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Geographic information systems (GISs) are a highly influential tool in today's society, and are used in a growing number of applications, including planning, engineering, land management,and environmental study. As the field of GISs continues to expand, it is very important to observe and account for the error that is unavoidable in computerized maps. Currently, both statistical and non-statistical models are available to do so, although there is very little implementation of these methods. In this dissertation, I have focused on improving the methods available for analyzing error in GIS vector data. In particular, I am incorporating Bayesian methodology into the currently popular G-band error model through the inclusion of a prior distribution on point locations. This has the advantage of working well with a small number of points, and being able to synthesize information from multiple sources. I have also calculated the boundary of the confidence region explicitly, which has not been done before, and this will aid in the eventual inclusion of these methods in GIS software. Finally, I have included a statistical point deletion algorithm, designed for use in situations where map precision has surpassed map accuracy. It is very similar to the Douglas-Peucker algorithm, and can be used in a general line simplification situation, but has the advantage that it works with the error information that is already known about a map rather than adding unknown error. These contributions will make it more realistic for GIS users to implement techniques for error analysis. Ph. D.

Bayesian optimal designs have received increasing attention in recent years, especially in biomedical and clinical trials. Bayesian design procedures can utilize the available prior information of the unknown parameters so that a better design can be achieved. However, a difficulty in dealing with the Bayesian design is the lack of efficient computational methods. In this research, a hybrid computational method, which consists of the combination of a rough global optima search and a more precise local optima search, is proposed to efficiently search for the Bayesian D-optimal designs for multi-variable generalized linear models. Particularly, Poisson regression models and logistic regression models are investigated. Designs are examined for a range of prior distributions and the equivalence theorem is used to verify the design optimality. Design efficiency for various models are examined and compared with non-Bayesian designs. Bayesian D-optimal designs are found to be more efficient and robust than non-Bayesian D-optimal designs. Furthermore, the idea of the Bayesian sequential design is introduced and the Bayesian two-stage D-optimal design approach is developed for generalized linear models. With the incorporation of the first stage data information into the second stage, the two-stage design procedure can improve the design efficiency and produce more accurate and robust designs. The Bayesian two-stage D-optimal designs for Poisson and logistic regression models are evaluated based on simulation studies. The Bayesian two-stage optimal design approach is superior to the one-stage approach in terms of a design efficiency criterion. Ph. D.

The goal of this research is to construct causal gene networks for genetical genomics experiments using expression Quantitative Trait Loci (eQTL) mapping and Structural Equation Modeling (SEM). Unlike Bayesian Networks, this approach is able to construct cyclic networks, while cyclic relationships are expected to be common in gene networks. Reconstruction of gene networks provides important knowledge about the molecular basis of complex human diseases and generally about living systems. In genetical genomics, a segregating population is expression profiled and DNA marker genotyped. An Encompassing Directed Network (EDN) of causal regulatory relationships among genes can be constructed with eQTL mapping and selection of candidate causal regulators. Several eQTL mapping approaches and local structural models were evaluated in their ability to construct an EDN. The edges in an EDN correspond to either direct or indirect causal relationships, and the EDN is likely to contain cycles or feedback loops. We implemented SEM with genetics algorithms to produce sub-models of the EDN containing fewer edges and being well supported by the data. The EDN construction and sparsification methods were tested on a yeast genetical genomics data set, as well as the simulated data. For the simulated networks, the SEM approach has an average detection power of around ninety percent, and an average false discovery rate of around ten percent. Ph. D.

Implementation of the Clean Water Act requires agencies to monitor aquatic sites on a regular basis and evaluate the quality of these sites. Sites are evaluated individually even though there may be numerous sites within a watershed. In some cases, sampling frequency is inadequate and the evaluation of site quality may have low reliability. This dissertation evaluates testing procedures for determination of site quality based on modelbased procedures that allow for other sites to contribute information to the data from the test site. Test procedures are described for situations that involve multiple measurements from sites within a region and single measurements when stressor information is available or when covariates are used to account for individual site differences. Tests based on analysis of variance methods are described for fixed effects and random effects models. The proposed model-based tests compare limits (tolerance limits or prediction limits) for the data with the known standard. When the sample size for the test site is small, using model-based tests improves the detection of impaired sites. The effects of sample size, heterogeneity of variance, and similarity between sites are discussed. Reference-based standards and corresponding evaluation of site quality are also considered. Regression-based tests provide methods for incorporating information from other sites when there is information on stressors or covariates. Extension of some of the methods to multivariate biological observations and stressors is also discussed. Redundancy analysis is used as a graphical method for describing the relationship between biological metrics and stressors. A clustering method for finding stressor-response relationships is presented and illustrated using data from the Mid-Atlantic Highlands. Multivariate elliptical and univariate regions for assessment of site quality are discussed. Ph. D.

In response surface methodology, the central composite design is the most popular choice for fitting a second order model. The choice of the distance for the axial runs, alpha, in a central composite design is very crucial to the performance of the design. In the literature, there are plenty of discussions and recommendations for the choice of alpha, among which a rotatable alpha and an orthogonal blocking alpha receive the greatest attention. Box and Hunter (1957) discuss and calculate the values for alpha that achieve rotatability, which is a way to stabilize prediction variance of the design. They also give the values for alpha that make the design orthogonally blocked, where the estimates of the model coefficients remain the same even when the block effects are added to the model. In the last ten years, people have begun to realize the importance of a split-plot structure in industrial experiments. Constructing response surface designs with a split-plot structure is a hot research area now. In this dissertation, Box and Hunters' choice of alpha for rotatablity and orthogonal blocking is extended to central composite designs with a split-plot structure. By assigning different values to the axial run distances of the whole plot factors and the subplot factors, we propose two-strata rotatable splitplot central composite designs and orthogonally blocked split-plot central composite designs. Since the construction of the two-strata rotatable split-plot central composite design involves an unknown variance components ratio d, we further study the robustness of the two-strata rotatability on d through simulation. Our goal is to provide practical recommendations for the value of the design parameter alpha based on the philosophy of traditional response surface methodology. Ph. D.

