423 research outputs found
Some covariance models based on normal scale mixtures
Modelling spatio-temporal processes has become an important issue in current
research. Since Gaussian processes are essentially determined by their second
order structure, broad classes of covariance functions are of interest. Here, a
new class is described that merges and generalizes various models presented in
the literature, in particular models in Gneiting (J. Amer. Statist. Assoc. 97
(2002) 590--600) and Stein (Nonstationary spatial covariance functions (2005)
Univ. Chicago). Furthermore, new models and a multivariate extension are
introduced.Comment: Published in at http://dx.doi.org/10.3150/09-BEJ226 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Sampling Sup-Normalized Spectral Functions for Brown-Resnick Processes
Sup-normalized spectral functions form building blocks of max-stable and
Pareto processes and therefore play an important role in modeling spatial
extremes. For one of the most popular examples, the Brown-Resnick process,
simulation is not straightforward. In this paper, we generalize two approaches
for simulation via Markov Chain Monte Carlo methods and rejection sampling by
introducing new classes of proposal densities. In both cases, we provide an
optimal choice of the proposal density with respect to sampling efficiency. The
performance of the procedures is demonstrated in an example.Comment: 11 pages, 2 figure
Systematic co-occurrence of tail correlation functions among max-stable processes
The tail correlation function (TCF) is one of the most popular bivariate
extremal dependence measures that has entered the literature under various
names. We study to what extent the TCF can distinguish between different
classes of well-known max-stable processes and identify essentially different
processes sharing the same TCF.Comment: 31 pages, 4 Tables, 5 Figure
Stochastic models which separate fractal dimension and Hurst effect
Fractal behavior and long-range dependence have been observed in an
astonishing number of physical systems. Either phenomenon has been modeled by
self-similar random functions, thereby implying a linear relationship between
fractal dimension, a measure of roughness, and Hurst coefficient, a measure of
long-memory dependence. This letter introduces simple stochastic models which
allow for any combination of fractal dimension and Hurst exponent. We
synthesize images from these models, with arbitrary fractal properties and
power-law correlations, and propose a test for self-similarity.Comment: 8 pages, 2 figure
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