SIDS deaths exhibit a seasonal pattern with a winter peak, and the cause of this seasonality is unknown. The seasonal pattern is not symmetrical and it has been thought that the relatively flat winter peak may be due to the existence of more than one underlying population, where each population corresponds to a different cause of seasonality. In this thesis, mixtures of von Mises distributions have been fitted using maximum likelihood estimation to determine whether there is heterogeneity in the UK SIDS data. Various computational problems arise with the fitting procedures and attempts to tackle these for the SIDS data are discussed. A bootstrap likelihood ratio method is used to assess the number of components in the mixture, and its properties are investigated by simulation. Changes in the seasonal pattern since the 'back to sleep' campaign are also examined as any differences might give clues as to what caused the fall in 1992, and what the reasons for the remaining deaths might be. The von Mises distributions are compared with cosinor analysis and skewed regression models to determine the most appropriate method for modelling the seasonality in the data. Mixtures of Weibull and Gamma distributions are used to model the age distribution in SIDS. The motivation for this was to determine whether there are two or more groups of babies whose age-at-death distributions are different and to examine any changes since the 'back to sleep' campaign. Generalised linear models have previously been used to determine whether month of birth is an independent risk factor in addition to month of death and age at death. In this thesis, mixtures of these generalised linear models have been fitted using the EM algorithm to determine whether there are different groups of babies with different risks. Childhood type 1 diabetes mellitus is another condition which exhibits a seasonal pattern in diagnosis. The thesis concludes by considering analysis of these data using the mixture modelling approach.

In this thesis, the problem of probability density function estimation using finite mixture models is considered. Gaussian mixture modelling is used to provide a semi-parametric density estimate for a given data set. The fundamental problem with this approach is that the number of mixtures required to adequately describe the data is not known in advance. In this work, a predictive validation technique [91] is studied and developed as a useful, operational tool that automatically selects the number of components for Gaussian mixture models. The predictive validation test approves a candidate model if, for the set of events they try to predict, the predicted frequencies derived from the model match the empirical ones derived from the data set. A model selection algorithm, based on the validation test, is developed which prevents both problems of over-fitting and under-fitting. We investigate the influence of the various parameters in the model selection method in order to develop it into a robust operational tool. The capability of the proposed method in real world applications is examined on the problem of face image segmentation for automatic initialisation of lip tracking systems. A segmentation approach is proposed which is based on Gaussian mixture modelling of the pixels RGB values using the predictive validation technique. The lip region segmentation is based on the estimated model. First a grouping of the model components is performed using a novel approach. The resulting groups are then the basis of a Bayesian decision making system which labels the pixels in the mouth area as lip or non-lip. The experimental results demonstrate the superiority of the method over the conventional clustering approaches. In order to improve the method computationally an image sampling technique is applied which is based on Sobol sequences. Also, the image modelling process is strengthened by incorporating spatial contextual information using two different methods, a Neigh-bourhood Expectation Maximisation technique and a spatial clustering method based on a Gibbs/Markov random field modelling approach. Both methods are developed within the proposed modelling framework. The results obtained on the lip segmentation application suggest that spatial context is beneficial.

Environmental exposure and outcomes assessment is a great challenge to scientists. Increasingly more and more detailed data are becoming available to understand the nature and complexity of the relationships involved. The methodology of mixture models provides a means to understand, quantify and describe features and relation- ships within complex data sets. In this thesis, we focussed on a number of applied problems to characterise complex environmental exposure and outcomes, including: assessing the interaction between environmental exposures as risk factors for health outcomes; identifying di®ering environmental outcomes across a region; and estab- lishing patterns in the size and concentration of aerosol particles over time. Mixture model approaches to address these problems are developed and examined for their suitability in these contexts.

