arXiv subjects

David Bolin

Publications and source records attributed to David Bolin.

76 records · Page 5Linked to original sources

arXiv2012

Excursion and contour uncertainty regions for latent Gaussian models

An interesting statistical problem is to find regions where some studied process exceeds a certain level. Estimating such regions so that the probability for exceeding the level in the entire set is equal to some predefined value is a difficult problem that occurs in several areas of applications ranging from brain imaging to astrophysics. In this work, a method for solving this problem, as well as the related problem of finding uncertainty regions for contour curves, for latent Gaussian models is proposed. The method is based on using a parametric family for the excursion sets in combination with a sequential importance sampling method for estimating joint probabilities. The accuracy of the method is investigated using simulated data and two environmental applications are presented. In the first application, areas where the air pollution in the Piemonte region in northern Italy exceeds the daily limit value, set by the European Union for human health protection, are estimated. In the second application, regions in the African Sahel that experienced an increase in vegetation after the drought period in the early 1980s are estimated.

stat.ME↗

arXiv2012

Spatial Matérn fields driven by non-Gaussian noise

The article studies non-Gaussian extensions of a recently discovered link between certain Gaussian random fields, expressed as solutions to stochastic partial differential equations (SPDEs), and Gaussian Markov random fields. The focus is on non-Gaussian random fields with Matérn covariance functions, and in particular we show how the SPDE formulation of a Laplace moving average model can be used to obtain an efficient simulation method as well as an accurate parameter estimation technique for the model. This should be seen as a demonstration of how these techniques can be used, and generalizations to more general SPDEs are readily available.

stat.ME↗

arXiv2011

How do Markov approximations compare with other methods for large spatial data sets?

The Matérn covariance function is a popular choice for modeling dependence in spatial environmental data. Standard Matérn covariance models are, however, often computationally infeasible for large data sets. In this work, recent results for Markov approximations of Gaussian Matérn 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. The results show that, for a given computational cost, the Markov methods have a substantial gain in accuracy compared with the other methods.

stat.CO↗

arXiv2011

Spatial models generated by nested stochastic partial differential equations, with an application to global ozone mapping

A 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 Matérn 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. The model class is used to estimate daily ozone maps using a large data set of spatially irregular global total column ozone data.

stat.AP↗