We develop statistical methods for evaluation of regional variation of ecological stressor-response relationships, and regional variation in temporal profiles of water quality, for application to data from monitoring stations on bodies of water. To evaluate regional variation in regression relationships, we use model-based clustering procedures with class-specific regression models. Units for clustering are taken to be basins, or combinations of basins and ecoregions. We rely on a Bayesian formulation and sample the posterior distribution using a Markov chain Monte Carlo algorithm. Two general approaches to the label-switching problem are considered, each leading to procedures that we apply in data analyses. Two applications are presented. We explore some relationships among priors with a Dirichlet distribution for class probabilities. We compare two rank-based criteria for grouping stations according to similarities in temporal profiles. The two criteria are illustrated in a hierarchical cluster analysis based on measurements of a water quality variable. Ph. D.

Environmental studies often employ data collected over large spatial regions. Although it is convenient, the conventional single model approach may fail to accurately describe the relationships between variables. Two alternative modeling approaches are available: one applies separate models for different regions; the other applies hierarchical models. The separate modeling approach has two major difficulties: first, we often do not know the underlying clustering structure of the entire data; second, it usually ignores possible dependence among clusters. To deal with the first problem, we propose a model-based clustering method to partition the entire data into subgroups according to the empirical relationships between the response and the predictors. To deal with the second, we propose Bayesian hierarchical models. We illustrate the use of the Bayesian hierarchical model under two situations. First, we apply the hierarchical model based on the empirical clustering structure. Second, we integrate the model-based clustering result to help determine the clustering structure used in the hierarchical model. The nature of the problem is classification since the response is categorical rather than continuous and logistic regression models are used to model the relationship between variables. Ph. D.

Oxidative stress is a harmful condition in a cell, tissue, or organ, caused by an imbalance between reactive oxygen species or other oxidants and the capacity of antioxidant defense systems to remove them. These oxidants cause wide-ranging damage to macromolecules, including proteins, lipids, DNA and carbohydrates. Oxidative stress is an important pathophysiologic component of a number of diseases, such as Alzheimer's disease, diabetes and certain cancers. Cells contain effective defense mechanisms to respond to oxidative stress. Despite much accumulated knowledge about these responses, their kinetics, especially the kinetics of early responses is still not clearly understood. The Yap1 transcription factor is crucial for the normal response to a variety of stress conditions including oxidative stress. Previous studies on Yap1 regulation started to measure gene expression profile at least 20 minutes after the induction of oxidative stress. Genes and pathways regulated by Yap1 in early oxidative stress response (within 20 minutes) were not identified in these studies. Here we study the kinetics of early oxidative stress response induced by the cumene hydroperoxide (CHP) in Saccharomyces cerevisiae wild type and yap1 mutant. Gene expression profiles after exposure to CHP were obtained in controlled conditions using Affymetrix Yeast Genome S98 arrays. The oxidative stress response was measured at 8 time points along 120 minutes after the addition of CHP, with the earliest time point at 3 minute after the exposure. Statistical analysis methods, including ANOVA, k-means clustering analysis, and pathway analysis were used to analyze the data. The results from this study provide a dynamic resolution of the oxidative stress responses in S. cerevisiae, and contribute to a richer understanding of the antioxidant defense systems. It also provides a global view of the roles that Yap1 plays under normal and oxidative stress conditions. Ph. D.

Modeling the complex relationships between habitat characteristics and a species' habitat preferences pose many difficult problems for ecological researchers. These problems are complicated further when information is collected over a range of time or space. Additionally, the variety of factors affecting these choices is difficult to understand and even more difficult to accurately collect information about. In light of these concerns, we evaluate the performance of current standard habitat preference models that are based on Bayesian methods and then present some extensions and supplements to those methods that prove to be very useful. More specifically, we demonstrate the value of extending the standard Bayesian hierarchical model using finite mixture model methods. Additionally, we demonstrate that an extension of the Bayesian hierarchical changepoint model to allow for estimating multiple changepoints simultaneously can be very informative when applied to data about multiple habitat locations or species. These models allow the researcher to compare the sites or species with respect to a very specific ecological question and consequently provide definitive answers that are often not available with more commonly used models containing many explanatory factors. Throughout our work we use a complex data set containing information about horseshoe crab spawning habitat preferences in the Delaware Bay over a five-year period. These data epitomize some of the difficult issues inherent to studying habitat preferences. The data are collected over time at many sites, have missing observations, and include explanatory variables that, at best, only provide surrogate information for what researchers feel is important in explaining spawning preferences throughout the bay. We also looked at a smaller data set of freshwater mussel habitat selection preferences in relation to bridge construction on the Kennerdell River in Western Pennsylvania. Together, these two data sets provided us with insight in developing and refining the methods we present. They also help illustrate the strengths and weaknesses of the methods we discuss by assessing their performance in real situations where data are inevitably complex and relationships are difficult to discern. Ph. D.

Dual response surface methodology (Vining and Myers (1990)) has been successfully used as a cost-effective approach to improve the quality of products and processes since Taguchi (Tauchi (1985)) introduced the idea of robust parameter design on the quality improvement in the United States in mid-1980s. The original procedure is to use the mean and the standard deviation of the characteristic to form a dual response system in linear model structure, and to estimate the model coefficients using least squares methods. In this dissertation, a Bayesian hierarchical approach is proposed to model the dual response system so that the inherent hierarchical variance structure of the response can be modeled naturally. The Bayesian model is developed for both univariate and multivariate dual response surfaces, and for both fully replicated and partially replicated dual response surface designs. To evaluate its performance, the Bayesian method has been compared with the original method under a wide range of scenarios, and it shows higher efficiency and more robustness. In applications, the Bayesian approach retains all the advantages provided by the original dual response surface modelling method. Moreover, the Bayesian analysis allows inference on the uncertainty of the model parameters, and thus can give practitioners complete information on the distribution of the characteristic of interest. Ph. D.

