Origin-Destination (O-D) matrices are required in order to model traffic routing behavior in networks. Direct techniques for collecting O-D information from home and roadside interviews have historically been utilized to estimate O-D tables. However, these techniques are not only very costly, labor intensive, and disruptive to trip makers, but traditionally also do not capture traffic peaking behavior, which is often required for traffic operational purposes. Consequently, more cost-effective indirect or synthetic O-D estimation techniques have been developed, and continue to be developed. They utilize readily available traffic volume counts to estimate the most likely O-D tables that may have generated the observed link counts. This thesis describes the basic formulations that have been proposed to formulate and solve the static O-D problem synthetically using link flow observations based on Maximum Entropy techniques. As is the case with many mathematical solutions to engineering problems, a number of simplifying assumptions have been made in order to solve the synthetic O-D problem. Unfortunately, the descriptions of these simplifying assumptions are often not fully described in the literature, and in some cases, these assumptions are not mentioned at all. Furthermore, the literature fails to systematically demonstrate what impact these assumptions have on the final O-D table estimate. Therefore, this thesis utilizes simple hypothetical networks to; 1. Demonstrate and compare the two main types of synthetic O-D formulations, namely the trip and volume based formulations. 2. Track the O-D estimation procedure from its initial formulation to its final formulation, demonstrating all significant assumptions that have been made and the implications of these assumptions on the final solution. 3. Demonstrate to what extent the final O-D estimation formulation remains valid when these assumptions are invoked. 4. Test the applicability of some packages which implement the various formulations and solution techniques that are available. / Master of Science

We have designed, developed, and assessed a novel preclinical positron emission tomography (PET) imaging system named ModPET. The system was developed using modular gamma cameras, originally developed for SPECT applications at the Center for Gamma Ray Imaging (CGRI), but configured for PET imaging by enabling coincidence timing. A pair of cameras are mounted on a exible system gantry that also allows for acquisition of optical images such that PET images can be registered to an anatomical reference. Data is acquired in a super list-mode form where raw PMT signals and event times are accumulated in events lists for each camera. Event parameter estimation of position and energy is carried out with maximum likelihood methods using careful camera calibrations accomplished with collimated beams of 511-keV photons and a new iterative mean-detector-response-function processing routine. Intrinsic lateral spatial resolution for 511-keV photons was found to be approximately 1.6 mm in each direction. Lists of coincidence pairs are found by comparing event times in the two independent camera lists. A timing window of 30 nanoseconds is used. By bringing the 4.5 inch square cameras in close proximity, with a 32-mm separation for mouse imaging, a solid angle coverage of ∼75% partially compensates for the relatively low stopping power in the 5-mm-thick NaI crystals to give a mea- sured sensitivity of up to 0.7%. An NECR analysis yields 11,000 pairs per second with 84 μCi of activity. A list-mode MLEM reconstruction algorithm was developed to reconstruct objects in a 88 x 88 x 30 mm field of view. Tomographic resolution tests with a phantom suggest a lateral resolution of 1.5 mm and a slightly degraded resolution of 2.5 mm in the direction normal to the camera faces. The system can also be configured to provide (99m)Tc planar scintigraphy images. Selected biological studies of inammation, apoptosis, tumor metabolism, and bone osteogenic activity are presented.

Dynamic panel data models are widely used by econometricians to study over time the economics of, for example, people, firms, regions, or countries, by pooling information over the cross-section. Though much of the panel research concerns inference in stationary models, macroeconomic data such as GDP, prices, and interest rates are typically trending over time and require in one way or another a nonstationary analysis. In time series analysis it is well-established how autoregressive unit roots give rise to stochastic trends, implying that random shocks to a dynamic process are persistent rather than transitory. Because the implications of, say, government policy actions are fundamentally different if shocks to the economy are lasting than if they are temporary, there are now a vast number of univariate time series unit root tests available. Similarly, panel unit root tests have been designed to test for the presence of stochastic trends within a panel data set and to what degree they are shared by the panel individuals. Today, growing data certainly offer new possibilities for panel data analysis, but also pose new problems concerning double-indexed limit theory, unobserved heterogeneity, and cross-sectional dependencies. For example, economic shocks, such as technological innovations, are many times global and make national aggregates cross-country dependent and related in international business cycles. Imposing a strong cross-sectional dependence, panel unit root tests often assume that the unobserved panel errors follow a dynamic factor model. The errors will then contain one part which is shared by the panel individuals, a common component, and one part which is individual-specific, an idiosyncratic component. This is appealing from the perspective of economic theory, because unobserved heterogeneity may be driven by global common shocks, which are well captured by dynamic factor models. Yet, only a handful of tests have been derived to test for unit roots in the common and in the idiosyncratic components separately. More importantly, likelihood-based methods, which are commonly used in classical factor analysis, have been ruled out for large dynamic factor models due to the considerable number of parameters. This thesis consists of four papers where we consider the exact factor model, in which the idiosyncratic components are mutually independent, and so any cross-sectional dependence is through the common factors only. Within this framework we derive some likelihood-based tests for common and idiosyncratic unit roots. In doing so we address an important issue for dynamic factor models, because likelihood-based tests, such as the Wald test, the likelihood ratio test, and the Lagrange multiplier test, are well-known to be asymptotically most powerful against local alternatives. Our approach is specific-to-general, meaning that we start with restrictions on the parameter space that allow us to use explicit maximum likelihood estimators. We then proceed with relaxing some of the assumptions, and consider a more general framework requiring numerical maximum likelihood estimation. By simulation we compare size and power of our tests with some established panel unit root tests. The simulations suggest that the likelihood-based tests are locally powerful and in some cases more robust in terms of size. / Solving Macroeconomic Problems Using Non-Stationary Panel Data

