Finn Lindgren
Going off grid: Computationally efficient inference for log-Gaussian Cox processes.
Fri, 11/04/2011 - 15:01 — SomNambulAuthors: Håvard Rue, Finn Lindgren, Daniel Simpson, Janine Illian, Sigrunn Sørbye
Subjects: Computation
AbstractIn this paper we introduce a new method for performing computational
inference on log-Gaussian Cox processes (LGCP). Contrary to current practice,
we do not approximate by a counting process on a partition of the domain, but
rather attack the point process likelihood directly. In order to do this, we
use the continuously specified Markovian random fields introduced by
\citet{Lindgren2011}. The inference is performed using the \texttt{R-INLA}
package of \citet{art451}, which allows us to perform fast approximate
inference on quite complicated models.Spatial wavelet Markov models are more efficient than covariance tapering and process convolutions.
Mon, 06/13/2011 - 15:01 — SomNambulAuthors: David Bolin, Finn Lindgren
Subjects: Computation
AbstractThe Mat\'ern covariance function is a popular choice for modeling dependence
in spatial environmental data. Standard Mat\'ern covariance models are,
however, often computationally infeasible for large data sets. In this work,
recent results for Markov approximations of Gaussian Mat\'ern fields based on
Hilbert space approximations are extended using wavelet basis functions. These
Markov approximations are compared with two of the most popular methods for
efficient covariance approximations; covariance tapering and the process
convolution method.Spatial models generated by nested stochastic partial differential equations, with an application to global ozone mapping.
Tue, 04/19/2011 - 15:01 — SomNambulAuthors: David Bolin, Finn Lindgren
Subjects: Applications
AbstractA new class of stochastic field models is constructed using nested stochastic
partial differential equations (SPDEs). The model class is computationally
efficient, applicable to data on general smooth manifolds, and includes both
the Gaussian Mat\'{e}rn fields and a wide family of fields with oscillating
covariance functions. Nonstationary covariance models are obtained by spatially
varying the parameters in the SPDEs, and the model parameters are estimated
using direct numerical optimization, which is more efficient than standard
Markov Chain Monte Carlo procedures.
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