In cluster analysis, a fundamental problem is to determine the best estimate of the number of clusters, which has a deterministic effect on the clustering results. However, a limitation in current applications is that no convincingly acceptable solution to the best-number-of-clusters problem is available due to high complexity of real data sets. In this dissertation, we tackle this problem of estimating the number of clusters, which is particularly oriented at processing very complicated data which may contain multiple types of cluster structure. Two new methods of choosing the number of clusters are proposed which have been shown empirically to be highly effective given clear and distinct cluster structure in a data set. In addition, we propose a sequential type of clustering approach, called multi-layer clustering, by combining these two methods. Multi-layer clustering not only functions as an efficient method of estimating the number of clusters, but also, by superimposing a sequential idea, improves the flexibility and effectiveness of any arbitrary existing one-layer clustering method. Empirical studies have shown that multi-layer clustering has higher efficiency than one layer clustering approaches, especially in detecting clusters in complicated data sets. The multi-layer clustering approach has been successfully implemented in clustering the WTCHP microarray data and the results can be interpreted very well based on known biological knowledge. Choosing an appropriate clustering method is another critical step in clustering. K-means clustering is one of the most popular clustering techniques used in practice. However, the k-means method tends to generate clusters containing a nearly equal number of objects, which is referred to as the ``equal-size'' problem. We propose a clustering method which competes with the k-means method. Our newly defined method is aimed at overcoming the so-called ``equal-size'' problem associated with the k-means method, while maintaining its advantage of computational simplicity. Advantages of the proposed method over k-means clustering have been demonstrated empirically using simulated data with low dimensionality. Ph. D.

This research is motivated by an issue frequently encountered in environmental water quality evaluation. Many times, the sample size of water monitoring data is too small to have adequate power. Here, we present a Bayesian power prior approach by incorporating the current data and historical data and/or the data collected at neighboring stations to make stronger statistical inferences on the parameters of interest. The elicitation of power prior distributions is based on the availability of historical data, and is realized by raising the likelihood function of the historical data to a fractional power. The power prior Bayesian analysis has been proven to be a useful class of informative priors in Bayesian inference. In this dissertation, we propose a modified approach to constructing the joint power prior distribution for the parameter of interest and the power parameter. The power parameter, in this modified approach, quantifies the heterogeneity between current and historical data automatically, and hence controls the influence of historical data on the current study in a sensible way. In addition, the modified power prior needs little to ensure its propriety. The properties of the modified power prior and its posterior distribution are examined for the Bernoulli and normal populations. The modified and the original power prior approaches are compared empirically in terms of the mean squared error (MSE) of parameter estimates as well as the behavior of the power parameter. Furthermore, the extension of the modified power prior to multiple historical data sets is discussed, followed by its comparison with the random effects model. Several sets of water quality data are studied in this dissertation to illustrate the implementation of the modified power prior approach with normal and Bernoulli models. Since the power prior method uses information from sources other than current data, it has advantages in terms of power and estimation precision for decisions with small sample sizes, relative to methods that ignore prior information. Ph. D.

In many industrial experiments, completely randomized designs (CRDs) are impractical due to restrictions on randomization, or the existence of one or more hard-to-change factors. Under these situations, split-plot experiments are more realistic. The two separate randomizations in split-plot experiments lead to different error structure from in CRDs, and hence this affects not only response modeling but also the choice of design. In this dissertation, two graphical tools, three-dimensional variance dispersion graphs (3-D VDGs) and fractions of design space (FDS) plots are adapted for split-plot designs (SPDs). They are used for examining and comparing different variations of central composite designs (CCDs) with standard, V- and G-optimal factorial levels. The graphical tools are shown to be informative for evaluating and developing strategies for improving the prediction performance of SPDs. The overall cost of a SPD involves two types of experiment units, and often each individual whole plot is more expensive than individual subplot and measurement. Therefore, considering only the total number of observations is likely not the best way to reflect the cost of split-plot experiments. In this dissertation, cost formulation involving the weighted sum of the number of whole plots and the total number of observations is discussed and the three cost adjusted optimality criteria are proposed. The effects of considering different cost scenarios on the choice of design are shown in two examples. Often in practice it is difficult for the experimenter to select only one aspect to find the optimal design. A realistic strategy is to select a design with good balance for multiple estimation and prediction criteria. Variations of the CCDs with the best cost-adjusted performance for estimation and prediction are studied for the combination of D-, G- and V-optimality criteria and each individual criterion. Ph. D.

Graphical summaries are becoming important tools for evaluating designs. The need to compare designs in term of their prediction variance properties advanced this development. A recent graphical tool, the Fraction of Design Space plot, is useful to calculate the fraction of the design space where the scaled prediction variance (SPV) is less than or equal to a given value. In this dissertation we adapt FDS plots, to study three specific design problems: robustness to model assumptions, robustness to measurement error and design properties for generalized linear models (GLM). This dissertation presents a graphical method for examining design robustness related to the SPV values using FDS plots by comparing designs across a number of potential models in a pre-specified model space. Scaling the FDS curves by the G-optimal bounds of each model helps compare designs on the same model scale. FDS plots are also adapted for comparing designs under the GLM framework. Since parameter estimates need to be specified, robustness to parameter misspecification is incorporated into the plots. Binomial and Poisson examples are used to study several scenarios. The third section involves a special type of response surface designs, mixture experiments, and deals with adapting FDS plots for two types of measurement error which can appear due to inaccurate measurements of the individual mixture component amounts. The last part of the dissertation covers mixture experiments for the GLM case and examines prediction properties of mixture designs using the adapted FDS plots. Ph. D.

Recent advancements in the general child disaster literature underscore the important role of coping in children's postdisaster adjustment. Religious coping in children, a potentially important category of coping strategies, has received little attention until recent years. Moreover, its role in the context of post fire adjustment has not been studied. The present study examined the psychometric soundness of the Religious Coping Activities Scale (RCAS; Pargament et al., 1990) in children and adolescents and explored its utility in predicting children's religious coping over time: moreover, the study evaluated its role in predicting PTSD symptomatology over an extended period of time. This investigation included 140 children and adolescents (ages 8-18). Factor analyses of the RCAS revealed a 6-factor solution very similar to the factor structure in the original study. This finding suggests that the RCAS is a promising instrument to measure children's religious coping efforts. Hypotheses concerning the prediction of children's religious coping were only partially supported. Regression analyses indicated mixed findings in terms of the contributions of selected variables to the prediction of children's Spiritually Based Coping and Religious Discontent. Overall, the regression model predicted Religious Discontent better than Spiritually Based Coping. A mixed-effects regression model and hierarchical regression analyses were both employed to examine the role of children's religious coping in predicting short-term and long-term PTSD symptomatology following the residential fires. Results from the mixed-effects regression indicated that loss, time since the fire, child's age, race, and race by age interaction significantly predicted children's PTSD symptoms over time. However, time specific regression analyses revealed different predictive power of the variables across the three assessment waves. Specifically, analyses with Time 1 data revealed the same findings as did the mixed-effects model, except that time since the fire was not a significant predictor in this analysis. General coping strategies appeared to be the only salient predictors for PTSD at Time 2. Finally, Religious Discontent appeared to be negatively related to PTSD at a later time. Ph. D.

