21,476 research outputs found
A multivariate semiparametric Bayesian spatial modeling framework for hurricane surface wind fields
Storm surge, the onshore rush of sea water caused by the high winds and low
pressure associated with a hurricane, can compound the effects of inland
flooding caused by rainfall, leading to loss of property and loss of life for
residents of coastal areas. Numerical ocean models are essential for creating
storm surge forecasts for coastal areas. These models are driven primarily by
the surface wind forcings. Currently, the gridded wind fields used by ocean
models are specified by deterministic formulas that are based on the central
pressure and location of the storm center. While these equations incorporate
important physical knowledge about the structure of hurricane surface wind
fields, they cannot always capture the asymmetric and dynamic nature of a
hurricane. A new Bayesian multivariate spatial statistical modeling framework
is introduced combining data with physical knowledge about the wind fields to
improve the estimation of the wind vectors. Many spatial models assume the data
follow a Gaussian distribution. However, this may be overly-restrictive for
wind fields data which often display erratic behavior, such as sudden changes
in time or space. In this paper we develop a semiparametric multivariate
spatial model for these data. Our model builds on the stick-breaking prior,
which is frequently used in Bayesian modeling to capture uncertainty in the
parametric form of an outcome. The stick-breaking prior is extended to the
spatial setting by assigning each location a different, unknown distribution,
and smoothing the distributions in space with a series of kernel functions.
This semiparametric spatial model is shown to improve prediction compared to
usual Bayesian Kriging methods for the wind field of Hurricane Ivan.Comment: Published at http://dx.doi.org/10.1214/07-AOAS108 in the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A Tutorial on Bayesian Nonparametric Models
A key problem in statistical modeling is model selection, how to choose a
model at an appropriate level of complexity. This problem appears in many
settings, most prominently in choosing the number ofclusters in mixture models
or the number of factors in factor analysis. In this tutorial we describe
Bayesian nonparametric methods, a class of methods that side-steps this issue
by allowing the data to determine the complexity of the model. This tutorial is
a high-level introduction to Bayesian nonparametric methods and contains
several examples of their application.Comment: 28 pages, 8 figure
On q-Gaussians and Exchangeability
The q-Gaussians are discussed from the point of view of variance mixtures of
normals and exchangeability. For each q< 3, there is a q-Gaussian distribution
that maximizes the Tsallis entropy under suitable constraints. This paper shows
that q-Gaussian random variables can be represented as variance mixtures of
normals. These variance mixtures of normals are the attractors in central limit
theorems for sequences of exchangeable random variables; thereby, providing a
possible model that has been extensively studied in probability theory. The
formulation provided has the additional advantage of yielding process versions
which are naturally q-Brownian motions. Explicit mixing distributions for
q-Gaussians should facilitate applications to areas such as option pricing. The
model might provide insight into the study of superstatistics.Comment: 14 page
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