126,756 research outputs found
Latent Gaussian modeling and INLA: A review with focus on space-time applications
Bayesian hierarchical models with latent Gaussian layers have proven very
flexible in capturing complex stochastic behavior and hierarchical structures
in high-dimensional spatial and spatio-temporal data. Whereas simulation-based
Bayesian inference through Markov Chain Monte Carlo may be hampered by slow
convergence and numerical instabilities, the inferential framework of
Integrated Nested Laplace Approximation (INLA) is capable to provide accurate
and relatively fast analytical approximations to posterior quantities of
interest. It heavily relies on the use of Gauss-Markov dependence structures to
avoid the numerical bottleneck of high-dimensional nonsparse matrix
computations. With a view towards space-time applications, we here review the
principal theoretical concepts, model classes and inference tools within the
INLA framework. Important elements to construct space-time models are certain
spatial Mat\'ern-like Gauss-Markov random fields, obtained as approximate
solutions to a stochastic partial differential equation. Efficient
implementation of statistical inference tools for a large variety of models is
available through the INLA package of the R software. To showcase the practical
use of R-INLA and to illustrate its principal commands and syntax, a
comprehensive simulation experiment is presented using simulated non Gaussian
space-time count data with a first-order autoregressive dependence structure in
time
Scalable iterative methods for sampling from massive Gaussian random vectors
Sampling from Gaussian Markov random fields (GMRFs), that is multivariate
Gaussian ran- dom vectors that are parameterised by the inverse of their
covariance matrix, is a fundamental problem in computational statistics. In
this paper, we show how we can exploit arbitrarily accu- rate approximations to
a GMRF to speed up Krylov subspace sampling methods. We also show that these
methods can be used when computing the normalising constant of a large
multivariate Gaussian distribution, which is needed for both any
likelihood-based inference method. The method we derive is also applicable to
other structured Gaussian random vectors and, in particu- lar, we show that
when the precision matrix is a perturbation of a (block) circulant matrix, it
is still possible to derive O(n log n) sampling schemes.Comment: 17 Pages, 4 Figure
Quantification of airfoil geometry-induced aerodynamic uncertainties - comparison of approaches
Uncertainty quantification in aerodynamic simulations calls for efficient
numerical methods since it is computationally expensive, especially for the
uncertainties caused by random geometry variations which involve a large number
of variables. This paper compares five methods, including quasi-Monte Carlo
quadrature, polynomial chaos with coefficients determined by sparse quadrature
and gradient-enhanced version of Kriging, radial basis functions and point
collocation polynomial chaos, in their efficiency in estimating statistics of
aerodynamic performance upon random perturbation to the airfoil geometry which
is parameterized by 9 independent Gaussian variables. The results show that
gradient-enhanced surrogate methods achieve better accuracy than direct
integration methods with the same computational cost
Modeling of Spatial Uncertainties in the Magnetic Reluctivity
In this paper a computationally efficient approach is suggested for the
stochastic modeling of an inhomogeneous reluctivity of magnetic materials.
These materials can be part of electrical machines, such as a single phase
transformer (a benchmark example that is considered in this paper). The
approach is based on the Karhunen-Lo\`{e}ve expansion. The stochastic model is
further used to study the statistics of the self inductance of the primary coil
as a quantity of interest.Comment: submitted to COMPE
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