The copious information generated from transcriptomes gives us an opportunity to learn biological processes as integrated systems; however, due to numerous sources of variation, high dimensions of data structure, various levels of data quality, and different formats of the inputs, dissecting and interpreting such data presents daunting challenges to scientists. The goal of this research is to provide improved and new statistical tools for analyzing transcriptomes data to identify gene expression patterns for classifying samples, to discover regulatory gene networks using natural genetic perturbations, to develop statistical methods for model fitting and comparison of biochemical networks, and eventually to advance our capability to understand the principles of biological processes at the system level. Ph. D.

In the field of linear regression analysis, a single outlier can dramatically influence ordinary least squares estimation while low-breakdown procedures such as M regression and bounded influence regression may be unable to combat a small percentage of outliers. A high-breakdown procedure such as least trimmed squares (LTS) regression can accommodate up to 50% of the data (in the limit) being outlying with respect to the general trend. Two available one-step improvement procedures based on LTS are Mallows 1-step (M1S) regression and Schweppe 1-step (S1S) regression (the current state-of-the-art method). Issues with these methods include (1) computational approximations and sub-sampling variability, (2) dramatic coefficient sensitivity with respect to very slight differences in initial values, (3) internal instability when determining the general trend and (4) performance in low-breakdown scenarios. A new high-breakdown regression procedure is introduced that addresses these issues, plus offers an insightful summary regarding the presence and structure of multivariate outliers. This proposed method blends a cluster analysis phase with a controlled bounded influence regression phase, thereby referred to as cluster-based bounded influence regression, or CBI. Representing the data space via a special set of anchor points, a collection of point-addition OLS regression estimators forms the basis of a metric used in defining the similarity between any two observations. Cluster analysis then yields a main cluster "halfset" of observations, with the remaining observations becoming one or more minor clusters. An initial regression estimator arises from the main cluster, with a multiple point addition DFFITS argument used to carefully activate the minor clusters through a bounded influence regression framework. CBI achieves a 50% breakdown point, is regression equivariant, scale equivariant and affine equivariant and distributionally is asymptotically normal. Case studies and Monte Carlo studies demonstrate the performance advantage of CBI over S1S and the other high breakdown methods regarding coefficient stability, scale estimation and standard errors. A dendrogram of the clustering process is one graphical display available for multivariate outlier detection. Overall, the proposed methodology represents advancement in the field of robust regression, offering a distinct philosophical viewpoint towards data analysis and the marriage of estimation with diagnostic summary. Ph. D.

Microarray experiments are used to perform gene expression profiling on a large scale. E- and A-optimality of mixed designs was established for experiments with up to 26 different varieties and with the restriction that the number of arrays available is equal to the number of varieties. Because the IBD setting only allows for a single blocking factor (arrays), the search for optimal designs was extended to the Row-Column Design (RCD) setting with blocking factors dye (row) and array (column). Relative efficiencies of these designs were further compared under analysis of variance (ANOVA) models. We also compared the performance of classification analysis for the interwoven loop and the replicated reference designs under four scenarios. The replicated reference design was favored when gene-specific sample variation was large, but the interwoven loop design was preferred for large variation among biological replicates. We applied mixed model methodology to detection and estimation of gene differential expression. For identification of differential gene expression, we favor contrasts which include both variety main effects and variety by gene interactions. In terms of t-statistics for these contrasts, we examined the equivalence between the one- and two-step analyses under both fixed and mixed effects models. We analytically established conditions for equivalence under fixed and mixed models. We investigated the difference of approximation with the two-step analysis in situations where equivalence does not hold. The significant difference between the one- and two-step mixed effects model was further illustrated through Monte Carlo simulation and three case studies. We implemented the one-step analysis for mixed models with the ASREML software. Ph. D.

Ecological data is often fraught with many problems such as Missing Data and Spatial Correlation. In this dissertation we use a data set collected by the Ohio EPA as motivation for studying techniques to address these problems. The data set is concerned with the benthic health of Ohio's waterways. A new method for incorporating covariate structure and missing data mechanisms into missing data analysis is considered. This method allows us to detect relationships other popular methods do not allow. We then further extend this method into model selection. In the special case where the unobserved covariates are assumed normally distributed we use the Bayesian Model Averaging method to average the models, select the highest probability model and do variable assessment. Accuracy in calculating the posterior model probabilities using the Laplace approximation and an approximation based on the Bayesian Information Criterion (BIC) are explored. It is shown that the Laplace approximation is superior to the BIC based approximation using simulation. Finally, Hierarchical Spatial Linear Models are considered for the data and we show how to combine analysis which have spatial correlation within and between clusters. Ph. D.

Circular or Angular data occur in many fields of applied statistics. A common problem of interest in circular data is estimating a preferred direction and its corresponding distribution. This problem is complicated by the so-called wrap-around effect, which exists because there is no minimum or maximum on the circle. The usual statistics employed for linear data are inappropriate for directional data, as they do not account for the circular nature of directional data. Common choices for summarizing the preferred direction are the sample circular mean, and sample circular median. A newly proposed circular analog of the Hodges-Lehmann estimator is proposed, as an alternative estimate of preferred direction. The new measure of preferred direction is a robust compromise between circular mean and circular median. Theoretical results show that the new measure of preferred direction is asymptotically more efficient than the circular median and that its asymptotic efficiency relative to the circular mean is quite comparable. Descriptions of how to use the methods for constructing confidence intervals and testing hypotheses are provided. Simulation results demonstrate the relative strengths and weaknesses of the new approach for a variety of distributions. Ph. D.

