Understanding Immigrants' Travel Behavior in Florida: Neighborhood Effects and Behavioral Assimilation

The goal of this study was to develop Multinomial Logit models for the mode choice behavior of immigrants, with key focuses on neighborhood effects and behavioral assimilation. The first aspect shows the relationship between social network ties and immigrants’ chosen mode of transportation, while the second aspect explores the gradual changes toward alternative mode usage with regard to immigrants’ migrating period in the United States (US). Mode choice models were developed for work, shopping, social, recreational, and other trip purposes to evaluate the impacts of various land use patterns, neighborhood typology, socioeconomic-demographic and immigrant related attributes on individuals’ travel behavior. Estimated coefficients of mode choice determinants were compared between each alternative mode (i.e., high-occupancy vehicle, public transit, and non-motorized transport) with single-occupant vehicles. The model results revealed the significant influence of neighborhood and land use variables on the usage of alternative modes among immigrants. Incorporating these indicators into the demand forecasting process will provide a better understanding of the diverse travel patterns for the unique composition of population groups in Florida.

Linking labour force participation, education, labour wages and household consumption in developing countries:push and pull effects in self-employment - evidence from Nigeria

The contribution of this thesis is in understanding the origins in developing countries of differences in labour wage and household consumption vis-à-vis educational abilities (and by extension employment statuses). This thesis adds to the labour market literature in developing countries by investigating the nature of employment and its consequences for labour wage and household consumption in a developing country. It utilizes multinomial probit, blinder-oaxaca, Heckman and quantile regressions to examine one human capital indicator: educational attainment; and two welfare proxies: labour wage and household consumption, in a developing country, Nigeria. It finds that, empirically, the self-employed are a heterogeneous group of individuals made up of a few highly educated individuals, and a significant majority of ‘not so educated’ individuals who mostly earn less than paid workers. It also finds that a significant number of employers enjoy labour wage premiums; and having a higher proportion of employers in the household has a positive relationship with household consumption. The thesis furthermore discovers an upper educational threshold for women employers not found for men. Interestingly, the thesis also finds that there is indeed an ordering of labour wages into low-income self-employment (which seems to be found mainly in “own account” self-employment), medium-income paid employment, and high-income self-employment (which seems to be found mainly among employers), and that this corresponds to a similar ordering of low human capital, medium human capital and high human capital among labour market participants, as expressed through educational attainments. These show that as a whole, employers can largely be classed as experiencing pulled self-employment, as they appear to be advantaged in all three criteria (educational attainments, labour wage and household consumption). A minority of self-employed “own account” workers (specifically those at the upper end of the income distribution who are well educated), can also be classed as experiencing pulled self-employment. The rest of the significant majority of self-employed “own account” workers in this study can be classed as experiencing pushed self-employment in terms of the indicators used.

