e-book Gaussian and Non-Gaussian Linear Time Series and Random Fields (Springer Series in Statistics)

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Bibliographic Information
Contents:
  1. High resolution simulation of nonstationary Gaussian random fields
  2. Modeling and statistical analysis of non-Gaussian random fields with heavy-tailed distributions

In this paper, we exploit the connections between Fourier feature representations, Gaussian processes and neural networks to generalise previous approaches and develop a simple and efficient framework to learn arbitrarily complex nonstationary kernel functions directly from the data, while taking care to avoid overfitting using state-of-the-art methods from deep learning.

We highlight the very broad array of kernel classes that could be created within this framework. We apply this to a time series dataset and a remote sensing problem involving land surface temperature in Eastern Africa. We show that without increasing the computational or storage complexity, nonstationary kernels can be used to improve generalisation performance and provide more interpretable results.


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We use cookies to help provide and enhance our service and tailor content and ads. By continuing you agree to the use of cookies. Download PDF Download. Spatial Statistics Volume 28 , December , Pages Murray Rosenblatt. Much of this book is concerned with autoregressive and moving av erage linear stationary sequences and random fields.

High resolution simulation of nonstationary Gaussian random fields

These models are part of the classical literature in time series analysis, particularly in the Gaussian case. There is a large literature on probabilistic and statistical aspects of these models-to a great extent in the Gaussian context. In the Gaussian case best predictors are linear and there is an extensive study of the asymptotics of asymptotically optimal esti mators. Some discussion of these classical results is given to provide a contrast with what may occur in the non-Gaussian case.

There the prediction problem may be nonlinear and problems of estima tion can have a certain complexity due to the richer structure that non-Gaussian models may have. Gaussian stationary sequences have a reversible probability struc ture, that is, the probability structure with time increasing in the usual manner is the same as that with time reversed.

Chapter 1 considers the question of reversibility for linear stationary sequences and gives necessary and sufficient conditions for the reversibility. A neat result of Breidt and Davis on reversibility is presented. A sim ple but elegant result of Cheng is also given that specifies conditions for the identifiability of the filter coefficients that specify a linear non-Gaussian random field. Minimum Phase Estimation. Homogeneous Gaussian Random Fields.

Modeling and statistical analysis of non-Gaussian random fields with heavy-tailed distributions

The Fluctuation of the QuasiGaussian Likelihood. Cumulants Mixing and Estimation for Gaussian Fields. Two Inequalities.