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Since the passing of the 1988 Education Reform Act British education, particularly at a secondary level, has been transformed. The changes enacted in this and subsequent legislation have opened up state-provided education to a market-oriented system which is led more by the preferences of parents than the dictation of local or national planners. This means that local authorities and other providers of education have been left in a situation where they are relatively powerless to provide adequate schooling in a proactive manner. It is also the case that there is a danger of a 'two-tier' education system developing whereby the better-informed middle classes are served by high achieving schools and less advantaged pupils are left to fill inner city 'sink' schools which cannot provide them with the same educational chances due to lower resource levels. This thesis presents a feasibility study of a variety of techniques drawn from academic and applied geography which can be utilised by such planners in order to better target the resources available to them and improve their reactions to the vagaries of the market. These tools concentrate on geographical information systems (GIS) and spatial modelling techniques. Although both of these sets of techniques have for many years been applied in other areas, including within local Government, they have yet to permeate to a decision-making level in education planning. Thus the time is ripe for their wider dissemination and application in this area. Several examples of the possible uses of GIS are given, using real data for Leeds schools and pupils. Various types of spatial model are described and the most appropriate are calibrated and applied using the same Leeds data. The thesis concludes that the benefits of modelling techniques for planners at all scales, from individual schools to national Government, could be enormous. Through the application of these tools planners will be better placed to provide an education service which caters for all pupils within it. However, there are caveats regarding the requirement for further research into improving model performance and ensuring that output is sufficiently user-friendly.

The major objective of the research is to assess the risk of preterm birth associated with maternal proximity to hazardous waste and pollution from the Sydney Tar Pond sites in Nova Scotia, Canada. The design is spatial modelling of risks of preterm birth in population living in the Cape Breton regional municipality in 1996. The subjects are: 1604 observed cases of preterm birth out of total population of 17559 at risk in 1996. The analysis was done using both the frequentist and the Bayesian approaches. In the frequentist approach, the Poisson model for aggregated data was fitted using the quasi-likelihood approach to accommodate over-dispersion. Weighted regression was also used. In order to accommodate both the random effect and the anticipated spatial effects, Bayesian hierarchical modelling was also used to fit the Poisson model. The result of the Bayesian modelling shows that there is no significant spatial association of risk in the area studied. All the models also show that there is no decrease in risk of preterm birth as we move from the Tar Pond site to other region. None of the other covariates in the model show any significant association with increase risk of preterm birth either. There was no obvious clustering of risk in any region or part. / Thesis / Master of Science (MS)

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Surrogate models are indispensable in the analysis of engineering systems. The quality of surrogate models is determined by the data quality and the model class but achieving a high standard of them is challenging in complex engineering systems. Heterogeneity, implicit constraints, and extreme events are typical examples of the factors that complicate systems, yet they have been underestimated or disregarded in machine learning. This dissertation is dedicated to tackling the challenges in surrogate modeling of complex engineering systems by developing the following machine learning methodologies. (i) Partitioned active learning partitions the design space according to heterogeneity in response features, thereby exploiting localized models to measure the informativeness of unlabeled data. (ii) For the systems with implicit constraints, failure-averse active learning incorporates constraint outputs to estimate the safe region and avoid undesirable failures in learning the target function. (iii) The multi-output extreme spatial learning enables modeling and simulating extreme events in composite fuselage assembly. The proposed methods were applied to real-world case studies and outperformed benchmark methods. / Doctor of Philosophy / Data-driven decisions are ubiquitous in the engineering domain, in which data-driven models are fundamental. Active learning is a subdomain in machine learning that enables data-efficient modeling, and extreme spatial modeling is suitable for analyzing rare events. Although they are superb techniques for data-driven modeling, existing methods thereof cannot effectively address modern engineering systems complicated by heterogeneity, implicit constraints, and rare events. This dissertation is dedicated to advancing active learning and extreme spatial modeling for complex engineering systems by proposing three methodologies. The first method is partitioned active learning that efficiently learns systems, changing their behaviors, by localizing the information measurement. Second, failure-averse active learning is established to learn systems subject to implicit constraints, which cannot be analytically solved, and to minimize constraint violations. Lastly, the multi-output extreme spatial model is developed to model and simulate rare events that are associated with extremely large values in the aircraft manufacturing system. The proposed methods overcome the limitations of existing methods and outperform benchmark methods in the case studies.

Bacteria occupy a wide range of niches with many different types coexisting. They compete directly, with some capable of producing antibiotics that kill other members of the niche. Despite this, long term survival of these ecosystems is possible. Here, we consider a lattice-based three-component system with antibiotic producers, non-producers (or cheaters), and susceptible cells competing. In our system, there is a metabolic cost tied to production rate, resulting in a decrease in growth rate for the producers. Non-producers behave as cheaters that gain the benefit of an antibiotic without the cost of producing it themselves. The susceptible cells are a faster growing different species. The model behaves in a fashion similar to the game “rock-paper-scissors", because producers beat susceptible cells, non-producers beat producers, and susceptible cells beat non-producers. We consider two spatial lattice models, one in which there is a nearest neighbour interaction between cells, and one in which the long-range diffusion of the antibiotic is explicitly included. We consider the parameter space in which the three cell types can coexist (taking into account cost and production rate), and determine the regions in which production rate is too high or too low to allow coexistence. We determine that antibiotic producers will evolve to an optimal production rate and that low-rate producers can outcompete complete cheaters (non-producers). We finally illustrate that the introduction of a fourth “resistant” cell type allows the system to survive with four members for some parameters. In other cases, addition of the resistant cells causes the extinction of the producers, which eventually favours the susceptible cells. / Thesis / Master of Science (MSc) / We looked at computational models of bacterial interaction involving producers, non-producers, and susceptible cell types that interacted in a manner similar to the game “rock-paper-scissors”. We determined that the system is stable for the long term for a given set of parameters, otherwise susceptible cells win as not enough antibiotic is being produced, or too much is being produced, significantly inhibiting the growth of producers. Moreover, we found that these systems can evolve, tending towards one production rate, in order to better allow the system to survive. Non-producers also evolve, tending to low production rates instead. These results have implications in understanding bacteria that cannot be cultured and perhaps aiding in the discovery of novel antibiotics.

<p>This thesis presents methods for multiple imputation that can be applied to missing data and data with confidential variables. Imputation is useful for missing data because it results in a data set that can be analyzed with complete data statistical methods. The missing data are filled in by values generated from a model fit to the observed data. The model specification will depend on the observed data pattern and the missing data mechanism. For example, when the reason why the data is missing is related to the outcome of interest, that is nonignorable missingness, we need to alter the model fit to the observed data to generate the imputed values from a different distribution. Imputation is also used for generating synthetic values for data sets with disclosure restrictions. Since the synthetic values are not actual observations, they can be released for statistical analysis. The interest is in fitting a model that approximates well the relationships in the original data, keeping the utility of the synthetic data, while preserving the confidentiality of the original data. We consider applications of these methods to data from social sciences and epidemiology.</p><p>The first method is for imputation of multivariate continuous data with nonignorable missingness. Regular imputation methods have been used to deal with nonresponse in several types of survey data. However, in some of these studies, the assumption of missing at random is not valid since the probability of missing depends on the response variable. We propose an imputation method for multivariate data sets when there is nonignorable missingness. We fit a truncated Dirichlet process mixture of multivariate normals to the observed data under a Bayesian framework to provide flexibility. With the posterior samples from the mixture model, an analyst can alter the estimated distribution to obtain imputed data under different scenarios. To facilitate that, I developed an R application that allows the user to alter the values of the mixture parameters and visualize the imputation results automatically. I demonstrate this process of sensitivity analysis with an application to the Colombian Annual Manufacturing Survey. I also include a simulation study to show that the correct complete data distribution can be recovered if the true missing data mechanism is known, thus validating that the method can be meaningfully interpreted to do sensitivity analysis.</p><p>The second method uses the imputation techniques for nonignorable missingness to implement a procedure for adaptive design in surveys. Specifically, I develop a procedure that agencies can use to evaluate whether or not it is effective to stop data collection. This decision is based on utility measures to compare the data collected so far with potential follow-up samples. The options are assessed by imputation of the nonrespondents under different missingness scenarios considered by the analyst. The variation in the utility measures is compared to the cost induced by the follow-up sample sizes. We apply the proposed method to the 2007 U.S. Census of Manufactures.</p><p>The third method is for imputation of confidential data sets with spatial locations using disease mapping models. We consider data that include fine geographic information, such as census tract or street block identifiers. This type of data can be difficult to release as public use files, since fine geography provides information that ill-intentioned data users can use to identify individuals. We propose to release data with simulated geographies, so as to enable spatial analyses while reducing disclosure risks. We fit disease mapping models that predict areal-level counts from attributes in the file, and sample new locations based on the estimated models. I illustrate this approach using data on causes of death in North Carolina, including evaluations of the disclosure risks and analytic validity that can result from releasing synthetic geographies.</p> / Dissertation