Advanced thermal analysis of microelectronics using spreading resistance models

Thermal analysis of electronic devices is one of the most important steps for designing of modern devices. Precise thermal analysis is essential for designing an effective thermal management system of modern electronic devices such as batteries, LEDs, microelectronics, ICs, circuit boards, semiconductors and heat spreaders. For having a precise thermal analysis, the temperature profile and thermal spreading resistance of the device should be calculated by considering the geometry, property and boundary conditions. Thermal spreading resistance occurs when heat enters through a portion of a surface and flows by conduction. It is the primary source of thermal resistance when heat flows from a tiny heat source to a thin and wide heat spreader. In this thesis, analytical models for modeling the temperature behavior and thermal resistance in some common geometries of microelectronic devices such as heat channels and heat tubes are investigated. Different boundary conditions for the system are considered. Along the source plane, a combination of discretely specified heat flux, specified temperatures and adiabatic condition are studied. Along the walls of the system, adiabatic or convective cooling boundary conditions are assumed. Along the sink plane, convective cooling with constant or variable heat transfer coefficient are considered. Also, the effect of orthotropic properties is discussed. This thesis contains nine chapters. Chapter one is the introduction and shows the concepts of thermal spreading resistance besides the originality and importance of the work. Chapter two reviews the literatures on the thermal spreading resistance in the past fifty years with a focus on the recent advances. In chapters three and four, thermal resistance of a twodimensional flux channel with non-uniform convection coefficient in the heat sink plane is studied. The non-uniform convection is modeled by using two functions than can simulate a wide variety of different heat sink configurations. In chapter five, a non-symmetrical flux channel with different heat transfer coefficient along the right and left edges and sink plane is analytically modeled. Due to the edge cooling and non-symmetry, the eigenvalues of the system are defined using the heat transfer coefficient on both edges and for satisfying the orthogonality condition, a normalized function is calculated. In chapter six, thermal behavior of two-dimensional rectangular flux channel with arbitrary boundary conditions on the source plane is presented. The boundary condition along the source plane can be a combination of the first kind boundary condition (Dirichlet or prescribed temperature) and the second kind boundary condition (Neumann or prescribed heat flux). The proposed solution can be used for modeling the flux channels with numerous different source plane boundary conditions without any limitations in the number and position of heat sources. In chapter seven, temperature profile of a circular flux tube with discretely specified boundary conditions along the source plane is presented. Also, the effect of orthotropic properties are discussed. In chapter 8, a three-dimensional rectangular flux channel with a non-uniform heat convection along the heat sink plane is analytically modeled. In chapter nine, a summary of the achievements is presented and some systems are proposed for the future studies. It is worth mentioning that all the models and case studies in the thesis are compared with the Finite Element Method (FEM).

Propriété d'universalité de la fonction zêta de Riemann

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Measured parental weight status and familial socio-economic status correlates with childhood overweight and obesity at age 9

Background: Parental obesity is a predominant risk factor for childhood obesity. Family factors including socio-economic status (SES) play a role in determining parent weight. It is essential to unpick how shared family factors impact on child weight. This study aims to investigate the association between measured parent weight status, familial socio-economic factors and the risk of childhood obesity at age 9. Methodology/Principal Findings: Cross sectional analysis of the first wave (2008) of the Growing Up in Ireland (GUI) study. GUI is a nationally representative study of 9-year-old children (N = 8,568). Schools were selected from the national total (response rate 82%) and age eligible children (response rate 57%) were invited to participate. Children and their parents had height and weight measurements taken using standard methods. Data were reweighted to account for the sampling design. Childhood overweight and obesity prevalence were calculated using International Obesity Taskforce definitions. Multinomial logistic regression examined the association between parent weight status, indicators of SES and child weight. Overall, 25% of children were either overweight (19.3%) or obese (6.6%). Parental obesity was a significant predictor of child obesity. Of children with normal weight parents, 14.4% were overweight or obese whereas 46.2% of children with obese parents were overweight or obese. Maternal education and household class were more consistently associated with a child being in a higher body mass index category than household income. Adjusted regression indicated that female gender, one parent family type, lower maternal education, lower household class and a heavier parent weight status significantly increased the odds of childhood obesity. Conclusions/Significance: Parental weight appears to be the most influential factor driving the childhood obesity epidemic in Ireland and is an independent predictor of child obesity across SES groups. Due to the high prevalence of obesity in parents and children, population based interventions are required.

Bayesian Inference in Large-scale Problems

Many modern applications fall into the category of "large-scale" statistical problems, in which both the number of observations n and the number of features or parameters p may be large. Many existing methods focus on point estimation, despite the continued relevance of uncertainty quantification in the sciences, where the number of parameters to estimate often exceeds the sample size, despite huge increases in the value of n typically seen in many fields. Thus, the tendency in some areas of industry to dispense with traditional statistical analysis on the basis that "n=all" is of little relevance outside of certain narrow applications. The main result of the Big Data revolution in most fields has instead been to make computation much harder without reducing the importance of uncertainty quantification. Bayesian methods excel at uncertainty quantification, but often scale poorly relative to alternatives. This conflict between the statistical advantages of Bayesian procedures and their substantial computational disadvantages is perhaps the greatest challenge facing modern Bayesian statistics, and is the primary motivation for the work presented here.

Two general strategies for scaling Bayesian inference are considered. The first is the development of methods that lend themselves to faster computation, and the second is design and characterization of computational algorithms that scale better in n or p. In the first instance, the focus is on joint inference outside of the standard problem of multivariate continuous data that has been a major focus of previous theoretical work in this area. In the second area, we pursue strategies for improving the speed of Markov chain Monte Carlo algorithms, and characterizing their performance in large-scale settings. Throughout, the focus is on rigorous theoretical evaluation combined with empirical demonstrations of performance and concordance with the theory.

One topic we consider is modeling the joint distribution of multivariate categorical data, often summarized in a contingency table. Contingency table analysis routinely relies on log-linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a reduced rank tensor factorization of the probability mass function for multivariate categorical data, while log-linear models achieve dimensionality reduction through sparsity. Little is known about the relationship between these notions of dimensionality reduction in the two paradigms. In Chapter 2, we derive several results relating the support of a log-linear model to nonnegative ranks of the associated probability tensor. Motivated by these findings, we propose a new collapsed Tucker class of tensor decompositions, which bridge existing PARAFAC and Tucker decompositions, providing a more flexible framework for parsimoniously characterizing multivariate categorical data. Taking a Bayesian approach to inference, we illustrate empirical advantages of the new decompositions.

Latent class models for the joint distribution of multivariate categorical, such as the PARAFAC decomposition, data play an important role in the analysis of population structure. In this context, the number of latent classes is interpreted as the number of genetically distinct subpopulations of an organism, an important factor in the analysis of evolutionary processes and conservation status. Existing methods focus on point estimates of the number of subpopulations, and lack robust uncertainty quantification. Moreover, whether the number of latent classes in these models is even an identified parameter is an open question. In Chapter 3, we show that when the model is properly specified, the correct number of subpopulations can be recovered almost surely. We then propose an alternative method for estimating the number of latent subpopulations that provides good quantification of uncertainty, and provide a simple procedure for verifying that the proposed method is consistent for the number of subpopulations. The performance of the model in estimating the number of subpopulations and other common population structure inference problems is assessed in simulations and a real data application.

In contingency table analysis, sparse data is frequently encountered for even modest numbers of variables, resulting in non-existence of maximum likelihood estimates. A common solution is to obtain regularized estimates of the parameters of a log-linear model. Bayesian methods provide a coherent approach to regularization, but are often computationally intensive. Conjugate priors ease computational demands, but the conjugate Diaconis--Ylvisaker priors for the parameters of log-linear models do not give rise to closed form credible regions, complicating posterior inference. In Chapter 4 we derive the optimal Gaussian approximation to the posterior for log-linear models with Diaconis--Ylvisaker priors, and provide convergence rate and finite-sample bounds for the Kullback-Leibler divergence between the exact posterior and the optimal Gaussian approximation. We demonstrate empirically in simulations and a real data application that the approximation is highly accurate, even in relatively small samples. The proposed approximation provides a computationally scalable and principled approach to regularized estimation and approximate Bayesian inference for log-linear models.

Another challenging and somewhat non-standard joint modeling problem is inference on tail dependence in stochastic processes. In applications where extreme dependence is of interest, data are almost always time-indexed. Existing methods for inference and modeling in this setting often cluster extreme events or choose window sizes with the goal of preserving temporal information. In Chapter 5, we propose an alternative paradigm for inference on tail dependence in stochastic processes with arbitrary temporal dependence structure in the extremes, based on the idea that the information on strength of tail dependence and the temporal structure in this dependence are both encoded in waiting times between exceedances of high thresholds. We construct a class of time-indexed stochastic processes with tail dependence obtained by endowing the support points in de Haan's spectral representation of max-stable processes with velocities and lifetimes. We extend Smith's model to these max-stable velocity processes and obtain the distribution of waiting times between extreme events at multiple locations. Motivated by this result, a new definition of tail dependence is proposed that is a function of the distribution of waiting times between threshold exceedances, and an inferential framework is constructed for estimating the strength of extremal dependence and quantifying uncertainty in this paradigm. The method is applied to climatological, financial, and electrophysiology data.

