In the field of radiation protection, complex computationally expensive algorithms are used to predict radiation doses, to organs in the human body from exposure to internally deposited radionuclides. These algorithms contain many inputs, the true values of which are uncertain. Current methods for assessing the effects of the input uncertainties on the output of the algorithms are based on Monte Carlo analyses, i.e. sampling from subjective prior distributions that represent the uncertainty on each input, evaluating the output of the model and calculating sample statistics. For complex computationally expensive algorithms, it is often not possible to get a large enough sample for a meaningful uncertainty analysis. This thesis presents an alternative general theory for uncertainty analysis, based on the use of stochastic process models, in a Bayesian context. The measures provided by the Monte Carlo analysis are obtained, plus extra more informative measures, but using a far smaller sample. The theory is initially developed in a general form and then specifically for algorithms with inputs whose uncertainty can be characterised by independent normal distributions. The Monte Carlo and Bayesian methodologies are then compared using two practical examples. The first example, is based on a simple model developed to calculate doses due to radioactive iodine. This model has two normally distributed uncertain parameters and due to its simplicity an independent measurement of the true uncertainty on the output is available for comparison. This exercise appears to show that the Bayesian methodology is superior in this simple case. The purpose of the second example is to determine if the methodology is practical in a 'real-life' situation and to compare it with a Monte Carlo analysis. A model for calculating doses due to plutonium contamination is used. This model is computationally expensive and has fourteen uncertain inputs. The Bayesian analysis compared favourably to the Monte Carlo, indicating that it has the potential to provide more accurate uncertainty analyses for the parameters of computationally expensive algorithms.

A new three-dimensional finite solid element (3D FE) model for dowel-type wood connections was developed using the concept of a beam on a nonlinear wood foundation, which addresses the intricate wood crushing behaviour under the connector in a dowel type connection. In order to implement the concept of wood foundation with solid elements, a 3D FE wood foundation model was defined within a prescribed foundation zone surrounding the dowel. Based on anisotropic plasticity material theory, the material model for the foundation zone was developed using effective foundation material constants that were defined from dowel-embedment test data. New 3D FE single nail connection models were developed that incorporated the wood foundation model. The 3D wood foundation model was justified and validated using dowel-embedment test data with a range of dowel diameters, from a 2.5-mm nail to a25.4-mm bolt. The connection models provided successful results in simulating the characteristics of load-slip behaviour that were experimentally observed. Based on the success of the single nail connection models, several applications of the3D FE connection models were investigated including statistical wood material models, bolted connection models and a multiple nail connection model. Throughout the application studies, discussion of the benefits and limitations of the new model approach using the 3D FE wood foundation are presented. Also, future areas of study are proposed in order to improve the 3D FE dowel-type wood connections models.

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Introduction: Alzheimer’s disease is an irreversible brain disorder characterized by distortion of memory and other mental functions. Although, several psychometric tests are available for diagnosis of Alzheimer’s, there is a great concern about the validity of these tests at recognizing the early onset of the disease. Currently, brain magnetic resonance imaging is not commonly utilized in the diagnosis of Alzheimer’s, because researchers are still puzzled by the association of brain regions with the disease status and its progress. Moreover, MRI data tend to be of high dimensional nature requiring advanced statistical methods to accurately analyze them. In the past decade, the application of Least Absolute Shrinkage and Selection Operator (LASSO) has become increasingly popular in the analysis of high dimensional data. With LASSO, only a small number of the regression coefficients are believed to have a non-zero value, and therefore allowed to enter the model; other coefficients are while others are shrunk to zero. Aim: Determine the non-zero regression coefficients in models predicting patients’ classification (Normal, mild cognitive impairment (MCI), or Alzheimer’s) using both non-ordinal and ordinal LASSO. Methods: Pre-processed high dimensional MRI data of the Alzheimer’s Disease Neuroimaging Initiative was analyzed. Predictors of the following model were differentiated: Alzheimer’s vs. normal, Alzheimer’s vs. normal and MCI, Alzheimer’s and MCI vs. Normal. Cross-validation followed by ordinal LASSO was executed on these same sets of models. Results: Results were inconclusive. Two brain regions, frontal lobe and putamen, appeared more frequently in the models than any other region. Non-ordinal multinomial models performed better than ordinal multinomial models with higher accuracy, sensitivity, and specificity rates. It was determined that majority of the models were best suited to predict MCI status than the other two statues. Discussion: In future research, the other stages of the disease, different statistical analysis methods, such as elastic net, and larger samples sizes should be explored when using brain MRI for Alzheimer’s disease classification.

