Descripción de parámetros glóticos basados en el modelado de los pliegues vocales para la detección de patología de la voz

Las patologías de la voz se han transformado en los últimos tiempos en una problemática social con cierto calado. La contaminación de las ciudades, hábitos como el de fumar, el uso de aparatos de aire acondicionado, etcétera, contribuyen a ello. Esto alcanza más relevancia en profesionales que utilizan su voz de manera frecuente, como, por ejemplo, locutores, cantantes, profesores o teleoperadores. Por todo ello resultan de especial interés las técnicas de ayuda al diagnóstico que son capaces de extraer conclusiones clínicas a partir de una muestra de la voz grabada con un micrófono, frente a otras invasivas que implican la exploración utilizando laringoscopios, fibroscopios o videoendoscopios, técnicas en cualquier caso mucho más molestas para los pacientes al exigir la introducción parcial del instrumental citado por la garganta, en actuaciones consideradas de tipo quirúrgico. Dentro de aquellas técnicas se ha avanzado mucho en un período de tiempo relativamente corto. En lo que se refiere al diagnóstico de patologías, hemos pasado en los últimos quince años de trabajar principalmente con parámetros extraídos de la señal de voz –tanto en el dominio del tiempo como en el de la frecuencia– y con escalas elaboradas con valoraciones subjetivas realizadas por expertos a hacerlo también con parámetros procedentes de estimaciones de la fuente glótica. La importancia de utilizar la fuente glótica reside, a grandes rasgos, en que se trata de una señal vinculada directamente al estado de la estructura laríngea del locutor y también en que está generalmente menos influida por el tracto vocal que la señal de voz. Es conocido que el tracto vocal guarda más relación con el mensaje hablado, y su presencia dificulta el proceso de detección de patología vocal. Estas estimaciones de la fuente glótica han sido obtenidas a través de técnicas de filtrado inverso desarrolladas por nuestro grupo de investigación. Hemos conseguido, además, profundizar en la naturaleza de la señal glótica: somos capaces de descomponerla y relacionarla con parámetros biomecánicos de los propios pliegues vocales, obteniendo estimaciones de elementos como la masa, la pérdida de energía o la elasticidad del cuerpo y de la cubierta del pliegue, entre otros. De las componentes de la fuente glótica surgen también los denominados parámetros biométricos, relacionados con la forma de la señal, que constituyen por sí mismos una firma biométrica del individuo. También trabajaremos con parámetros temporales, relacionados con las diferentes etapas que se observan dentro de la señal glótica durante un ciclo de fonación. Por último, consideraremos parámetros clásicos de perturbación y energía de la señal. En definitiva, contamos ahora con una considerable cantidad de parámetros glóticos que conforman una base estadística multidimensional, destinada a ser capaz de discriminar personas con voces patológicas o disfónicas de aquellas que no presentan patología en la voz o con voces sanas o normofónicas. Esta tesis doctoral se ocupa de varias cuestiones: en primer lugar, es necesario analizar cuidadosamente estos nuevos parámetros, por lo que ofreceremos una completa descripción estadística de los mismos. También estudiaremos cuestiones como la distribución de los parámetros atendiendo a criterios como el de normalidad estadística de los mismos, ocupándonos especialmente de la diferencia entre las distribuciones que presentan sujetos sanos y sujetos con patología vocal. Para todo ello emplearemos diferentes técnicas estadísticas: generación de elementos y diagramas descriptivos, pruebas de normalidad y diversos contrastes de hipótesis, tanto paramétricos como no paramétricos, que considerarán la diferencia entre los grupos de personas sanas y los grupos de personas con alguna patología relacionada con la voz. Además, nos interesa encontrar relaciones estadísticas entre los parámetros, de cara a eliminar posibles redundancias presentes en el modelo, a reducir la dimensionalidad del problema y a establecer un criterio de importancia relativa en los parámetros en cuanto a su capacidad discriminante para el criterio patológico/sano. Para ello se aplicarán técnicas estadísticas como la Correlación Lineal Bivariada y el Análisis Factorial basado en Componentes Principales. Por último, utilizaremos la conocida técnica de clasificación Análisis Discriminante, aplicada a diferentes combinaciones de parámetros y de factores, para determinar cuáles de ellas son las que ofrecen tasas de acierto más prometedoras. Para llevar a cabo la experimentación se ha utilizado una base de datos equilibrada y robusta formada por doscientos sujetos, cien de ellos pertenecientes al género femenino y los restantes cien al género masculino, con una proporción también equilibrada entre los sujetos que presentan patología vocal y aquellos que no la presentan. Una de las aplicaciones informáticas diseñada para llevar a cabo la recogida de muestras también es presentada en esta tesis. Los distintos estudios estadísticos realizados nos permitirán identificar aquellos parámetros que tienen una mayor contribución a la hora de detectar la presencia de patología vocal. Alguno de los estudios, además, nos permitirá presentar una ordenación de los parámetros en base a su importancia para realizar la detección. Por otra parte, también concluiremos que en ocasiones es conveniente realizar una reducción de la dimensionalidad de los parámetros para mejorar las tasas de detección. Por fin, las propias tasas de detección constituyen quizá la conclusión más importante del trabajo. Todos los análisis presentes en el trabajo serán realizados para cada uno de los dos géneros, de acuerdo con diversos estudios previos que demuestran que los géneros masculino y femenino deben