The remainder of this thesis focuses on posterior computation by Markov chain Monte Carlo. The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It has long been common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention has been paid to convergence and estimation error in these approximating Markov Chains. In Chapter 6, we propose a framework for assessing when to use approximations in MCMC algorithms, and how much error in the transition kernel should be tolerated to obtain optimal estimation performance with respect to a specified loss function and computational budget. The results require only ergodicity of the exact kernel and control of the kernel approximation accuracy. The theoretical framework is applied to approximations based on random subsets of data, low-rank approximations of Gaussian processes, and a novel approximating Markov chain for discrete mixture models.

Data augmentation Gibbs samplers are arguably the most popular class of algorithm for approximately sampling from the posterior distribution for the parameters of generalized linear models. The truncated Normal and Polya-Gamma data augmentation samplers are standard examples for probit and logit links, respectively. Motivated by an important problem in quantitative advertising, in Chapter 7 we consider the application of these algorithms to modeling rare events. We show that when the sample size is large but the observed number of successes is small, these data augmentation samplers mix very slowly, with a spectral gap that converges to zero at a rate at least proportional to the reciprocal of the square root of the sample size up to a log factor. In simulation studies, moderate sample sizes result in high autocorrelations and small effective sample sizes. Similar empirical results are observed for related data augmentation samplers for multinomial logit and probit models. When applied to a real quantitative advertising dataset, the data augmentation samplers mix very poorly. Conversely, Hamiltonian Monte Carlo and a type of independence chain Metropolis algorithm show good mixing on the same dataset.

New Advancements of Scalable Statistical Methods for Learning Latent Structures in Big Data

Constant technology advances have caused data explosion in recent years. Accord- ingly modern statistical and machine learning methods must be adapted to deal with complex and heterogeneous data types. This phenomenon is particularly true for an- alyzing biological data. For example DNA sequence data can be viewed as categorical variables with each nucleotide taking four different categories. The gene expression data, depending on the quantitative technology, could be continuous numbers or counts. With the advancement of high-throughput technology, the abundance of such data becomes unprecedentedly rich. Therefore efficient statistical approaches are crucial in this big data era.

Previous statistical methods for big data often aim to find low dimensional struc- tures in the observed data. For example in a factor analysis model a latent Gaussian distributed multivariate vector is assumed. With this assumption a factor model produces a low rank estimation of the covariance of the observed variables. Another example is the latent Dirichlet allocation model for documents. The mixture pro- portions of topics, represented by a Dirichlet distributed variable, is assumed. This dissertation proposes several novel extensions to the previous statistical methods that are developed to address challenges in big data. Those novel methods are applied in multiple real world applications including construction of condition specific gene co-expression networks, estimating shared topics among newsgroups, analysis of pro- moter sequences, analysis of political-economics risk data and estimating population structure from genotype data.

Advances in Dynamic Modeling and Computation for Count Data

A class of multi-process models is developed for collections of time indexed count data. Autocorrelation in counts is achieved with dynamic models for the natural parameter of the binomial distribution. In addition to modeling binomial time series, the framework includes dynamic models for multinomial and Poisson time series. Markov chain Monte Carlo (MCMC) and Po ́lya-Gamma data augmentation (Polson et al., 2013) are critical for fitting multi-process models of counts. To facilitate computation when the counts are high, a Gaussian approximation to the P ́olya- Gamma random variable is developed.