Pharmaceuticals are contaminants of emerging concern which have been a target of increasing attention by the scientific community. Pharmaceuticals presenting high consumption, incomplete metabolism and incomplete removal at wastewater treatment plants have been frequently detected in aquatic ecosystems worldwide. This is the case of the pharmaceuticals metformin (MET), bisoprolol (BIS), sotalol (SOT) and ranitidine (RAN). However, ecotoxicity data for these contaminants are scarce, especially regarding behavior effects and chronic toxicity. In addition, the knowledge regarding the joint toxicity of these pharmaceuticals on non-target organisms is still incipient, which makes their environment risk assessment uncertain. This study aimed to fill these knowledge gaps for these four pharmaceuticals, by carrying out toxicity tests using five test organisms from three trophic levels. Different endpoints were assessed in tests with Raphidocelis subcapitata (algae), Lemna minor (macrophyte), Daphnia similis (crustacean), Hydra attenuate (cnidarian) and Danio rerio (fish). The binary and quaternary mixture acute toxicity for these pharmaceuticals were assessed on D. similis and D. rerio embryo tests, respectively. This study also aimed to evaluate the predictive accuracy of the Concentration addition (CA) and the Independent action (IA) classic models. In addition, the nature of the possible toxicological interactions between the pharmaceuticals in binary mixtures were also evaluated, using the Combination Index-isobologram (CI) method. The modelling of the concentration-response curves and the associated statistical analyses were performed using the automated spreadsheet ToxCalcMix v.1.0 and the software OriginPro 2015. The software CompuSyn was used for performing the mixture analyses with the CI method. The experimental planning of the binary mixture tests was performed using the fractioned factorial design, in order to cover several possible ratio and level-dependent effects with a reduced number of test organisms. The results obtained in this study are shown in four articles. In article 1, we provided a critical review and discussed the misunderstandings, deficiencies and data gaps on the ecotoxicity data of pharmaceuticals and personal care products mixtures published in the literature. In the following articles, the results obtained from the single and mixture toxicity tests performed in this study were presented and discussed. The pharmaceuticals MET (article 2) and BIS (article 3) were classified as hazardous to the aquatic environment, in the acute toxicity category. However, an ecological risk is not expected for the pelagic freshwater species exposed to these two pharmaceuticals, based on the chronic data obtained. The results obtained from the mixture toxicity tests (article 4) showed that most of the observed toxicity effects from the binary mixtures were in the zone between the predicted effects by the CA and IA models. The CI model showed to be an useful tool to describe the possible toxicological interactions occurring between the pharmaceuticals in joint action. Even statistically significant non-effect concentrations of the pharmaceuticals added up to induce significant adverse effects in mixtures (something from nothing). It was concluded that ecological risk assessment based on single toxic effects can underestimate the real impact of environmental contaminants on aquatic ecosystems. / A contaminação ambiental por fármacos tem sido alvo de crescente preocupação pela comunidade científica. Fármacos de elevado consumo, incompleto metabolismo e remoção incompleta em estações de tratamento de esgoto, como é o caso da metformina (MET), bisoprolol (BIS), sotalol (SOT) e ranitidina (RAN), têm sido frequentemente detectados em matrizes aquáticas do mundo todo. Apesar disso, dados ecotoxicológicos consistentes para esses contaminantes são escassos, principalmente com relação a efeitos comportamentais e oriundos de estudos crônicos. Além disso, o entendimento dos efeitos de suas ações combinadas em organismos não-alvo é ainda incipiente, o que gera incertezas na avaliação dos seus riscos ambientais. Esta pesquisa teve por objetivo preencher essas lacunas de conhecimentos para esses quatro fármacos, por meio da realização de testes com cinco diferentes organismos-teste de três diferentes níveis tróficos. Foram analisados diferentes parâmetros avaliativos em testes com os organismos aquáticos Raphidocelis subcapitata (alga), Lemna minor (macrófita), Daphnia similis (crustáceo), Hydra attenuata (cnidário) e Danio rerio (peixe). As toxicidades agudas das misturas binárias e quaternárias desses quatro fármacos também foram avaliadas em testes com D. similis e embriões de D. rerio, respectivamente. Este trabalho também teve por objetivo avaliar a acurácia preditiva dos modelos de adição de concentração (CA) e ação independente (IA) e analisar a natureza das possíveis interações toxicológicas entre os fármacos, em misturas binárias, usando o modelo do Índice de Combinação (CI). A modelagem das relações concentração-resposta e as análises estatísticas associadas foram realizadas empregando-se a planilha automatizada ToxCalcMix versão 1.0 e o software OriginPro 2015. O software CompuSyn foi utilizado para as análises envolvendo o CI. O planejamento experimental dos testes de misturas binárias foi realizado por meio do design fatorial fracionado, a fim de cobrir diversas possíveis interações em várias proporções e níveis de efeitos, com a redução do número de organismos-teste. Os resultados desta pesquisa estão apresentados em quatro artigos. No artigo 1, realizou-se uma revisão crítica com relação às lacunas de conhecimentos e deficiências identificadas a partir da análise da literatura sobre a ecotoxicologia de misturas de fármacos e de produtos de higiene pessoal. Nos artigos seguintes, foram apresentados e discutidos os resultados oriundos dos testes com os quatro fármacos avaliados neste estudo. Os fármacos MET (artigo 2) e BIS (artigo 3) foram classificados como perigosos para o ambiente aquático, na categoria de toxicidade aguda. Contudo, um risco ecológico não é esperado para as espécies pelágicas de água doce expostas a esses dois fármacos, com base nos dados de toxicidade crônica obtidos. Os resultados dos testes de misturas (artigo 4) permitiram concluir que a maior parte dos efeitos observados das misturas binárias estiveram na zona entre os efeitos preditos pelos modelos clássicos de CA e IA. O modelo do CI mostrou-se uma ferramenta útil para descrever a natureza das possíveis interações toxicológicas que ocorrem entre os fármacos em ações combinadas. Mesmo concentrações de nenhum efeito estatisticamente significativo dos fármacos causaram efeitos adversos significativos quando em misturas (something from nothing). Concluiu-se que avaliações de risco ecológicas baseadas em efeitos tóxicos individuais de contaminantes ambientais podem subestimar o real impacto desses compostos em ecossistemas aquáticos.