Os métodos de estimação para modelos de fragilidade vêm sendo bastante discutidos na literatura estatística devido a sua grande utilização em estudos de Análise de Sobrevivência. Vários métodos de estimação de parâmetros dos modelos foram desenvolvidos: procedimentos de estimação baseados no algoritmo EM, cadeias de Markov de Monte Carlo, processos de estimação usando verossimilhança parcial, verossimilhança penalizada, quasi-verossimilhança, entro outros. Uma alternativa que vem sendo utilizada atualmente é a utilização da verossimilhança hierárquica. O objetivo principal deste trabalho foi estudar as vantagens e desvantagens da verossimilhança hierárquica para a inferência em modelos de fragilidade em relação a verossimilhança penalizada, método atualmente mais utilizado. Nós aplicamos as duas metodologias a um banco de dados real, utilizando os pacotes estatísticos disponíveis no software R, e fizemos um estudo de simulação, visando comparar o viés e o erro quadrático médio das estimativas de cada abordagem. Pelos resultados encontrados, as duas metodologias apresentaram estimativas muito próximas, principalmente para os termos fixos. Do ponto de vista prático, a maior diferença encontrada foi o tempo de execução do algoritmo de estimação, muito maior na abordagem hierárquica. / Estimation procedures for frailty models have been widely discussed in the statistical literature due its widespread use in survival studies. Several estimation methods were developed: procedures based on the EM algorithm, Monte Carlo Markov chains, estimation processes based on parcial likelihood, penalized likelihood and quasi-likelihood etc. An alternative currently used is the hierarchical likelihood. The main objective of this work was to study the hierarchical likelihood advantages and disadvantages for inference in frailty models when compared with the penalized likelihood method, which is the most used one. We applied both approaches to a real data set, using R packages available. Besides, we performed a simulation study in order to compare the methods through out the bias and the mean square error of the estimators. Both methodologies presented very similar estimates, mainly for the fixed effects. In practice, the great difference was the computational cost, much higher in the hierarchical approach.

Os métodos de estimação para modelos de fragilidade vêm sendo bastante discutidos na literatura estatística devido a sua grande utilização em estudos de Análise de Sobrevivência. Vários métodos de estimação de parâmetros dos modelos foram desenvolvidos: procedimentos de estimação baseados no algoritmo EM, cadeias de Markov de Monte Carlo, processos de estimação usando verossimilhança parcial, verossimilhança penalizada, quasi-verossimilhança, entro outros. Uma alternativa que vem sendo utilizada atualmente é a utilização da verossimilhança hierárquica. O objetivo principal deste trabalho foi estudar as vantagens e desvantagens da verossimilhança hierárquica para a inferência em modelos de fragilidade em relação a verossimilhança penalizada, método atualmente mais utilizado. Nós aplicamos as duas metodologias a um banco de dados real, utilizando os pacotes estatísticos disponíveis no software R, e fizemos um estudo de simulação, visando comparar o viés e o erro quadrático médio das estimativas de cada abordagem. Pelos resultados encontrados, as duas metodologias apresentaram estimativas muito próximas, principalmente para os termos fixos. Do ponto de vista prático, a maior diferença encontrada foi o tempo de execução do algoritmo de estimação, muito maior na abordagem hierárquica. / Estimation procedures for frailty models have been widely discussed in the statistical literature due its widespread use in survival studies. Several estimation methods were developed: procedures based on the EM algorithm, Monte Carlo Markov chains, estimation processes based on parcial likelihood, penalized likelihood and quasi-likelihood etc. An alternative currently used is the hierarchical likelihood. The main objective of this work was to study the hierarchical likelihood advantages and disadvantages for inference in frailty models when compared with the penalized likelihood method, which is the most used one. We applied both approaches to a real data set, using R packages available. Besides, we performed a simulation study in order to compare the methods through out the bias and the mean square error of the estimators. Both methodologies presented very similar estimates, mainly for the fixed effects. In practice, the great difference was the computational cost, much higher in the hierarchical approach.

