Thesis (M. Land Res. Sc.)--University of Queensland, 2002. / Includes bibliographical references.

In recent years, the application of resampling methods to dependent data, such as time series or spatial data, has been a growing field in the study of statistics. In this dissertation, we discuss two such applications. In spatial statistics, the reliability of Kriging prediction methods relies on the observations coming from an underlying Gaussian process. When the observed data set is not from a multivariate Gaussian distribution, but rather is a transformation of Gaussian data, Kriging methods can produce biased predictions. Bootstrap resampling methods present a potential bias correction. We propose a parametric bootstrap methodology for the calculation of either a multiplicative or additive bias correction factor when dealing with Trans-Gaussian data. Furthermore, we investigate the asymptotic properties of the new bootstrap based predictors. Finally, we present the results for both simulated and real world data. In time series analysis, the estimation of covariance parameters is often of utmost importance. Furthermore, the understanding of the distributional behavior of parameter estimates, particularly the variance, is useful but often difficult. Block bootstrap methods have been particularly useful in such analyses. We introduce a new procedure for the estimation of covariance parameters for replicated time series data.

This thesis addresses spatial interpolation and temporal prediction using air pollution data by several space-time modelling approaches. Firstly, we implement the dynamic linear modelling (DLM) approach in spatial interpolation and find various potential problems with that approach. We develop software to implement our approach. Secondly, we implement a Bayesian spatial prediction (BSP) approach to model spatio-temporal ground-level ozone fields and compare the accuracy of that approach with that of the DLM. Thirdly, we develop a Bayesian version empirical orthogonal function (EOF) method to incorporate the uncertainties due to temporally varying spatial process, and the spatial variations at broad- and fine- scale. Finally, we extend the BSP into the DLM framework to develop a unified Bayesian spatio-temporal model for univariate and multivariate responses. The result generalizes a number of current approaches in this field.

This thesis addresses spatial interpolation and temporal prediction using air pollution data by several space-time modelling approaches. Firstly, we implement the dynamic linear modelling (DLM) approach in spatial interpolation and find various potential problems with that approach. We develop software to implement our approach. Secondly, we implement a Bayesian spatial prediction (BSP) approach to model spatio-temporal ground-level ozone fields and compare the accuracy of that approach with that of the DLM. Thirdly, we develop a Bayesian version empirical orthogonal function (EOF) method to incorporate the uncertainties due to temporally varying spatial process, and the spatial variations at broad- and fine- scale. Finally, we extend the BSP into the DLM framework to develop a unified Bayesian spatio-temporal model for univariate and multivariate responses. The result generalizes a number of current approaches in this field.

This thesis addresses spatial interpolation and temporal prediction using air pollution data by several space-time modelling approaches. Firstly, we implement the dynamic linear modelling (DLM) approach in spatial interpolation and find various potential problems with that approach. We develop software to implement our approach. Secondly, we implement a Bayesian spatial prediction (BSP) approach to model spatio-temporal ground-level ozone fields and compare the accuracy of that approach with that of the DLM. Thirdly, we develop a Bayesian version empirical orthogonal function (EOF) method to incorporate the uncertainties due to temporally varying spatial process, and the spatial variations at broad- and fine- scale. Finally, we extend the BSP into the DLM framework to develop a unified Bayesian spatio-temporal model for univariate and multivariate responses. The result generalizes a number of current approaches in this field. / Science, Faculty of / Statistics, Department of / Graduate

For a stationary two dimensional random field, we utilize the classical Kolmogorov-Wiener theory to develop prediction methodology which requires minimal assumptions on the dependence structure of the random field. We also provide solutions for several non-standard prediction problems which deals with the "modified past," in which a finite number of observations are added to the past. These non-standard prediction problems are motivated by the network site selection in the environmental and geostatistical applications. Unlike the time series situation, the prediction results for random fields seem to be expressible only in terms of the moving average parameters, and attempts to express them in terms of the autoregressive parameters lead to a new and mysterious projection operator which captures the nature of edge-effects. We put forward an approach for estimating the predictor coefficients by carrying out an extension of the exponential models. Through simulation studies and real data example, we demonstrate the impressive performance of our prediction method. To the best of our knowledge, the proposed method is the first to deliver a unified framework for forecasting random fields both in the time and spectral domain without making a subjective choice of the covariance structure. Finally, we focus on the estimation of the hurst parameter for long range dependence stationary random fields, which draws its motivation from applications in the environmental and atmospheric processes. Current methods for estimation of the Hurst parameter include parametric models like fractional autoregressive integrated moving average models, and semiparametric estimators which are either inefficient or inconsistent. We propose a novel semiparametric estimator based on the fractional exponential spectrum. We develop three data-driven methods which can automatically select the optimal model order for the fractional exponential models. Extensive simulation studies and analysis of Mercer and Hall?s wheat data are used to illustrate the performance of the proposed estimator and model order selection criteria. The results show that our estimator outperforms existing estimators, including the GPH (Geweke and Porter-Hudak) estimator. We show that the proposed estimator is consistent, works for different definitions of long range dependent random fields, is computationally simple and is not susceptible to model misspecification or poor efficiency.