A literature review of metal mixture interaction analyses identified that there was not a consistent method to determine the impact of metal mixtures on an aquatic organism. The review also revealed that a majority of the research on mixtures made use of water concentrations only. Therefore research was conducted to determine the relationship between exposure, bioaccumulation and chronic effects of the four elements As, Co, Cr and Mn individually. Mechanistically based saturation models of bioaccumulation and toxicity were determined for the benthic invertebrate Hyalella azteca, from which lethal water concentrations and body concentrations were also determined. These models were then combined with those previously done for the metals Cd, Cu, Ni, Pb, Tl and Zn to model the impact of 10 metal mixtures on bioaccumulation in short term (1-week) exposures and on bioaccumulation and toxicity in chronic (4-week) exposures at “equi-toxic” concentrations. Interactions between the metals were identified in which; Cd, Co and Ni bioaccumulations were significantly inhibited, Tl and Zn bioaccumulations were marginally inhibited, there was no impact on Cr, Cu or Mn bioaccumulation, and both As and Pb bioaccumulation were enhanced by some mixtures of metals. It was determined that strict competitive inhibition may be a plausible mechanism of interaction affecting Co, Cd and Ni bioaccumulation but not for any of the other metals. However, it is possible that other interactions such as non-competitive or anti-competitive inhibition may have been responsible. A metal effects addition model (MEAM) was developed for Hyalella azteca based on both the bioaccumulation (body concentrations) to effects and the exposure (water concentration) to effects relationships developed from the single metal only studies The MEAM was used to predict the impact of metal mixture exposures on mortality. Toxicity was under-estimated when based on measured water or body concentrations, however, its best prediction was based on body concentrations. The MEAM, when based on measured body concentrations, takes bioavailability into account, which is important since the chemical characteristics of water can greatly alter the bioavailability and therefore toxicity of metals. The MEAM was compared to the traditional Concentration Addition Model (CAM), which calculates toxic units based on water concentrations and LC50s or body concentrations and LBC50s. The CAM overestimated toxicity, but had its best prediction when based on water concentrations. Over all, the best fit to observed mortality was the prediction by the MEAM, based on body concentrations. The measurement of bioaccumulated metals and the use of the MEAM could be important in field site assessments since it takes into account changes in bioavailability due to different site water chemistries whereas the traditional CAM based on water concentration does not.

A literature review of metal mixture interaction analyses identified that there was not a consistent method to determine the impact of metal mixtures on an aquatic organism. The review also revealed that a majority of the research on mixtures made use of water concentrations only. Therefore research was conducted to determine the relationship between exposure, bioaccumulation and chronic effects of the four elements As, Co, Cr and Mn individually. Mechanistically based saturation models of bioaccumulation and toxicity were determined for the benthic invertebrate Hyalella azteca, from which lethal water concentrations and body concentrations were also determined. These models were then combined with those previously done for the metals Cd, Cu, Ni, Pb, Tl and Zn to model the impact of 10 metal mixtures on bioaccumulation in short term (1-week) exposures and on bioaccumulation and toxicity in chronic (4-week) exposures at “equi-toxic” concentrations. Interactions between the metals were identified in which; Cd, Co and Ni bioaccumulations were significantly inhibited, Tl and Zn bioaccumulations were marginally inhibited, there was no impact on Cr, Cu or Mn bioaccumulation, and both As and Pb bioaccumulation were enhanced by some mixtures of metals. It was determined that strict competitive inhibition may be a plausible mechanism of interaction affecting Co, Cd and Ni bioaccumulation but not for any of the other metals. However, it is possible that other interactions such as non-competitive or anti-competitive inhibition may have been responsible. A metal effects addition model (MEAM) was developed for Hyalella azteca based on both the bioaccumulation (body concentrations) to effects and the exposure (water concentration) to effects relationships developed from the single metal only studies The MEAM was used to predict the impact of metal mixture exposures on mortality. Toxicity was under-estimated when based on measured water or body concentrations, however, its best prediction was based on body concentrations. The MEAM, when based on measured body concentrations, takes bioavailability into account, which is important since the chemical characteristics of water can greatly alter the bioavailability and therefore toxicity of metals. The MEAM was compared to the traditional Concentration Addition Model (CAM), which calculates toxic units based on water concentrations and LC50s or body concentrations and LBC50s. The CAM overestimated toxicity, but had its best prediction when based on water concentrations. Over all, the best fit to observed mortality was the prediction by the MEAM, based on body concentrations. The measurement of bioaccumulated metals and the use of the MEAM could be important in field site assessments since it takes into account changes in bioavailability due to different site water chemistries whereas the traditional CAM based on water concentration does not.