Investigation of stains from crime scenes are commonly used in the search for criminals. At The National Laboratory of Forensic Science, where these stains are examined, a number of questions of theoretical and practical interest regarding the databases of DNA profiles and the strength of DNA evidence against a suspect in a trial are not fully investigated. The first part of this thesis deals with how a sample of DNA profiles from a population is used in the process of estimating the strength of DNA evidence in a trial, taking population genetic factors into account. We then consider how to combine hypotheses regarding the relationship between a suspect and other possible donors of the stain from the crime scene by two applications of Bayes’ theorem. After that we assess the DNA profiles that minimize the strength of DNA evidence against a suspect, and investigate how the strength is affected by sampling error using the bootstrap method and a Bayesian method. In the last part of the thesis we examine discrepancies between different databases of DNA profiles by both descriptive and inferential statistics, including likelihood ratio tests and Bayes factor tests. Little evidence of major differences is found.

A composite likelihood consists of a combination of valid likelihood objects, and in particular it is of typical interest to adopt lower dimensional marginal likelihoods. Composite marginal likelihood appears to be an attractive alternative for modeling complex data, and has received increasing attention in handling high dimensional data sets when the joint distribution is computationally difficult to evaluate, or intractable due to complex structure of dependence. We present some aspects of methodological development in composite likelihood inference. The resulting estimator enjoys desirable asymptotic properties such as consistency and asymptotic normality. Composite likelihood based test statistics and their asymptotic distributions are summarized. Higher order asymptotic properties of the signed composite likelihood root statistic are explored. Moreover, we aim to compare accuracy and efficiency of composite likelihood estimation relative to estimation based on ordinary likelihood. Analytical and simulation results are presented for different models, which include multivariate normal distributions, times series model, and correlated binary data.

A composite likelihood consists of a combination of valid likelihood objects, and in particular it is of typical interest to adopt lower dimensional marginal likelihoods. Composite marginal likelihood appears to be an attractive alternative for modeling complex data, and has received increasing attention in handling high dimensional data sets when the joint distribution is computationally difficult to evaluate, or intractable due to complex structure of dependence. We present some aspects of methodological development in composite likelihood inference. The resulting estimator enjoys desirable asymptotic properties such as consistency and asymptotic normality. Composite likelihood based test statistics and their asymptotic distributions are summarized. Higher order asymptotic properties of the signed composite likelihood root statistic are explored. Moreover, we aim to compare accuracy and efficiency of composite likelihood estimation relative to estimation based on ordinary likelihood. Analytical and simulation results are presented for different models, which include multivariate normal distributions, times series model, and correlated binary data.

This paper uses Maximum likelihood estimation method to estimate the common correlation coefficients for multivariate datasets. We discuss a graphical tool, Q-Q plot, to test equality of the common intraclass correlation coefficients. Kolmogorov-Smirnov test and Cramér-von Mises test are used to check if the intraclass correlation coefficients are the same among populations. Bootstrap and empirical likelihood methods are applied to construct the confidence interval of the common intraclass correlation coefficients.

Cox Proportional Hazard Model is one of the most popular tools used in the study of Survival Analysis. Empirical Likelihood (EL) method has been used to study the Cox Proportional Hazard Model. In recent work by Qin and Jing (2001), empirical likelihood based confidence region is constructed with the assumption that the baseline hazard function is known. However, in Cox’s regression model the baseline hazard function is unspecified. In this thesis, we re-formulate empirical likelihood for the vector of regression parameters by estimating the baseline hazard function. The EL confidence regions are obtained accordingly. In addition, Adjusted Empirical Likelihood (AEL) method is proposed. Furthermore, we conduct extensive simulation studies to evaluate the performance of the proposed empirical likelihood methods in terms of coverage probabilities by comparing with the Normal Approximation based method. The simulation studies show that all the three methods produce similar coverage probabilities.