Optimal experimental designs for generalized linear models have received increasing attention in recent years. Yet, most of the current research focuses on binary data models especially the one-variable first-order logistic regression model. This research extends this topic to count data models. The primary goal of this research is to develop efficient and robust experimental designs for the Poisson regression model in toxicity studies. D-optimal designs for both the one-toxicant second-order model and the two-toxicant interaction model are developed and their dependence upon the model parameters is investigated. Application of the D-optimal designs is very limited due to the fact that these optimal designs, in terms of ED levels, depend upon the unknown parameters. Thus, some practical designs like equally spaced designs and conditional D-optimal designs, which, in terms of ED levels, are independent of the parameters, are studied. It turns out that these practical designs are quite efficient when the design space is restricted. Designs found in terms of ED levels like D-optimal designs are not robust to parameters misspecification. To deal with this problem, sequential designs are proposed for Poisson regression models. Both fully sequential designs and two-stage designs are studied and they are found to be efficient and robust to parameter misspecification. For experiments that involve two or more toxicants, restrictions on the survival proportion lead to restricted design regions dependent on the unknown parameters. It is found that sequential designs perform very well under such restrictions. In most of this research, the log link is assumed to be the true link function for the model. However, in some applications, more than one link functions fit the data very well. To help identify the link function that generates the data, experimental designs for discrimination between two competing link functions are investigated. T-optimal designs for discrimination between the log link and other link functions such as the square root link and the identity link are developed. To relax the dependence of T-optimal designs on the model truth, sequential designs are studied, which are found to converge to T-optimal designs for large experiments. Ph. D.

The Design of an experiment involves selection of levels of one or more factor in order to optimize one or more criteria such as prediction variance or parameter variance criteria. Good experimental designs will have several desirable properties. Typically, one can not achieve all the ideal properties in a single design. Therefore, there are frequently several good designs and choosing among them involves tradeoffs. This dissertation contains three different components centered around the area of optimal design: developing a new graphical evaluation technique, discussing designs for non-regular regions for first order models with interaction for the two- and three-factor case, and using the standard designs in the case of generalized linear models (GLM). The Fraction of Design Space (FDS) technique is proposed as a new graphical evaluation technique that addresses good prediction. The new technique is comprised of two tools that give the researcher more detailed information by quantifying the fraction of design space where the scaled predicted variance is less than or equal to any pre-specified value. The FDS technique complements Variance Dispersion Graphs (VDGs) to give the researcher more insight about the design prediction capability. Several standard designs are studied with both methods: VDG and FDS. Many Standard designs are constructed for a factor space that is either a p-dimensional hypercube or hypersphere and any point inside or on the boundary of the shape is a candidate design point. However, some economic, or practical constraints may occur that restrict factor settings and result in an irregular experimental region. For the two- and three-factor case with one corner of the cuboidal design space excluded, three sensible alternative designs are proposed and compared. Properties of these designs and relative tradeoffs are discussed. Optimum experimental designs for GLM depend on the values of the unknown parameters. Several solutions to the dependency of the parameters of the optimality function were suggested in the literature. However, they are often unrealistic in practice. The behavior of the factorial designs, the well-known standard designs of the linear case, is studied for the GLM case. Conditions under which these designs have high G-efficiency are formulated. Ph. D.

Bayesian Model Averaging (BMA) is a new area in modern applied statistics that provides data analysts with an efficient tool for discovering promising models and obtaining esti-mates of their posterior probabilities via Markov chain Monte Carlo (MCMC). These probabilities can be further used as weights for model averaged predictions and estimates of the parameters of interest. As a result, variance components due to model selection are estimated and accounted for, contrary to the practice of conventional data analysis (such as, for example, stepwise model selection). In addition, variable activation probabilities can be obtained for each variable of interest. This dissertation is aimed at connecting BMA and various ramifications of the multivari-ate technique called Reduced-Rank Regression (RRR). In particular, we are concerned with Canonical Correspondence Analysis (CCA) in ecological applications where the data are represented by a site by species abundance matrix with site-specific covariates. Our goal is to incorporate the multivariate techniques, such as Redundancy Analysis and Ca-nonical Correspondence Analysis into the general machinery of BMA, taking into account such complicating phenomena as outliers and clustering of observations within a single data-analysis strategy. Traditional implementations of model averaging are concerned with selection of variables. We extend the methodology of BMA to selection of subgroups of observations and im-plement several approaches to cluster and outlier analysis in the context of the multivari-ate regression model. The proposed algorithm of cluster analysis can accommodate re-strictions on the resulting partition of observations when some of them form sub-clusters that have to be preserved when larger clusters are formed. Ph. D.

The purpose of this research is to examine whether accounting methods for business combinations (purchase and pooling-of-interests accounting) have a different effect on firms' market value of equity in the combination year and thereafter. In particular, after the accounting method is no longer disclosed in the financial statements, does it have an impact on market value of equity of the combined firms because the accounting figures are different? A five-year period subsequent to a particular business combination is used because public companies are not required to disclose the details of the combination for more than three years after the effective date of the combination. This research, thus, tests whether market participants still take into consideration the accounting method of past business combinations when this information is no longer disclosed in the financial statements. In addition to the testing of the impact of the accounting methods, the value-relevance of goodwill amortization is investigated. The sample consisted of 100 U.S. business combination transactions during the period 1985–1995 (77 pooling firms and 23 purchase firms). The results do not indicate that market participants price pooling firms and purchase firms differently at the time of business combinations. The results, in addition, do not confirm that when the details of a particular business combinations do not appear in the financial statements, pooling firms' accounting figures have a more positive effect on security prices than those of purchase firms. It seems that market participant are able, even in the long term, to account for the accounting difference between purchase and pooling-of-interests. Also, goodwill amortization does not appear to be value relevant. Ph. D.

