|Series||Pitman monographs and surveys in pure and applied mathematics -- 48|
|The Physical Object|
|Number of Pages||400|
Try the new Google Books. Check out the new look and enjoy easier access to your favorite features. Try it now. No thanks. Try the new Google Books Get print book. No eBook available Random Fields Estimation Theory. Alexander G. Ramm. Longman Scientific & Technical, - Estimation - pages. 0 Reviews. No assumption about the Gaussian or Markovian nature of the fields are made. The theory, constructed entirely within the framework of covariance theory, is based on a detailed analytical study of a new class of multidimensional integral equations basic in estimation theory. This book is suitable for graduate courses in random fields estimation. It can also be used in courses in functional analysis, . Random fields provide a general theoretical framework for the development of spatial models and their applications in data analysis. The contents of the book include topics from classical statistics and random field theory (regression models, Gaussian random fields, stationarity, correlation functions) spatial statistics (variogram estimation, model inference, kriging-based prediction) and . The purpose of this book is to bring together existing and new methodologies of random field theory and indicate how they can be applied to these diverse areas where a "deterministic treatment is inefficient and conventional statistics insufficient.".
INTRODUCTION This work deals with the analytic theory of random fields estimation within the framework of covariance theory. No assumptions about distribution laws are made and the fields are not necessarily Gaussian or Markovian. ESTIMATION OF RANDOM FIELDS A.G. Ramm LMA/CNRS, Marseille , ce France one can develop an analytic theory of random ﬁelds estimation. If the functions (3) Although the literature on ﬁltering and estimation theory is large (dozens of books and hundreds −1. Random fields are random functions of several variables. Wiener’s theory was based on the analytical solution of the basic integral equation of estimation theory. This equation for estimation of stationary random processes was Wiener-Hopf-type of equation, originally on a positive : n.n. A new method for efficient discretization of random fields (i.e., their representation in terms of random variables) is introduced. The efficiency of the discretization is measured by the number of random variables required to represent the field with a specified level of accuracy.
This book presents analytic theory of random elds estimation optimal by the criterion of minimum of the variance of the error of the estimate. This theory is a generalization of the classical Wiener theory. Wiener’s theory has been developed for optimal estimation of stationary random processes, that is, random functions of one variable. In this chapter, the nonparametric methods of estimating the spectra and correlation functions of stationary processes and homogeneous fields are considered. It is assumed that the principal concepts and definitions of the corresponding theory are known (see Anderson, ; Box and Jenkins, ; Jenkins and Watts, ; Kendall and Stuart, ; Loeve, ; Parzen, ; Yaglom, An Introduction to Random Field Theory Matthew Brett∗, Will Penny †and Stefan Kiebel ∗ MRC Cognition and Brain Sciences Unit, Cambridge UK; † Functional Imaging Laboratory, Institute of Neurology, London, UK. March 4, 1 Introduction This chapter is an introduction to the multiple comparison problem in func-. Markov Random Fields Markov random ﬁeld theory holds the promise of providing a systematic approach to the analysis of images in the framework of Bayesian probability theory. Markov random ﬁelds (MRFs) model the statistical properties of images. This allows a host of statistical tools.