Three applied analyses are presented to explore the utility and versatility of the framework. The first analysis develops a model for complex dynamic behavior of themes in collections of text documents. Documents are modeled as a “bag of words”, and the multinomial distribution is used to characterize uncertainty in the vocabulary terms appearing in each document. State-space models for the natural parameters of the multinomial distribution induce autocorrelation in themes and their proportional representation in the corpus over time.

The second analysis develops a dynamic mixed membership model for Poisson counts. The model is applied to a collection of time series which record neuron level firing patterns in rhesus monkeys. The monkey is exposed to two sounds simultaneously, and Gaussian processes are used to smoothly model the time-varying rate at which the neuron’s firing pattern fluctuates between features associated with each sound in isolation.

The third analysis presents a switching dynamic generalized linear model for the time-varying home run totals of professional baseball players. The model endows each player with an age specific latent natural ability class and a performance enhancing drug (PED) use indicator. As players age, they randomly transition through a sequence of ability classes in a manner consistent with traditional aging patterns. When the performance of the player significantly deviates from the expected aging pattern, he is identified as a player whose performance is consistent with PED use.

All three models provide a mechanism for sharing information across related series locally in time. The models are fit with variations on the P ́olya-Gamma Gibbs sampler, MCMC convergence diagnostics are developed, and reproducible inference is emphasized throughout the dissertation.

Scheduling Optimization with LDA and Greedy Algorithm

Scheduling optimization is concerned with the optimal allocation of events to time slots. In this paper, we look at one particular example of scheduling problems - the 2015 Joint Statistical Meetings. We want to assign each session among similar topics to time slots to reduce scheduling conflicts. Chapter 1 briefly talks about the motivation for this example as well as the constraints and the optimality criterion. Chapter 2 proposes use of Latent Dirichlet Allocation (LDA) to identify the topic proportions in each session and talks about the fitting of the model. Chapter 3 translates these ideas into a mathematical formulation and introduces a Greedy Algorithm to minimize conflicts. Chapter 4 demonstrates the improvement of the scheduling with this method.

Wear and its effects on dental topography measures in howling monkeys (Alouatta palliata).

OBJECTIVES: Three dental topography measurements: Dirichlet Normal Energy (DNE), Relief Index (RFI), and Orientation Patch Count Rotated (OPCR) are examined for their interaction with measures of wear, within and between upper and lower molars in Alouatta palliata. Potential inferences of the "dental sculpting" phenomenon are explored. MATERIALS AND METHODS: Fifteen occluding pairs of howling monkey first molars (15 upper, 15 lower) opportunistically collected from La Pacifica, Costa Rica, were selected to sample wear stages ranging from unworn to heavily worn as measured by the Dentine Exposure Ratio (DER). DNE, RFI, and OPCR were measured from three-dimensional surface reconstructions (PLY files) derived from high-resolution CT scans. Relationships among the variables were tested with regression analyses. RESULTS: Upper molars have more cutting edges, exhibiting significantly higher DNE, but have significantly lower RFI values. However, the relationships among the measures are concordant across both sets of molars. DER and EDJL are curvilinearly related. DER is positively correlated with DNE, negatively correlated with RFI, and uncorrelated with OPCR. EDJL is not correlated with DNE, or RFI, but is positively correlated with OPCR among lower molars only. DISCUSSION: The relationships among these metrics suggest that howling monkey teeth adaptively engage macrowear. DNE increases with wear in this sample presumably improving food breakdown. RFI is initially high but declines with wear, suggesting that the initially high RFI safeguards against dental senescence. OPCR values in howling monkey teeth do not show a clear relationship with wear changes.