Point processes are common in many physical applications found in engineering and biology. These processes can be observed in one-dimension as a time series or two-dimensions as a spatial point pattern with extensive amounts of literature devoted to their analyses. However, if the observed process is a hybrid of spatial and temporal point process, very few practical methods exist. In such cases, practitioners often remove the temporal component and analyze the spatial dependencies. This marginal spatial analysis may lead to misleading results if time is an important factor in the process. In this dissertation we extend the current analysis of spatial point patterns to include a temporal dimension. First- and second-order intensity measures for analyzing spatiotemporal point patterns are explicitly defined. Estimation of first-order intensities are examined using 3-dimensional smoothing techniques. Conditions for weak stationarity are provided so that subsequent second-order analysis can be conducted. We consider second-order analysis of spatiotemporal point patterns first in the space-time domain through an extension of Ripley's Κ-function. An alternative analysis is given in the frequency domain though construction of a spatiotemporal periodogram. The methodology provided is tested through simulation of spatiotemporal point patterns and by analysis of a real data set. The biological application concerns the estimation of the homerange of groups of the endangered red-cockaded woodpecker in the Fort Bragg area of North Carolina. Monthly or bimonthly point patterns of the bird distribution are analyzed and integrated over a 23 month period. Ph. D.

Discrete optimization problems are defined by a finite set of solutions together with an objective function value assigned to each solution. Local search algorithms provide useful tools for addressing a wide variety of intractable discrete optimization problems. Each such algorithm offers a distinct set of rules to intelligently exploit the solution space with the hope of finding an optimal/near optimal solution using a reasonable amount of computing time. This research studies and analyses randomly generated instances of 3-SATISFIABILITY to gain insights into the structure of the underlying solution space. Two random variables are defined and analyzed to assess the probability that a fixed solution will be assigned a particular objective function value in a randomly generated instance of 3-SATISFIABILITY. Then, a random vector is defined and analyzed to investigate how the solutions in the solution space are distributed over their objective function values. These results are then used to define a stopping criterion for local search algorithms applied to MAX 3-SATISFIABILITY. This research also analyses and compares the effectiveness of two local search algorithms, tabu search and random restart local search, on MAX 3-SATISFIABILITY. Computational results with tabu search and random restart local search on randomly generated instances of 3-SATISFIABILITY are reported. These results suggest that, given a limited computing budget, tabu search offers an effective alternative to random restart local search. On the other hand, these two algorithms yield similar results in terms of the best solution found. The computational results also suggest that for randomly generated instances of 3-SATISFIABILITY (of the same size), the globally optimal solution objective function values are typically concentrated over a narrow range. Ph. D.

This dissertation developed a comprehensive model conceptualizing the factors affecting children's choice of influence strategy and relative influence in family consumption decisions. In particular, the model asserted that antecedent variables (i.e., family variables, individual characteristics of children, individual characteristics of parents, and parent-child interdependence) affect both directly and indirectly children's choice of influence strategy and relative influence. Process variables (i.e., family socialization and power structure) mediate the effects of the antecedent variables. In addition, effects of family socialization and power structure on children's choice of influence strategy and subsequent relative influence vary with the product type, decision stage, and subdecision. Finally, children's relative influence is also dependent on their choice of influence strategy. An empirical study was advanced to partially test the model. Specifically, relationships among family socialization, power structure, children's choice of influence strategy, and their relative influence were empirically examined. A field experimental interaction procedure was designed for data collection from parent/child dyads. Multiple regressions were conducted to analyze the data. Results showed moderate support to the hypothesized relationships. However, most links in the testing model presented significant results. It appears that the integration of consumer socialization theory and power relational theory provides better explanation to children's influence behavior than either theory does individually. Ph. D.

The standard methodology when building statistical models has been to use one of several algorithms to systematically search the model space for a good model. If the number of variables is small then all possible models or best subset procedures may be used, but for data sets with a large number of variables, a stepwise procedure is usually implemented. The stepwise procedure of model selection was designed for its computational efficiency and is not guaranteed to find the best model with respect to any optimality criteria. While the model selected may not be the best possible of those in the model space, commonly it is almost as good as the best model. Many times there will be several models that exist that may be competitors of the best model in terms of the selection criterion, but classical model building dictates that a single model be chosen to the exclusion of all others. An alternative to this is Bayesian model averaging (BMA), which uses the information from all models based on how well each is supported by the data. Using BMA allows a variance component due to the uncertainty of the model selection process to be estimated. The variance of any statistic of interest is conditional on the model selected so if there is model uncertainty then variance estimates should reflect this. BMA methodology can also be used for variable assessment since the probability that a given variable is active is readily obtained from the individual model posterior probabilities. The multivariate methods considered in this research are principal components analysis (PCA), canonical variate analysis (CVA), and canonical correlation analysis (CCA). Each method is viewed as a particular multivariate extension of univariate multiple regression. The marginal likelihood of a univariate multiple regression model has been approximated using the Bayes information criteria (BIC), hence the marginal likelihood for these multivariate extensions also makes use of this approximation. One of the main criticisms of multivariate techniques in general is that they are difficult to interpret. To aid interpretation, BMA methodology is used to assess the contribution of each variable to the methods investigated. A second issue that is addressed is displaying of results of an analysis graphically. The goal here is to effectively convey the germane elements of an analysis when BMA is used in order to obtain a clearer picture of what conclusions should be drawn. Finally, the model uncertainty variance component can be estimated using BMA. The variance due to model uncertainty is ignored when the standard model building tenets are used giving overly optimistic variance estimates. Even though the model attained via standard techniques may be adequate, in general, it would be difficult to argue that the chosen model is in fact the correct model. It seems more appropriate to incorporate the information from all plausible models that are well supported by the data to make decisions and to use variance estimates that account for the uncertainty in the model estimation as well as model selection. Ph. D.

