Computationally efficient methods in spatial statistics : Applications in environmental modeling
(2009) Abstract
 In this thesis, computationally efficient statistical models for large spatial environmental data sets are constructed.
In the first part of the thesis, a method for estimating spatially dependent temporal trends is developed. A spacevarying regression model, where the regression coefficients for the spatial locations are dependent, is used. The spatial dependence structure is specified by a Gaussian Markov Random Field model, and the model parameters are estimated using the Expectation Maximization algorithm, which allows for feasible computation times for relatively large data sets. The model is used to analyze temporal trends in vegetation data from the African Sahel, and the results indicate a substantial gain in... (More)  In this thesis, computationally efficient statistical models for large spatial environmental data sets are constructed.
In the first part of the thesis, a method for estimating spatially dependent temporal trends is developed. A spacevarying regression model, where the regression coefficients for the spatial locations are dependent, is used. The spatial dependence structure is specified by a Gaussian Markov Random Field model, and the model parameters are estimated using the Expectation Maximization algorithm, which allows for feasible computation times for relatively large data sets. The model is used to analyze temporal trends in vegetation data from the African Sahel, and the results indicate a substantial gain in accuracy compared with methods based on independent ordinary least squares regressions for the individual pixels in the data set.
In the second part of the thesis, explicit computationally efficient wavelet Markov approximations of Gaussian Matérn fields are derived using Hilbert space approximations. Using a simulationbased study, the wavelet approximations are compared with two of the most popular methods for efficient covariance approximations. The study indicates that, for a given computational cost, the wavelet Markov methods have a substantial gain in accuracy compared with the other methods.
Finally, 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. As examples of areas of application, the model class is used to approximate popular models in random ocean wave theory, and applied to a large data set of global Total Column Ozone (TCO) data. The TCO data set contains approximately 180 000 measurements, showing that the models allow for efficient inference, even for large environmental data sets. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1859144
 author
 Bolin, David ^{LU}
 supervisor

 Finn Lindgren ^{LU}
 Krzysztof Podgórski ^{LU}
 organization
 publishing date
 2009
 type
 Thesis
 publication status
 published
 subject
 pages
 114 pages
 publisher
 Centre for Mathematical Sciences, Lund University
 language
 English
 LU publication?
 yes
 id
 4e6b51d8ec58420c9cc5bcfcbc466a9b (old id 1859144)
 alternative location
 http://www.maths.lth.se/matstat/staff/bolin/papers/bolin_lic.pdf
 date added to LUP
 20160401 13:42:47
 date last changed
 20181121 20:19:05
@misc{4e6b51d8ec58420c9cc5bcfcbc466a9b, abstract = {{In this thesis, computationally efficient statistical models for large spatial environmental data sets are constructed. <br/><br> <br/><br> In the first part of the thesis, a method for estimating spatially dependent temporal trends is developed. A spacevarying regression model, where the regression coefficients for the spatial locations are dependent, is used. The spatial dependence structure is specified by a Gaussian Markov Random Field model, and the model parameters are estimated using the Expectation Maximization algorithm, which allows for feasible computation times for relatively large data sets. The model is used to analyze temporal trends in vegetation data from the African Sahel, and the results indicate a substantial gain in accuracy compared with methods based on independent ordinary least squares regressions for the individual pixels in the data set. <br/><br> <br/><br> In the second part of the thesis, explicit computationally efficient wavelet Markov approximations of Gaussian Matérn fields are derived using Hilbert space approximations. Using a simulationbased study, the wavelet approximations are compared with two of the most popular methods for efficient covariance approximations. The study indicates that, for a given computational cost, the wavelet Markov methods have a substantial gain in accuracy compared with the other methods.<br/><br> <br/><br> Finally, 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<br/><br> Markov Chain Monte Carlo procedures. As examples of areas of application, the model class is used to approximate popular models in random ocean wave theory, and applied to a large data set of global Total Column Ozone (TCO) data. The TCO data set contains approximately 180 000 measurements, showing that the models allow for efficient inference, even for large environmental data sets.}}, author = {{Bolin, David}}, language = {{eng}}, note = {{Licentiate Thesis}}, publisher = {{Centre for Mathematical Sciences, Lund University}}, title = {{Computationally efficient methods in spatial statistics : Applications in environmental modeling}}, url = {{http://www.maths.lth.se/matstat/staff/bolin/papers/bolin_lic.pdf}}, year = {{2009}}, }