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Bayesian Methods for Large Spatial Data Sets with Materials and Environmental Science Applications.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Bayesian Methods for Large Spatial Data Sets with Materials and Environmental Science Applications./
作者:	Miller, Matthew John.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
面頁冊數:	125 p.
附註:	Source: Dissertations Abstracts International, Volume: 83-02, Section: B.
Contained By:	Dissertations Abstracts International83-02B.
標題:	Crystal structure. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28663429
ISBN:	9798522954857

Bayesian Methods for Large Spatial Data Sets with Materials and Environmental Science Applications.
Miller, Matthew John.

Bayesian Methods for Large Spatial Data Sets with Materials and Environmental Science Applications. - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 125 p.

Source: Dissertations Abstracts International, Volume: 83-02, Section: B.

Thesis (Ph.D.)--North Carolina State University, 2021.

This item must not be sold to any third party vendors.

Prediction and inference for spatially-dependent data quickly become computationally challenging as the number of observations increases. Bayesian hierarchical modeling is popular for spatial data settings, and with it Markov chain Monte Carlo (MCMC) methods. MCMC samplers require repeatedly evaluating the likelihood function, which due to spatial correlation includes performing computationally expensive operations on covariance matrices with dimensions determined by the number of observations. As the number of observations grows, even storing these matrices may be burdensome. As such, there is a growing body of literature that seeks to lower the cost of spatial data analysis while still providing useful results. Here, we contribute three new methods to this literature and apply them to materials and environmental science problems.The first project explores location measurement error in the context of Scanning Transmission Electron Microscopy (STEM), which can directly image the atomic structure of materials. When properly aligned, STEM images of crystalline materials display projected columns of atoms. The local relationships between the intensities and distances of these projected atom columns can inform our understanding of structure-property relationships to ultimately improve the materials. Measurement error in the atom column locations can, however, introduce bias into parameter estimates. Here, we create a spatial Bayesian hierarchical model that treats the locations as parameters to account for measurement error, and lower the computational burden by approximating the likelihood using a non-contiguous block design around the atom columns. We conduct a simulation study and analyze real data to compare our model to standard spatial and non-spatial models. The results show our method corrects the bias in the parameter of interest, drastically improving upon the standard models.The second and third projects both take advantage of the spectral representation of Gaussian processes to create low-rank approximations of spatial random effects in univariate and multivariate settings, respectively. Spectral methods are important for both theory and computation in spatial data analysis. When data lie on a grid, spectral approaches can take advantage of the discrete Fourier transform for fast computation. If data are not on a grid, then low-rank processes with Fourier basis functions may be sufficient approximations. In our second project, we introduce new approach called Bayesian Random Fourier Frequencies (BRFF). BRFF treats the spectral frequencies as random parameters, which unlike other low-rank methods, allows us to recover the true correlation function of the Gaussian process. We apply this method in simulation to non-gridded continuous and binary data, and in practice to counts of annual poor air quality days in the United States. We compare BRFF to another popular low-rank method, the predictive processes (PP) model. BRFF is faster than PP, and outperforms or matches the predictive performance of the PP model in settings with high numbers of observations.The third and final project extends the low-rank spectral approach of the second project to multivariate data. In multivariate spatial data analysis, we are interested in modeling the spatial correlation for multiple outcomes as well as the cross-correlation between them. We connect the spatial correlation for each outcome via frequencies following an underlying spectral density. We model the cross-correlation as a function of the magnitude of these frequencies by using a convex combination of correlation matrices, allowing for the cross-correlation to vary at different resolutions. Our low-rank method is computationally reasonable and flexible, allowing for different spatial correlation functions for each outcome. We compare our method via simulation study to the Linear Model of Coregionalization (LMC) approach in bivariate and trivariate simulations, as well as to the Bivariate Mat´ern (BM) approach for bivariate simulations. Our model is competitive with LMC, and we use it to make annual mean pollution prediction maps for twelve air pollutants throughout the United States.

ISBN: 9798522954857Subjects--Topical Terms:

3561040
Crystal structure.

Bayesian Methods for Large Spatial Data Sets with Materials and Environmental Science Applications.
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500 $a Source: Dissertations Abstracts International, Volume: 83-02, Section: B.
500 $a Advisor: Reich, Brian.
502 $a Thesis (Ph.D.)--North Carolina State University, 2021.
506 $a This item must not be sold to any third party vendors.
520 $a Prediction and inference for spatially-dependent data quickly become computationally challenging as the number of observations increases. Bayesian hierarchical modeling is popular for spatial data settings, and with it Markov chain Monte Carlo (MCMC) methods. MCMC samplers require repeatedly evaluating the likelihood function, which due to spatial correlation includes performing computationally expensive operations on covariance matrices with dimensions determined by the number of observations. As the number of observations grows, even storing these matrices may be burdensome. As such, there is a growing body of literature that seeks to lower the cost of spatial data analysis while still providing useful results. Here, we contribute three new methods to this literature and apply them to materials and environmental science problems.The first project explores location measurement error in the context of Scanning Transmission Electron Microscopy (STEM), which can directly image the atomic structure of materials. When properly aligned, STEM images of crystalline materials display projected columns of atoms. The local relationships between the intensities and distances of these projected atom columns can inform our understanding of structure-property relationships to ultimately improve the materials. Measurement error in the atom column locations can, however, introduce bias into parameter estimates. Here, we create a spatial Bayesian hierarchical model that treats the locations as parameters to account for measurement error, and lower the computational burden by approximating the likelihood using a non-contiguous block design around the atom columns. We conduct a simulation study and analyze real data to compare our model to standard spatial and non-spatial models. The results show our method corrects the bias in the parameter of interest, drastically improving upon the standard models.The second and third projects both take advantage of the spectral representation of Gaussian processes to create low-rank approximations of spatial random effects in univariate and multivariate settings, respectively. Spectral methods are important for both theory and computation in spatial data analysis. When data lie on a grid, spectral approaches can take advantage of the discrete Fourier transform for fast computation. If data are not on a grid, then low-rank processes with Fourier basis functions may be sufficient approximations. In our second project, we introduce new approach called Bayesian Random Fourier Frequencies (BRFF). BRFF treats the spectral frequencies as random parameters, which unlike other low-rank methods, allows us to recover the true correlation function of the Gaussian process. We apply this method in simulation to non-gridded continuous and binary data, and in practice to counts of annual poor air quality days in the United States. We compare BRFF to another popular low-rank method, the predictive processes (PP) model. BRFF is faster than PP, and outperforms or matches the predictive performance of the PP model in settings with high numbers of observations.The third and final project extends the low-rank spectral approach of the second project to multivariate data. In multivariate spatial data analysis, we are interested in modeling the spatial correlation for multiple outcomes as well as the cross-correlation between them. We connect the spatial correlation for each outcome via frequencies following an underlying spectral density. We model the cross-correlation as a function of the magnitude of these frequencies by using a convex combination of correlation matrices, allowing for the cross-correlation to vary at different resolutions. Our low-rank method is computationally reasonable and flexible, allowing for different spatial correlation functions for each outcome. We compare our method via simulation study to the Linear Model of Coregionalization (LMC) approach in bivariate and trivariate simulations, as well as to the Bivariate Mat´ern (BM) approach for bivariate simulations. Our model is competitive with LMC, and we use it to make annual mean pollution prediction maps for twelve air pollutants throughout the United States.
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650 4 $a Atmospheric chemistry. $3 544140
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