The behavior of repairable equipment is often modeled under assumptions such as perfect repair, minimal repair, or negligible repair. However the majority of equipment behavior does not fall into any of these categories. Rather, repair actions do take time and the condition of equipment following repair is not strictly "as good as new" or "as bad as it was" prior to repair. Non-homogeneous processes that reflect this type of behavior are not studied nearly as much as the minimal repair case, but they far more realistic in many situations. For this reason, the quasi-renewal process provides an appealing alternative to many existing models for describing a non-homogeneous process. A quasi-renewal process is characterized by a parameter that indicates process deterioration or improvement by falling in the interval [0,1) or (1,Infinity) respectively. This parameter is the amount by which subsequent operation or repair intervals are scaled in terms of the immediately previous operation or repair interval. Two equivalent expressions for the point availability of a system with operation intervals and repair intervals that deteriorate according to a quasi-renewal process are constructed. In addition to general expressions for the point availability, several theoretical distributions on the operation and repair intervals are considered and specific forms of the quasi-renewal and point availability functions are developed. The two point availability expressions are used to provide upper and lower bounds on the approximated point availability. Numerical results and general behavior of the point availability and quasi-renewal functions are examined. The framework provided here allows for the description and prediction of the time-dependent behavior of a non-homogeneous process without the assumption of limiting behavior, a specific cost structure, or minimal repair. Ph. D.

Same types of systems with the same age usually have different amounts of cumulated usage. These systems when in operation usually have different performance and effectiveness. In this case the existing models of the univariate measures of system effectiveness are inadequate and incomplete. For example, the univariate availability measures for these same-aged systems are all the same even though with different amounts of usage. This is the motivation for this research to pursue a bivariate approach in reliability and maintenance modeling. This research presents a framework for bivariate modeling of a single-unit system. Five key efforts are identified and organized as: (i) bivariate failure modeling, (ii) bivariate renewal modeling, (iii) bivariate corrective maintenance (CM) modeling, (iv) bivariate preventive maintenance (PM) modeling, and (v) bivariate availability modeling. The results provide a foundation for further study of bivariate and multivariate models. For bivariate failure modeling, several bivariate failure models are constructed to represent the possible correlation structures of the two system aging variables, time and usage. The behavior of these models is examined under various correlation structures. The developed models are used to analyze example maintenance problems. Models for bivariate renewal, bivariate CM, and bivariate PM are derived based on the constructed bivariate failure models and the developed bivariate renewal theory. For bivariate CM modeling, corrective maintenance is modeled as an alternating bivariate renewal process or simply an ordinary bivariate renewal process. For bivariate PM modeling, PM models are examined under a bivariate age replacement preventive maintenance policy. The Laplace transforms of the renewal functions (and densities) for these models are obtained. Definitions for bivariate availability functions are developed. Based on the derived CM and PM models, the Laplace transforms for their corresponding bivariate availability models are constructed. The idea of the quality of availability measure is also defined in terms of bivariate availability models. The most significant observation is that this framework provides a new way to study the reliability and maintenance of equipment for which univariate measures are incomplete. Therefore, a new area of reliability research is identified. The definitions offered may be modified and the approach to model formulation presented may be used to define other models. Ph. D.

In this research, Bayesian two-stage D-D optimal designs for mixture experiments with or without process variables under model uncertainty are developed. A Bayesian optimality criterion is used in the first stage to minimize the determinant of the posterior variances of the parameters. The second stage design is then generated according to an optimality procedure that collaborates with the improved model from first stage data. Our results show that the Bayesian two-stage D-D optimal design is more efficient than both the Bayesian one-stage D-optimal design and the non-Bayesian one-stage D-optimal design in most cases. We also use simulations to investigate the ratio between the sample sizes for two stages and to observe least sample size for the first stage. On the other hand, we discuss D-optimal second or higher order designs, and show that Ds-optimal designs are a reasonable alternative to D-optimal designs. Ph. D.

Random variables defined on the natural numbers may often be approximated by Poisson variables. Just as normal approximations may be improved by saddlepoint methods, Poisson approximations may be substantially improved by tilting, expansion, and other related methods. This work will develop and examine the use of these methods, as well as present examples where such methods may be needed. Ph. D.

This dissertation represented an initial effort to model spousal family purchase decision behavior in terms of spousal coercion propensity. Two major issues concerning how spouses resolve conflicts were investigated: (1) What are the spousal behavioral interactions in household conflict resolution processes? (2) What are the temporal aspects of spousal family decision behaviors? It was hypothesized that spouses tend to not reciprocate their partners' uses of coercive influence strategies in a decision, given their avoidance of conflict. Also, spouses who used more power in the past tend to use less power in order to maintain equity in the long-term marital relationship. It was also hypothesized that spousal coercion propensity are contingent upon marital power, love, and preference intensity. Marital power and preference intensity are positively related to spousal coercion propensity while love predicts weaker coercive decision behavior. Consistently, it was proposed that coercive influence strategies are more effective in the short run, given the spouses' conflict avoidance and sense of equity in marriage. Thus, spouses who used coercive strategies are more satisfied with the decision outcome but less satisfied with the decision process. A dynamic simultaneous equations model (DSE) was developed to test the major hypotheses of this dissertation. The model was calibrated by means of an Autoregressive Two-Stage Least Square (A2SLS) approach. MANOVAs and a set of binary logistic regressions and linear multiple regressions were used to test the other hypotheses. The empirical study involving a random sample provided adequate support for the model. The implications of the findings, theoretical and managerial alike, limitations of the study, and future research directions were discussed. Ph. D.

This paper examines the extent to which thin markets in conjunction with tax induced kinks in the budget constraint cause consumer demand to be skewed. To illustrate the principles I focus on the demand for owner-occupied housing. Housing units are indivisible and heterogeneous while tastes for housing are at least partly idiosyncratic, causing housing markets to be thin. In addition, prior to 1998, capital gains tax provisions introduced a sharp kink in the budget constraint of existing owner-occupiers in search of a new home: previous homeowners under age 55 paid no capital gains tax if they bought up, but were subject to capital gains tax if they bought down. I first characterize the economic conditions under which households err on the up or down side when choosing a home in the presence of a thin market and a kinked budget constraint. I then specify an empirical model that takes such effects into account. Results based on Monte Carlo experiments indicate that failing to allow for skewness in the demand for housing leads to biased estimates of the elasticities of demand when such skewness is actually present. In addition, estimates based on American Housing Survey data suggest that such bias is substantial: controlling for skewness reduces the price elasticity of demand among previous owner-occupiers from 1.6 to 0.3. Moreover, 58% of previous homeowners err on the up while only 42% err on the down side. Thus, housing demand is skewed. Ph. D.

