2 research outputs found
Modeling complex systems by Generalized Factor Analysis
We propose a new modeling paradigm for large dimensional aggregates of
stochastic systems by Generalized Factor Analysis (GFA) models. These models
describe the data as the sum of a flocking plus an uncorrelated idiosyncratic
component. The flocking component describes a sort of collective orderly motion
which admits a much simpler mathematical description than the whole ensemble
while the idiosyncratic component describes weakly correlated noise. We first
discuss static GFA representations and characterize in a rigorous way the
properties of the two components. The extraction of the dynamic flocking
component is discussed for time-stationary linear systems and for a simple
classes of separable random fields.Comment: 15 pages, preprint submitted for publication to IEEE Trans. on
Automatic Contro
On a class of space-time intrinsic random functions
Power law generalized covariance functions provide a simple model for
describing the local behavior of an isotropic random field. This work seeks to
extend this class of covariance functions to spatial-temporal processes for
which the degree of smoothness in space and in time may differ while
maintaining other desirable properties for the covariance functions, including
the availability of explicit convergent and asymptotic series expansions.Comment: Published in at http://dx.doi.org/10.3150/11-BEJ405 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm