\}\) is called a G-MAP (Gaussian, Markov-associated process). The author gives several examples of G-MAPs and studies their properties. One of the most important problems is the choice of S such that \(| S| =n\) and the error process \(\{X_ t-E^ SX_ t\), \(t\in T\}\) is in some sense minimal. It leads to natural prediction and design questions. The case of a process observed with error is also considered.
Mathematics Subject Classification ID: 62M20
Mathematics Subject Classification ID: 60J99
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 62K05
zbMATH DE Number: 4054858
zbMATH Keywords: Gaussian fields
zbMATH Keywords: Markov property
zbMATH Keywords: Bayesian models
zbMATH Keywords: G-MAP
zbMATH Keywords: Gaussian, Markov-associated process
zbMATH Keywords: prediction
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176350247
OpenAlex ID: W1968927470
DOI: 10.1214/AOS/1176350247
description: scientific article; zbMATH DE number 4054858