tratarse de forma independiente debido a las diferencias orgánicas observadas entre ambos. Sin embargo, en lo referente a la detección de patología vocal contemplaremos también la posibilidad de trabajar con la base de datos unificada, comprobando que las tasas de acierto son también elevadas. Abstract Voice pathologies have become recently in a social problem that has reached a certain concern. Pollution in cities, smoking habits, air conditioning, etc. contributes to it. This problem is more relevant for professionals who use their voice frequently: speakers, singers, teachers, actors, telemarketers, etc. Therefore techniques that are capable of drawing conclusions from a sample of the recorded voice are of particular interest for the diagnosis as opposed to other invasive ones, involving exploration by laryngoscopes, fiber scopes or video endoscopes, which are techniques much less comfortable for patients. Voice quality analysis has come a long way in a relatively short period of time. In regard to the diagnosis of diseases, we have gone in the last fifteen years from working primarily with parameters extracted from the voice signal (both in time and frequency domains) and with scales drawn from subjective assessments by experts to produce more accurate evaluations with estimates derived from the glottal source. The importance of using the glottal source resides broadly in that this signal is linked to the state of the speaker's laryngeal structure. Unlike the voice signal (phonated speech) the glottal source, if conveniently reconstructed using adaptive lattices, may be less influenced by the vocal tract. As it is well known the vocal tract is related to the articulation of the spoken message and its influence complicates the process of voice pathology detection, unlike when using the reconstructed glottal source, where vocal tract influence has been almost completely removed. The estimates of the glottal source have been obtained through inverse filtering techniques developed by our research group. We have also deepened into the nature of the glottal signal, dissecting it and relating it to the biomechanical parameters of the vocal folds, obtaining several estimates of items such as mass, loss or elasticity of cover and body of the vocal fold, among others. From the components of the glottal source also arise the so-called biometric parameters, related to the shape of the signal, which are themselves a biometric signature of the individual. We will also work with temporal parameters related to the different stages that are observed in the glottal signal during a cycle of phonation. Finally, we will take into consideration classical perturbation and energy parameters. In short, we have now a considerable amount of glottal parameters in a multidimensional statistical basis, designed to be able to discriminate people with pathologic or dysphonic voices from those who do not show pathology. This thesis addresses several issues: first, a careful analysis of these new parameters is required, so we will offer a complete statistical description of them. We will also discuss issues such as distribution of the parameters, considering criteria such as their statistical normality. We will take special care in the analysis of the difference between distributions from healthy subjects and the distributions from pathological subjects. To reach these goals we will use different statistical techniques such as: generation of descriptive items and diagramas, tests for normality and hypothesis testing, both parametric and nonparametric. These latter techniques consider the difference between the groups of healthy subjects and groups of people with an illness related to voice. In addition, we are interested in finding statistical relationships between parameters. There are various reasons behind that: eliminate possible redundancies in the model, reduce the dimensionality of the problem and establish a criterion of relative importance in the parameters. The latter reason will be done in terms of discriminatory power for the criterion pathological/healthy. To this end, statistical techniques such as Bivariate Linear Correlation and Factor Analysis based on Principal Components will be applied. Finally, we will use the well-known technique of Discriminant Analysis classification applied to different combinations of parameters and factors to determine which of these combinations offers more promising success rates. To perform the experiments we have used a balanced and robust database, consisting of two hundred speakers, one hundred of them males and one hundred females. We have also used a well-balanced proportion where subjects with vocal pathology as well as subjects who don´t have a vocal pathology are equally represented. A computer application designed to carry out the collection of samples is also presented in this thesis. The different statistical analyses performed will allow us to determine which parameters contribute in a more decisive way in the detection of vocal pathology. Therefore, some of the analyses will even allow us to present a ranking of the parameters based on their importance for the detection of vocal pathology. On the other hand, we will also conclude that it is sometimes desirable to perform a dimensionality reduction in order to improve the detection rates. Finally, detection rates themselves are perhaps the most important conclusion of the work. All the analyses presented in this work have been performed for each of the two genders in agreement with previous studies showing that male and female genders should be treated independently, due to the observed functional differences between them. However, with regard to the detection of vocal pathology we will consider the possibility of working with the unified database, ensuring that the success rates obtained are also high.