While designed and adopted at the federal level, the Clean Air Act (CAA) and Clean Water Act (CWA) rely on states for implementation. The result of this implementation framework is a disparity in environmental conditions across the nation. The objective of this research is to examine how the implementation stage of the policy process affects program outcomes. The findings indicate that the primary means of shaping program outcomes are the decision-making criterion and subsequent behavior of implementing officials, where their value based actions dictate service delivery. These decisions are, in turn, shaped by the context of the work, where organizations and the socio-political environment influence the basis for decision-making. These findings connect broader organizational and socio-political factors with program outcomes through an indirect relationship, rather than assume a direct relationship as previous authors have done. The findings explain a significant portion of the variance in both air and water program outcomes across the nation. This research indicates the importance of front-line operators in the implementation process, an issue that has been left-out of other work. These conclusions can be used to enhance performance management by practitioners, through a greater understanding of how organizations and individuals affect program outcomes. Finally, the theoretical framework and methodological techniques suggest that previous implementation research has failed to properly specify statistical models, which enhances the literature on the subject.

A general approach for conducting power analysis in two-and three-level hierarchical linear models (HLMs) is described. The method can be used to perform power analysis to detect fixed effects at any level of a HLM with dichotomous or continuous covariates. It can easily be extended to perform power analysis for functions of parameters. Important steps in the derivation of this approach are illustrated and numerical examples are provided. Sample code implementing this approach is provided using the free program R.

Doctor of Philosophy / Department of Statistics / John E. Boyer Jr., Dallas E. Johnson / A crossover design is an experimental design in which each experimental unit receives a series of experimental treatments over time. The order that an experimental unit receives its treatments is called a sequence (example, the sequence AB means that treatment A is given first, and then followed by treatment B). A period is the time interval during which a treatment is administered to the experimental unit. A period could range from a few minutes to several months depending on the study. Sequences usually involve subjects receiving a different treatment in each successive period. However, treatments may occur more than once in any sequence (example, ABAB). Treatments and periods are compared within subjects, i.e. each subject serves as his/her own control. Therefore, any effect that is related to subject differences is removed from treatment and period comparisons. Carryover effects are residual effects from a previous treatment manifesting themselves in subsequent periods. Crossover designs both with and without carryover are traditionally analyzed assuming that the response due to different treatments have equal variances. The effects of unequal variances on traditional tests for treatment and carryover difference were recently considered in crossover designs assuming that the response due to treatments have unequal variances with a compound symmetry correlation structure. The likelihood function for the two treatment/two sequence crossover design has closed form maximum likelihood solutions for the parameters at both the null hypothesis, H0 : sigma_A^2 =\sigma_B^2, and at alternative hypothesis, HA : not H0. Under HA : not H0, the method of moment estimators and the maximum likelihood estimators of sigma_A^2,sigma_B^2 and rho are identical. The dual balanced design, ABA=BAB, which is balanced for carryover effects is also considered. The dual balanced design has a closed form solution that maximizes the likelihood function under the null hypothesis, H0 :sigma_A^2=sigma_B^2, but not for the alternative hypothesis, HA : not H0. Similarly, the three treatment/three sequence crossover design, ABC=BCA=CAB, has a closed form solution that maximizes the likelihood function at the null hypothesis, H0 : sigma_A^2=sigma_B^2 = sigma_C^2, but not for the alternative hypothesis, HA : not H0. An iterative procedure is introduced to estimate the parameters for the two and three treatment crossover designs. To check the performance of the likelihood ratio tests, Type I error rates and power comparisons are explored using simulations.

Nanostring technology provides a new method to measure gene expressions. It's more sensitive than microarrays and able to do more gene measurements than RT-PCR with similar sensitivity. This system produces counts for each target gene and tabulates them. Counts can be normalized by using an Excel macro or nSolver before analysis. Both methods rely on data normalization prior to statistical analysis to identify differentially expressed genes. Alternatively, we propose to model gene expressions as a function of positive controls and reference gene measurements. Simulations and examples are used to compare this model with Nanostring normalization methods. The results show that our model is more stable, efficient, and able to control false positive proportions. In addition, we also derive asymptotic properties of a normalized test of control versus treatment.