Introducing molaR: a New R Package for Quantitative Topographic Analysis of Teeth (and Other Topographic Surfaces)

© 2016 Springer Science+Business Media New YorkResearchers studying mammalian dentitions from functional and adaptive perspectives increasingly have moved towards using dental topography measures that can be estimated from 3D surface scans, which do not require identification of specific homologous landmarks. Here we present molaR, a new R package designed to assist researchers in calculating four commonly used topographic measures: Dirichlet Normal Energy (DNE), Relief Index (RFI), Orientation Patch Count (OPC), and Orientation Patch Count Rotated (OPCR) from surface scans of teeth, enabling a unified application of these informative new metrics. In addition to providing topographic measuring tools, molaR has complimentary plotting functions enabling highly customizable visualization of results. This article gives a detailed description of the DNE measure, walks researchers through installing, operating, and troubleshooting molaR and its functions, and gives an example of a simple comparison that measured teeth of the primates Alouatta and Pithecia in molaR and other available software packages. molaR is a free and open source software extension, which can be found at the doi:10.13140/RG.2.1.3563.4961(molaR v. 2.0) as well as on the Internet repository CRAN, which stores R packages.

Sensor Planning for Bayesian Nonparametric Target Modeling

Bayesian nonparametric models, such as the Gaussian process and the Dirichlet process, have been extensively applied for target kinematics modeling in various applications including environmental monitoring, traffic planning, endangered species tracking, dynamic scene analysis, autonomous robot navigation, and human motion modeling. As shown by these successful applications, Bayesian nonparametric models are able to adjust their complexities adaptively from data as necessary, and are resistant to overfitting or underfitting. However, most existing works assume that the sensor measurements used to learn the Bayesian nonparametric target kinematics models are obtained a priori or that the target kinematics can be measured by the sensor at any given time throughout the task. Little work has been done for controlling the sensor with bounded field of view to obtain measurements of mobile targets that are most informative for reducing the uncertainty of the Bayesian nonparametric models. To present the systematic sensor planning approach to leaning Bayesian nonparametric models, the Gaussian process target kinematics model is introduced at first, which is capable of describing time-invariant spatial phenomena, such as ocean currents, temperature distributions and wind velocity fields. The Dirichlet process-Gaussian process target kinematics model is subsequently discussed for modeling mixture of mobile targets, such as pedestrian motion patterns.

Novel information theoretic functions are developed for these introduced Bayesian nonparametric target kinematics models to represent the expected utility of measurements as a function of sensor control inputs and random environmental variables. A Gaussian process expected Kullback Leibler divergence is developed as the expectation of the KL divergence between the current (prior) and posterior Gaussian process target kinematics models with respect to the future measurements. Then, this approach is extended to develop a new information value function that can be used to estimate target kinematics described by a Dirichlet process-Gaussian process mixture model. A theorem is proposed that shows the novel information theoretic functions are bounded. Based on this theorem, efficient estimators of the new information theoretic functions are designed, which are proved to be unbiased with the variance of the resultant approximation error decreasing linearly as the number of samples increases. Computational complexities for optimizing the novel information theoretic functions under sensor dynamics constraints are studied, and are proved to be NP-hard. A cumulative lower bound is then proposed to reduce the computational complexity to polynomial time.

Three sensor planning algorithms are developed according to the assumptions on the target kinematics and the sensor dynamics. For problems where the control space of the sensor is discrete, a greedy algorithm is proposed. The efficiency of the greedy algorithm is demonstrated by a numerical experiment with data of ocean currents obtained by moored buoys. A sweep line algorithm is developed for applications where the sensor control space is continuous and unconstrained. Synthetic simulations as well as physical experiments with ground robots and a surveillance camera are conducted to evaluate the performance of the sweep line algorithm. Moreover, a lexicographic algorithm is designed based on the cumulative lower bound of the novel information theoretic functions, for the scenario where the sensor dynamics are constrained. Numerical experiments with real data collected from indoor pedestrians by a commercial pan-tilt camera are performed to examine the lexicographic algorithm. Results from both the numerical simulations and the physical experiments show that the three sensor planning algorithms proposed in this dissertation based on the novel information theoretic functions are superior at learning the target kinematics with

little or no prior knowledge

Dynamic Programming Approaches for Estimating and Applying Large-scale Discrete Choice Models