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This thesis focuses on the developing of statistical methodology in reliability and quality engineering, and to assist the decision-makings at enterprise level, process level, and product level. In Chapter II, we propose a multi-level statistical modeling strategy to characterize data from spatial logistics systems. The model can support business decisions at different levels. The information available from higher hierarchies is incorporated into the multi-level model as constraint functions for lower hierarchies. The key contributions include proposing the top-down multi-level spatial models which improve the estimation accuracy at lower levels; applying the spatial smoothing techniques to solve facility location problems in logistics. In Chapter III, we propose methods for modeling system service reliability in a supply chain, which may be disrupted by uncertain contingent events. This chapter applies an approximation technique for developing first-cut reliability analysis models. The approximation relies on multi-level spatial models to characterize patterns of store locations and demands. The key contributions in this chapter are to bring statistical spatial modeling techniques to approximate store location and demand data, and to build system reliability models entertaining various scenarios of DC location designs and DC capacity constraints. Chapter IV investigates the power law process, which has proved to be a useful tool in characterizing the failure process of repairable systems. This chapter presents a procedure for detecting and estimating a mixture of conforming and nonconforming systems. The key contributions in this chapter are to investigate the property of parameter estimation in mixture repair processes, and to propose an effective way to screen out nonconforming products. The key contributions in Chapter V are to propose a new method to analyze heavily censored accelerated life testing data, and to study the asymptotic properties. This approach flexibly and rigorously incorporates distribution assumptions and regression structures into estimating equations in a nonparametric estimation framework. Derivations of asymptotic properties of the proposed method provide an opportunity to compare its estimation quality to commonly used parametric MLE methods in the situation of mis-specified regression models.

Wind generating resources have been increasing more rapidly than any other renewable generating resources. Wind power forecasting is an important issue for deploying higher wind power penetrations on power grids. The existing work on power output forecasting for wind farms has focused on the temporal issues. As wind farm outputs depend on natural wind resources that vary over space and time, spatial analysis and modeling is also needed. Predictions about suitability for locating new wind generating resources can be performed using spatial modeling. In this dissertation, we propose a new approach to spatial prediction of wind farm outputs for grid integration based on Kriging techniques. First, we investigate the characteristics of wind farm outputs. Wind power is variable, uncontrollable, and uncertain compared to traditional generating resources. In order to understand the characteristics of wind power outputs, we study the variability of wind farm outputs using correlation analysis. We estimate the Power Spectrum Density (PSD) from empirical data. Following Apt[1], we classify the estimated PSD into four frequency ranges having different slopes. We subsequently focus on phenomena relating to the slope of the estimated PSD at a low frequency range because our spatial prediction is based on the period over daily to monthly timescales. Since most of the energy is in the lower frequency components (the second, third, and fourth slope regions have much lower spectral density than the first), the conclusion is that the dominant issues regarding energy will be captured by the low frequency behavior. Consequently, most of the issues regarding energy (at least at longer timescales) will be captured by the first slope, since relatively little energy is in the other regions. We propose the slope estimation model of new wind farm production. When the existing wind farms are highly correlated and the slope of each wind farm is estimated at a low frequency range, we can predict the slope with low frequency components of a new wind farm through the proposed spatial interpolation techniques. Second, we propose a new approach, based on Kriging techniques, to predict wind farm outputs. We introduce Kriging techniques for spatial prediction, modeling semivariograms for spatial correlation, and mathematical formulation of the Kriging system. The aim of spatial modeling is to calculate a target value of wind production at unmeasured or new locations based on the existing values that have already been measured at locations considering the spatial correlation relationship between measured values. We propose the multivariate spatial approach based on Co-Kriging to consider multiple variables for better prediction. Co-Kriging is a multivariate spatial technique to predict spatially distributed and correlated variables and it adds auxiliary variables to a single variable of interest at unmeasured locations. Third, we develop the Augmented Kriging-based Model, to predict power outputs at unmeasured or new wind farms that are geographically distributed in a region. The proposed spatial prediction model consists of three stages: collection of wind farm data for spatial analysis, performance of spatial analysis and prediction, and verification of the predicted wind farm outputs. The proposed spatial prediction model provides the univariate prediction based on Universal Kriging techniques and the multivariate prediction based on Universal and Co-Kriging techniques. The proposed multivariate prediction model considers multiple variables: the measured wind power output as a primary variable and the type or hub height of wind turbines, or the slope with low frequency components as a secondary variable. The multivariate problem is solved by Co-Kriging techniques. In addition, we propose $p$ indicator as a categorical variable considering the data configuration of wind farms connected to electrical power grids. Although the interconnection voltage does not influence the wind regime, it does affect transmission system issues such as the level of curtailments, which, in turn, affect power production. Voltage level is therefore used as a proxy to the effect of the transmission system on power output. The Augmented Kriging-based Model (AKM) is implemented in the R system environments and the latest Gstat library is used for the implementation of the AKM. Fourth, we demonstrate the performance of the proposed spatial prediction model based on Kriging techniques in the context of the McCamey and Central areas of ERCOT CREZ. Spatial prediction of ERCOT wind farms is performed in daily, weekly, and monthly time scales for January to September 2009. These time scales all correspond to the lowest frequency range of the estimated PSD. We propose a merit function to provide practical information to find optimal wind farm sites based on spatial wind farm output prediction, including correlation with other wind farms. Our approach can predict what will happen when a new wind farm is added at various locations. Fifth, we propose the Augmented Sequential Outage Checker (ASOC) as a possible approach to study the transmission system, including grid integration of wind-powered generation resources. We analyze cascading outages caused by a combination of thermal overloads, low voltages, and under-frequencies following an initial disturbance using the ASOC. / text

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