Face verification is a challenging pattern recognition problem. The face is a biometric that, we as humans, know can be recognised. However, the face is highly deformable and its appearance alters significantly when the pose, illumination or expression changes. These changes in appearance are most notable for texture images, or two-dimensional (2D) data. But the underlying structure of the face, or three dimensional (3D) data, is not changed by pose or illumination variations. Over the past five years methods have been investigated to combine 2D and 3D face data to improve the accuracy and robustness of face verification. Much of this research has examined the fusion of a 2D verification system and a 3D verification system, known as multi-modal classifier score fusion. These verification systems usually compare two feature vectors (two image representations), a and b, using distance or angular-based similarity measures. However, this does not provide the most complete description of the features being compared as the distances describe at best the covariance of the data, or the second order statistics (for instance Mahalanobis based measures). A more complete description would be obtained by describing the distribution of the feature vectors. However, feature distribution modelling is rarely applied to face verification because a large number of observations is required to train the models. This amount of data is usually unavailable and so this research examines two methods for overcoming this data limitation: 1. the use of holistic difference vectors of the face, and 2. by dividing the 3D face into Free-Parts. The permutations of the holistic difference vectors is formed so that more observations are obtained from a set of holistic features. On the other hand, by dividing the face into parts and considering each part separately many observations are obtained from each face image; this approach is referred to as the Free-Parts approach. The extra observations from both these techniques are used to perform holistic feature distribution modelling and Free-Parts feature distribution modelling respectively. It is shown that the feature distribution modelling of these features leads to an improved 3D face verification system and an effective 2D face verification system. Using these two feature distribution techniques classifier score fusion is then examined. This thesis also examines methods for performing classifier fusion score fusion. Classifier score fusion attempts to combine complementary information from multiple classifiers. This complementary information can be obtained in two ways: by using different algorithms (multi-algorithm fusion) to represent the same face data for instance the 2D face data or by capturing the face data with different sensors (multimodal fusion) for instance capturing 2D and 3D face data. Multi-algorithm fusion is approached as combining verification systems that use holistic features and local features (Free-Parts) and multi-modal fusion examines the combination of 2D and 3D face data using all of the investigated techniques. The results of the fusion experiments show that multi-modal fusion leads to a consistent improvement in performance. This is attributed to the fact that the data being fused is collected by two different sensors, a camera and a laser scanner. In deriving the multi-algorithm and multi-modal algorithms a consistent framework for fusion was developed. The consistent fusion framework, developed from the multi-algorithm and multimodal experiments, is used to combine multiple algorithms across multiple modalities. This fusion method, referred to as hybrid fusion, is shown to provide improved performance over either fusion system on its own. The experiments show that the final hybrid face verification system reduces the False Rejection Rate from 8:59% for the best 2D verification system and 4:48% for the best 3D verification system to 0:59% for the hybrid verification system; at a False Acceptance Rate of 0:1%.

