Reduced-Dimension Hierarchical Statistical Models for Spatial and Spatio-Temporal Data

Reduced-Dimension Hierarchical Statistical Models for Spatial and Spatio-Temporal Data

Bibliographic Details
Main Author: Kang, Lei
Language:English
Published: The Ohio State University / OhioLINK 2009
Subjects:
Statistics
Aerosol optical depth (AOD)
Fixed Rank Filtering (FRF)
Fixed Rank Kriging (FRK)
Givens angles
Multi-angle Imaging SpectroRadiometer (MISR) instrument
regional climate models (RCMs)
Spatio-Temporal Random Effects (STRE) model
Online Access:http://rave.ohiolink.edu/etdc/view?acc_num=osu1259168805
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spelling ndltd-OhioLink-oai-etd.ohiolink.edu-osu12591688052021-08-03T05:57:36Z Reduced-Dimension Hierarchical Statistical Models for Spatial and Spatio-Temporal Data Kang, Lei Statistics Aerosol optical depth (AOD) Fixed Rank Filtering (FRF) Fixed Rank Kriging (FRK) Givens angles Multi-angle Imaging SpectroRadiometer (MISR) instrument regional climate models (RCMs) Spatio-Temporal Random Effects (STRE) model <p>Environmental datasets such as those from remote-sensing platforms and sensor networks are often spatial, temporal, and very large or even massive. Analyzing large spatial or spatio-temporal datasets can be challenging and dimension reduction is usually necessary. In this work, we exploit the Spatial Random Effects (SRE) model with a fixed number of known but not necessarily orthogonal (multi-resolutional) spatial basis functions. The SRE model allows a flexible family of nonstationary covariance functions and the fixed number of basis functions results in dimension reduction and thus efficient computation. We propose priors on the parameters of the SRE model in a fully Bayesian framework. These priors are based on the covariance matrix parameterized in terms of Givens angles and eigenvalues, and they recognize the multi-resolutional nature of the basis functions. We compare this Givens-angle prior to other methods in a simulation study, to show its advantages and apply it to a large remote-sensing spatial dataset. We also apply the SRE model with the Givens-angle prior in a Bayesian meta analysis, where outputs from six different regional climate outputs (RCMs) are combined to construct a consensus climate signal with “votes” from each RCM.</p><p>Moreover, we extend the SRE model to the Spatio-Temporal Random Effects (STRE) model for massive spatio-temporal datasets. We explicitly model the measurement error, the non-dynamic fine-scale variation, the dynamic spatial variation, and the trend. The optimal spatio-temporal predictions are derived efficiently through the fixed-rank model and a rapid recursive updating procedure through the Kalman filter. Formulas for optimal smoothing, filtering, and forecasting are derived. The improvement of combining past and current data using the methodology called Fixed Rank Filtering (FRF) to predict the current hidden process of interest, is illustrated with a simulation experiment. The methodology is also applied to a large spatio-temporal remote-sensing dataset.</p> 2009 English text The Ohio State University / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=osu1259168805 http://rave.ohiolink.edu/etdc/view?acc_num=osu1259168805 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.
collection NDLTD
language English
sources NDLTD
topic Statistics
Aerosol optical depth (AOD)
Fixed Rank Filtering (FRF)
Fixed Rank Kriging (FRK)
Givens angles
Multi-angle Imaging SpectroRadiometer (MISR) instrument
regional climate models (RCMs)
Spatio-Temporal Random Effects (STRE) model
spellingShingle Statistics
Aerosol optical depth (AOD)
Fixed Rank Filtering (FRF)
Fixed Rank Kriging (FRK)
Givens angles
Multi-angle Imaging SpectroRadiometer (MISR) instrument
regional climate models (RCMs)
Spatio-Temporal Random Effects (STRE) model
Kang, Lei
Reduced-Dimension Hierarchical Statistical Models for Spatial and Spatio-Temporal Data
author Kang, Lei
author_facet Kang, Lei
author_sort Kang, Lei
title Reduced-Dimension Hierarchical Statistical Models for Spatial and Spatio-Temporal Data
title_short Reduced-Dimension Hierarchical Statistical Models for Spatial and Spatio-Temporal Data
title_full Reduced-Dimension Hierarchical Statistical Models for Spatial and Spatio-Temporal Data
title_fullStr Reduced-Dimension Hierarchical Statistical Models for Spatial and Spatio-Temporal Data
title_full_unstemmed Reduced-Dimension Hierarchical Statistical Models for Spatial and Spatio-Temporal Data
title_sort reduced-dimension hierarchical statistical models for spatial and spatio-temporal data
publisher The Ohio State University / OhioLINK
publishDate 2009
url http://rave.ohiolink.edu/etdc/view?acc_num=osu1259168805
work_keys_str_mv AT kanglei reduceddimensionhierarchicalstatisticalmodelsforspatialandspatiotemporaldata
_version_ 1719428426270507008

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