Feature selection by multi-objective optimisation: Application to network anomaly detection by hierarchical self-organising maps

Feature selection is an important and active issue in clustering and classification problems. By choosing an adequate feature subset, a dataset dimensionality reduction is allowed, thus contributing to decreasing the classification computational complexity, and to improving the classifier performance by avoiding redundant or irrelevant features. Although feature selection can be formally defined as an optimisation problem with only one objective, that is, the classification accuracy obtained by using the selected feature subset, in recent years, some multi-objective approaches to this problem have been proposed. These either select features that not only improve the classification accuracy, but also the generalisation capability in case of supervised classifiers, or counterbalance the bias toward lower or higher numbers of features that present some methods used to validate the clustering/classification in case of unsupervised classifiers. The main contribution of this paper is a multi-objective approach for feature selection and its application to an unsupervised clustering procedure based on Growing Hierarchical Self-Organising Maps (GHSOMs) that includes a new method for unit labelling and efficient determination of the winning unit. In the network anomaly detection problem here considered, this multi-objective approach makes it possible not only to differentiate between normal and anomalous traffic but also among different anomalies. The efficiency of our proposals has been evaluated by using the well-known DARPA/NSL-KDD datasets that contain extracted features and labelled attacks from around 2 million connections. The selected feature sets computed in our experiments provide detection rates up to 99.8% with normal traffic and up to 99.6% with anomalous traffic, as well as accuracy values up to 99.12%.

Fitness assessment of document model

Document classification is a supervised machine learning process, where predefined category labels are assigned to documents based on the hypothesis derived from training set of labelled documents. Documents cannot be directly interpreted by a computer system unless they have been modelled as a collection of computable features. Rogati and Yang [M. Rogati and Y. Yang, Resource selection for domain-specific cross-lingual IR, in SIGIR 2004: Proceedings of the 27th annual international conference on Research and Development in Information Retrieval, ACM Press, Sheffied: United Kingdom, pp. 154-161.] pointed out that the effectiveness of document classification system may vary in different domains. This implies that the quality of document model contributes to the effectiveness of document classification. Conventionally, model evaluation is accomplished by comparing the effectiveness scores of classifiers on model candidates. However, this kind of evaluation methods may encounter either under-fitting or over-fitting problems, because the effectiveness scores are restricted by the learning capacities of classifiers. We propose a model fitness evaluation method to determine whether a model is sufficient to distinguish positive and negative instances while still competent to provide satisfactory effectiveness with a small feature subset. Our experiments demonstrated how the fitness of models are assessed. The results of our work contribute to the researches of feature selection, dimensionality reduction and document classification.

Effectiveness of document representation for classification

Conventionally, document classification researches focus on improving the learning capabilities of classifiers. Nevertheless, according to our observation, the effectiveness of classification is limited by the suitability of document representation. Intuitively, the more features that are used in representation, the more comprehensive that documents are represented. However, if a representation contains too many irrelevant features, the classifier would suffer from not only the curse of high dimensionality, but also overfitting. To address this problem of suitableness of document representations, we present a classifier-independent approach to measure the effectiveness of document representations. Our approach utilises a labelled document corpus to estimate the distribution of documents in the feature space. By looking through documents in this way, we can clearly identify the contributions made by different features toward the document classification. Some experiments have been performed to show how the effectiveness is evaluated. Our approach can be used as a tool to assist feature selection, dimensionality reduction and document classification.

An advanced real-time predictive maintenance framework for large scale machine systems

This thesis introduces and develops a novel real-time predictive maintenance system to estimate the machine system parameters using the motion current signature. Recently, motion current signature analysis has been addressed as an alternative to the use of sensors for monitoring internal faults of a motor. A maintenance system based upon the analysis of motion current signature avoids the need for the implementation and maintenance of expensive motion sensing technology. By developing nonlinear dynamical analysis for motion current signature, the research described in this thesis implements a novel real-time predictive maintenance system for current and future manufacturing machine systems. A crucial concept underpinning this project is that the motion current signature contains infor­mation relating to the machine system parameters and that this information can be extracted using nonlinear mapping techniques, such as neural networks. Towards this end, a proof of con­cept procedure is performed, which substantiates this concept. A simulation model, TuneLearn, is developed to simulate the large amount of training data required by the neural network ap­proach. Statistical validation and verification of the model is performed to ascertain confidence in the simulated motion current signature. Validation experiment concludes that, although, the simulation model generates a good macro-dynamical mapping of the motion current signature, it fails to accurately map the micro-dynamical structure due to the lack of knowledge regarding performance of higher order and nonlinear factors, such as backlash and compliance. Failure of the simulation model to determine the micro-dynamical structure suggests the pres­ence of nonlinearity in the motion current signature. This motivated us to perform surrogate data testing for nonlinearity in the motion current signature. Results confirm the presence of nonlinearity in the motion current signature, thereby, motivating the use of nonlinear tech­niques for further analysis. Outcomes of the experiment show that nonlinear noise reduction combined with the linear reverse algorithm offers precise machine system parameter estimation using the motion current signature for the implementation of the real-time predictive maintenance system. Finally, a linear reverse algorithm, BJEST, is developed and applied to the motion current signature to estimate the machine system parameters.