In this thesis a number of statistical methods have been developed and applied to habitat suitability modelling for rare and threatened species. Data available on these species are typically limited. Therefore, developing these models from these data can be problematic and may produce prediction biases. To address these problems there are three aims of this thesis. The _rst aim is to develop and implement frequentist and Bayesian statistical modelling approaches for these types of data. The second aim is develop and implement expert elicitation methods. The third aim is to apply these novel approaches to Australian rare and threatened species case studies with the intention of habitat suitability modelling. The _rst aim is ful_lled by investigating two innovative approaches for habitat suitability modelling and sensitivity analysis of the second approach to priors. The _rst approach is a new multilevel framework developed to model the species distribution at multiple scales and identify excess zeros (absences outside the species range). Applying a statistical modelling approach to the identi_cation of excess zeros has not previously been conducted. The second approach is an extension and application of Bayesian classi_cation trees to modelling the habitat suitability of a threatened species. This is the _rst `real' application of this approach in ecology. Lastly, sensitivity analysis of the priors in Bayesian classi_cation trees are examined for a real case study. Previously, sensitivity analysis of this approach to priors has not been examined. To address the second aim, expert elicitation methods are developed, extended and compared in this thesis. In particular, one elicitation approach is extended from previous research, there is a comparison of three elicitation methods, and one new elicitation approach is proposed. These approaches are illustrated for habitat suitability modelling of a rare species and the opinions of one or two experts are elicited. The _rst approach utilises a simple questionnaire, in which expert opinion is elicited on whether increasing values of a covariate either increases, decreases or does not substantively impact on a response. This approach is extended to express this information as a mixture of three normally distributed prior distributions, which are then combined with available presence/absence data in a logistic regression. This is one of the _rst elicitation approaches within the habitat suitability modelling literature that is appropriate for experts with limited statistical knowledge and can be used to elicit information from single or multiple experts. Three relatively new approaches to eliciting expert knowledge in a form suitable for Bayesian logistic regression are compared, one of which is the questionnaire approach. Included in this comparison of three elicitation methods are a summary of the advantages and disadvantages of these three methods, the results from elicitations and comparison of the prior and posterior distributions. An expert elicitation approach is developed for classi_cation trees, in which the size and structure of the tree is elicited. There have been numerous elicitation approaches proposed for logistic regression, however no approaches have been suggested for classi_cation trees. The last aim of this thesis is addressed in all chapters, since the statistical approaches proposed and extended in this thesis have been applied to real case studies. Two case studies have been examined in this thesis. The _rst is the rare native Australian thistle (Stemmacantha australis), in which the dataset contains a large number of absences distributed over the majority of Queensland, and a small number of presence sites that are only within South-East Queensland. This case study motivated the multilevel modelling framework. The second case study is the threatened Australian brush-tailed rock-wallaby (Petrogale penicillata). The application and sensitivity analysis of Bayesian classi_cation trees, and all expert elicitation approaches investigated in this thesis are applied to this case study. This work has several implications for conservation and management of rare and threatened species. Novel statistical approaches addressing the _rst aim provide extensions to currently existing methods, or propose a new approach, for identi _cation of current and potential habitat. We demonstrate that better model predictions can be achieved using each method, compared to standard techniques. Elicitation approaches addressing the second aim ensure expert knowledge in various forms can be harnessed for habitat modelling, a particular bene_t for rare and threatened species which typically have limited data. Throughout, innovations in statistical methodology are both motivated and illustrated via habitat modelling for two rare and threatened species: the native thistle Stemmacantha australis and the brush-tailed rock wallaby Petrogale penicillata.

Esta tesis presenta diversas contribuciones en los campos de la clasificación automática de texto, traducción automática y traducción asistida por ordenador bajo el marco estadístico. En clasificación automática de texto, se propone una nueva aplicación llamada clasificación de texto bilingüe junto con una serie de modelos orientados a capturar dicha información bilingüe. Con tal fin se presentan dos aproximaciones a esta aplicación; la primera de ellas se basa en una asunción naive que contempla la independencia entre las dos lenguas involucradas, mientras que la segunda, más sofisticada, considera la existencia de una correlación entre palabras en diferentes lenguas. La primera aproximación dió lugar al desarrollo de cinco modelos basados en modelos de unigrama y modelos de n-gramas suavizados. Estos modelos fueron evaluados en tres tareas de complejidad creciente, siendo la más compleja de estas tareas analizada desde el punto de vista de un sistema de ayuda a la indexación de documentos. La segunda aproximación se caracteriza por modelos de traducción capaces de capturar correlación entre palabras en diferentes lenguas. En nuestro caso, el modelo de traducción elegido fue el modelo M1 junto con un modelo de unigramas. Este modelo fue evaluado en dos de las tareas más simples superando la aproximación naive, que asume la independencia entre palabras en differentes lenguas procedentes de textos bilingües. En traducción automática, los modelos estadísticos de traducción basados en palabras M1, M2 y HMM son extendidos bajo el marco de la modelización mediante mixturas, con el objetivo de definir modelos de traducción dependientes del contexto. Asimismo se extiende un algoritmo iterativo de búsqueda basado en programación dinámica, originalmente diseñado para el modelo M2, para el caso de mixturas de modelos M2. Este algoritmo de búsqueda n / Civera Saiz, J. (2008). Novel statistical approaches to text classification, machine translation and computer-assisted translation [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/2502 / Palancia