People go through their life making all kinds of decisions, and some of these decisions affect their demand for transportation, for example, their choices of where to live and where to work, how and when to travel and which route to take. Transport related choices are typically time dependent and characterized by large number of alternatives that can be spatially correlated. This thesis deals with models that can be used to analyze and predict discrete choices in large-scale networks. The proposed models and methods are highly relevant for, but not limited to, transport applications. We model decisions as sequences of choices within the dynamic discrete choice framework, also known as parametric Markov decision processes. Such models are known to be difficult to estimate and to apply to make predictions because dynamic programming problems need to be solved in order to compute choice probabilities. In this thesis we show that it is possible to explore the network structure and the flexibility of dynamic programming so that the dynamic discrete choice modeling approach is not only useful to model time dependent choices, but also makes it easier to model large-scale static choices. The thesis consists of seven articles containing a number of models and methods for estimating, applying and testing large-scale discrete choice models. In the following we group the contributions under three themes: route choice modeling, large-scale multivariate extreme value (MEV) model estimation and nonlinear optimization algorithms. Five articles are related to route choice modeling. We propose different dynamic discrete choice models that allow paths to be correlated based on the MEV and mixed logit models. The resulting route choice models become expensive to estimate and we deal with this challenge by proposing innovative methods that allow to reduce the estimation cost. For example, we propose a decomposition method that not only opens up for possibility of mixing, but also speeds up the estimation for simple logit models, which has implications also for traffic simulation. Moreover, we compare the utility maximization and regret minimization decision rules, and we propose a misspecification test for logit-based route choice models. The second theme is related to the estimation of static discrete choice models with large choice sets. We establish that a class of MEV models can be reformulated as dynamic discrete choice models on the networks of correlation structures. These dynamic models can then be estimated quickly using dynamic programming techniques and an efficient nonlinear optimization algorithm. Finally, the third theme focuses on structured quasi-Newton techniques for estimating discrete choice models by maximum likelihood. We examine and adapt switching methods that can be easily integrated into usual optimization algorithms (line search and trust region) to accelerate the estimation process. The proposed dynamic discrete choice models and estimation methods can be used in various discrete choice applications. In the area of big data analytics, models that can deal with large choice sets and sequential choices are important. Our research can therefore be of interest in various demand analysis applications (predictive analytics) or can be integrated with optimization models (prescriptive analytics). Furthermore, our studies indicate the potential of dynamic programming techniques in this context, even for static models, which opens up a variety of future research directions.

Propriété d'universalité de la fonction zêta de Riemann

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Access to Better Education: The School Choice Experience of Families Served by Low-Performing Elementary Public Schools in Miami-Dade County

Public school choice education policy attempts to create an education marketplace. Although school choice research has focused on the parent role in the school choice process, little is known about parents served by low-performing schools. Following market theory, students attending low-performing schools should be the primary students attempting to use school choice policy to access high performing schools rather than moving to a better school. However, students remain in these low-performing schools. This study took place in Miami-Dade County, which offers a wide variety of school choice options through charter schools, magnet schools, and open-choice schools. This dissertation utilized a mixed-methods design to examine the decision-making process and school choice options utilized by the parents of students served by low-performing elementary schools in Miami-Dade County. Twenty-two semi-structured interviews were conducted with the parents of students served by low-performing schools. Binary logistic regression models were fitted to the data to compare the demographic characteristics, academic achievement and distance from alternative schooling options between transfers and non-transfers. Multinomial logistic regression models were fitted to the data to evaluate how demographic characteristics, distance to transfer school, and transfer school grade influenced the type of school a transfer student chose. A geographic analysis was conducted to determine how many miles students lived from alternative schooling options and the miles transfer students lived away from their transfer school. The findings of the interview data illustrated that parents’ perceived needs are not being adequately addressed by state policy and county programs. The statistical analysis found that students from higher socioeconomic social groups were not more likely to transfer than students from lower socioeconomic social groups. Additionally, students who did transfer were not likely to end up at a high achieving school. The findings of the binary logistic regression demonstrated that transfer students were significantly more likely to live near alternative school options.