Data can be collected in the form of counts in many situations. In other words, the number of deaths from an accident, the number of days until a machine stops working or the number of annual visitors to a city may all be considered as interesting variables for study. This study is motivated by two facts; first, the vital role of the continuous Weibull distribution in survival analyses and failure time studies. Hence, the discrete Weibull (DW) is introduced analogously to the continuous Weibull distribution, (see, Nakagawa and Osaki (1975) and Kulasekera (1994)). Second, researchers usually focus on modeling count data, which take only non-negative integer values as a function of other variables. Therefore, the DW, introduced by Nakagawa and Osaki (1975), is considered to investigate the relationship between count data and a set of covariates. Particularly, this DW is generalised by allowing one of its parameters to be a function of covariates. Although the Poisson regression can be considered as the most common model for count data, it is constrained by its equi-dispersion (the assumption of equal mean and variance). Thus, the negative binomial (NB) regression has become the most widely used method for count data regression. However, even though the NB can be suitable for the over-dispersion cases, it cannot be considered as the best choice for modeling the under-dispersed data. Hence, it is required to have some models that deal with the problem of under-dispersion, such as the generalized Poisson regression model (Efron (1986) and Famoye (1993)) and COM-Poisson regression (Sellers and Shmueli (2010) and Sáez-Castillo and Conde-Sánchez (2013)). Generally, all of these models can be considered as modifications and developments of Poisson models. However, this thesis develops a model based on a simple distribution with no modification. Thus, if the data are not following the dispersion system of Poisson or NB, the true structure generating this data should be detected. Applying a model that has the ability to handle different dispersions would be of great interest. Thus, in this study, the DW regression model is introduced. Besides the exibility of the DW to model under- and over-dispersion, it is a good model for inhomogeneous and highly skewed data, such as those with excessive zero counts, which are more disperse than Poisson. Although these data can be fitted well using some developed models, namely, the zero-inated and hurdle models, the DW demonstrates a good fit and has less complexity than these modifed models. However, there could be some cases when a special model that separates the probability of zeros from that of the other positive counts must be applied. Then, to cope with the problem of too many observed zeros, two modifications of the DW regression are developed, namely, zero-inated discrete Weibull (ZIDW) and hurdle discrete Weibull (HDW) models. Furthermore, this thesis considers another type of data, where the response count variable is censored from the right, which is observed in many experiments. Applying the standard models for these types of data without considering the censoring may yield misleading results. Thus, the censored discrete Weibull (CDW) model is employed for this case. On the other hand, this thesis introduces the median discrete Weibull (MDW) regression model for investigating the effect of covariates on the count response through the median which are more appropriate for the skewed nature of count data. In other words, the likelihood of the DW model is re-parameterized to explain the effect of the predictors directly on the median. Thus, in comparison with the generalized linear models (GLMs), MDW and GLMs both investigate the relations to a set of covariates via certain location measurements; however, GLMs consider the means, which is not the best way to represent skewed data. These DW regression models are investigated through simulation studies to illustrate their performance. In addition, they are applied to some real data sets and compared with the related count models, mainly Poisson and NB models. Overall, the DW models provide a good fit to the count data as an alternative to the NB models in the over-dispersion case and are much better fitting than the Poisson models. Additionally, contrary to the NB model, the DW can be applied for the under-dispersion case.

Understanding the factors shaping neuronal spiking is a central problem in neuroscience. Neurons may have complicated sensitivity and, often, are embedded in dynamic networks whose ongoing activity may influence their likelihood of spiking. One approach to characterizing neuronal spiking is the point process generalized linear model (GLM), which decomposes spike probability into explicit factors. This model represents a higher level of abstraction than biophysical models, such as Hodgkin-Huxley, but benefits from principled approaches for estimation and validation. Here we address how to infer factors affecting neuronal spiking in different types of neural systems. We first extend the point process GLM, most commonly used to analyze single neurons, to model population-level voltage discharges recorded during human seizures. Both GLMs and descriptive measures reveal rhythmic bursting and directional wave propagation. However, we show that GLM estimates account for covariance between these features in a way that pairwise measures do not. Failure to account for this covariance leads to confounded results. We interpret the GLM results to speculate the mechanisms of seizure and suggest new therapies. The second chapter highlights flexibility of the GLM. We use this single framework to analyze enhancement, a statistical phenomenon, in three distinct systems. Here we define the enhancement score, a simple measure of shared information between spike factors in a GLM. We demonstrate how to estimate the score, including confidence intervals, using simulated data. In real data, we find that enhancement occurs prominently during human seizure, while redundancy tends to occur in mouse auditory networks. We discuss implications for physiology, particularly during seizure. In the third part of this thesis, we apply point process modeling to spike trains recorded from single units in vitro under external stimulation. We re-parameterize models in a low-dimensional and physically interpretable way; namely, we represent their effects in principal component space. We show that this approach successfully separates the neurons observed in vitro into different classes consistent with their gene expression profiles. Taken together, this work contributes a statistical framework for analyzing neuronal spike trains and demonstrates how it can be applied to create new insights into clinical and experimental data sets.