Numerous studies have documented the existence of nonlinearity within various financial time series. But how important of a finding is this? This dissertation examines this issue from a number of perspectives. First, is the nonlinearity that has been found a statistical anomaly that is isolated to a few of the more widely known financial time series or is nonlinearity a statistical regularity inherent in such series? Second, even if nonlinearity is pervasive, does this finding have any practical relevance for finance practitioners or academics? Using the relatively financially isolated but nonetheless well-traded Taiwan Stock Exchange as a case study, it is found that virtually all of the stocks trading on this exchange exhibit nonlinearity. The pervasiveness of nonlinearity within this market, combined with earlier results from other markets, suggests that nonlinearity is an inherent aspect of financial time series. Furthermore, closer examination of the time-paths of various measures of this nonlinearity via both windowed testing and recursive testing and parameter estimation reveals an additional complication, the possibility of nonstationarity. The serial dependency structures, especially for the nonlinear dependencies, do not appear to be constant, but instead appear to exhibit a number of brief episodes of extremely strong dependencies, followed by longer stretches of relatively quiet behavior. On average, though, these nonlinearities appear with sufficient strength to be significant for the full sample. Continuing on to examine the relevance of such nonlinearities for empirical work in finance, a variety of conditionally heteroskedastic models were fit to the returns for a subsample Taiwanese stocks, the Taiwanese stock index, and stock indices for other stock markets, including New York, London, Tokyo, Hong Kong, and Singapore. In a majority of cases, such models appear to be successful at filtering out the extant nonlinearity from these series of returns; however, a variety of indicators suggest that these models are not statistically well-specified for these returns, calling into question the inferences obtained from these models. Furthermore, a comparison of the various conditionally heteroskedastic models with each other and with a dynamic linear regression model reveals that, for many of the data series, the inferences obtained from these models regarding the day-of-the-week effect and the extant autocorrelation within the data varied from model to model. This finding suggests the importance of adequately accounting for nonlinear serial dependencies (and of ensuring data stationarity) when studying financial time series, even when other empirical aspects of the data are the focus of attention. Ph. D.

Industrial processes are subject to changes that can adversely affect product quality. A change in the process that increases the variability of the output of the process causes the output to be less uniform and increases the probability that individual items will not meet specifications. Statistical control charts for monitoring process variance can be used to detect an increase in the variability of the output of a process so that the situation can be repaired and product uniformity restored. Control charts that increase the sampling rate when there is evidence the variance has changed gather information more quickly and detect changes in the variance more quickly (on average) than fixed sampling rate procedures. Several variable sampling rate procedures for detecting increases in the process variance will be developed and compared with fixed sampling rate methods. A control chart for the variance is usually used with a separate control chart for the mean so that changes in the average level of the process and the variability of the process can both be detected. A simple method for applying variable sampling rate techniques to dual monitoring of mean and variance will be developed. This control chart procedure increases the sampling rate when there is evidence the mean or variance has changed so that changes in either parameter that will negatively impact product quality will be detected quickly. Ph. D.

Generalized hill climbing (GHC) algorithms provide a unifying framework for describing several discrete optimization problem local search heuristics, including simulated annealing and tabu search. A necessary and a sufficient convergence condition for GHC algorithms are presented. The convergence conditions presented in this dissertation are based upon a new iteration classification scheme for GHC algorithms. The convergence theory for particular formulations of GHC algorithms is presented and the implications discussed. Examples are provided to illustrate the relationship between the new convergence conditions and previously existing convergence conditions in the literature. The contributions of the necessary and the sufficient convergence conditions for GHC algorithms are discussed and future research endeavors are suggested. Ph. D.

In simple linear regression, it is assumed that two variables are linearly related, with unknown intercept and slope parameters. In particular, a regressor variable is assumed to be precisely measurable, and a response is assumed to be a random variable whose mean depends on the regressor via a linear function. For the simple linear regression problem, interest typically centers on estimation of the unknown model parameters, and perhaps application of the resulting estimated linear relationship to make predictions about future response values corresponding to given regressor values. The linear statistical calibration problem (or, more precisely, the absolute linear calibration problem), bears a resemblance to simple linear regression. It is still assumed that the two variables are linearly related, with unknown intercept and slope parameters. However, in calibration, interest centers on estimating an unknown value of the regressor, corresponding to an observed value of the response variable. We consider Bayesian methods of analysis for the linear statistical calibration problem, based on noninformative priors. Posterior analyses are assessed and compared with classical inference procedures. It is shown that noninformative prior Bayesian analysis is a strong competitor, yielding posterior inferences that can, in many cases, be correctly interpreted in a frequentist context. We also consider extensions of the linear statistical calibration problem to polynomial models and multivariate regression models. For these models, noninformative priors are developed, and posterior inferences are derived. The results are illustrated with analyses of published data sets. In addition, a certain type of heteroscedasticity is considered, which relaxes the traditional assumptions made in the analysis of a statistical calibration problem. It is shown that the resulting analysis can yield more reliable results than an analysis of the homoscedastic model. Ph. D.

The EPA recently completed a major study to evaluate exposure and risk associated with a primary contaminant, radon and its progeny in drinking water (EPA, 1995). This work resulted in the development of a Monte Carlo Simulation model written in the programming language C. The model developed by the EPA has been used to estimate the cancer fatality risk from radon in water for exposed populations served by community ground water supplies, and to provide a quantitative analysis of the uncertainty associated with the calculations (EPA, 1995). This research is a continuation of the study conducted by the EPA. In this project, a Monte Carlo computer model will be developed to evaluate the risk associated with exposure to volatile compounds in drinking water. The model will be based on a computer program (developed previously by the EPA) for estimating the risks associated with exposure to radon in drinking water. The model will be re-implemented in the form of a computer program written in C. The analysis for radon will be extended to include the entire range of contaminants found in drinking water supplies. The initial focus of the project has been on extending the analysis to cover the ingestion exposure pathway for volatile compounds, but ultimately the risk via ingestion and dermal sorption will also be evaluated. The integrated model can estimate the risks associated with various levels of contaminants in drinking water and should prove valuable in establishing Maximum Contaminant Levels (MCLs) for the entire range of contaminants found in water supplies and generated in water treatment and distribution systems. Master of Science