Feature Extraction for Classification in the Data Mining Process

Dimensionality reduction is a very important step in the data mining process. In this paper, we consider feature extraction for classification tasks as a technique to overcome problems occurring because of “the curse of dimensionality”. Three different eigenvector-based feature extraction approaches are discussed and three different kinds of applications with respect to classification tasks are considered. The summary of obtained results concerning the accuracy of classification schemes is presented with the conclusion about the search for the most appropriate feature extraction method. The problem how to discover knowledge needed to integrate the feature extraction and classification processes is stated. A decision support system to aid in the integration of the feature extraction and classification processes is proposed. The goals and requirements set for the decision support system and its basic structure are defined. The means of knowledge acquisition needed to build up the proposed system are considered.

Entropy Based Approach to Finding Interacting Genes Responsible for Complex Human Disease

2000 Mathematics Subject Classification: 62P10, 92D10, 92D30, 94A17, 62L10.

Denoising Manifolds for Dimension

2000 Mathematics Subject Classification: 68T01, 62H30, 32C09.

Visualisation and browsing of image databases

In this chapter we provide a comprehensive overview of the emerging field of visualising and browsing image databases. We start with a brief introduction to content-based image retrieval and the traditional query-by-example search paradigm that many retrieval systems employ. We specify the problems associated with this type of interface, such as users not being able to formulate a query due to not having a target image or concept in mind. The idea of browsing systems is then introduced as a means to combat these issues, harnessing the cognitive power of the human mind in order to speed up image retrieval.We detail common methods in which the often high-dimensional feature data extracted from images can be used to visualise image databases in an intuitive way. Systems using dimensionality reduction techniques, such as multi-dimensional scaling, are reviewed along with those that cluster images using either divisive or agglomerative techniques as well as graph-based visualisations. While visualisation of an image collection is useful for providing an overview of the contained images, it forms only part of an image database navigation system. We therefore also present various methods provided by these systems to allow for interactive browsing of these datasets. A further area we explore are user studies of systems and visualisations where we look at the different evaluations undertaken in order to test usability and compare systems, and highlight the key findings from these studies. We conclude the chapter with several recommendations for future work in this area. © 2011 Springer-Verlag Berlin Heidelberg.

Semi-supervised Gaussian process latent variable model with pairwise constraints

In machine learning, Gaussian process latent variable model (GP-LVM) has been extensively applied in the field of unsupervised dimensionality reduction. When some supervised information, e.g., pairwise constraints or labels of the data, is available, the traditional GP-LVM cannot directly utilize such supervised information to improve the performance of dimensionality reduction. In this case, it is necessary to modify the traditional GP-LVM to make it capable of handing the supervised or semi-supervised learning tasks. For this purpose, we propose a new semi-supervised GP-LVM framework under the pairwise constraints. Through transferring the pairwise constraints in the observed space to the latent space, the constrained priori information on the latent variables can be obtained. Under this constrained priori, the latent variables are optimized by the maximum a posteriori (MAP) algorithm. The effectiveness of the proposed algorithm is demonstrated with experiments on a variety of data sets. © 2010 Elsevier B.V.

Investigation and modelling of tremor reducer with the technology of targeted energy transfer

This thesis presents the study of a two-degree-of-freedom (2 DOF) nonlinear system consisting of two grounded linear oscillators coupled to two separate light weight nonlinear energy sinks of an essentially nonlinear stiffness. In this thesis, Targeted Energy Transfer (TET) and NES concept are introduced. Previous studies and research of Energy pumping and NES are presented. The characters in nonlinear energy pumping have been introduced at the start of the thesis. For the aim to design the application of a tremor reduction assessment device, the knowledge of tremor reduction has also been mentioned. Two main parties have been presented in the research: dynamical theoretic method of nonlinear energy pumping study and experiments of nonlinear vibration reduction model. In this thesis, nonlinear energy sink (NES) has been studied and used as a core attachment for the research. A new theoretic method of nonlinear vibration reduction which with two NESs has been attached to a primary system has been designed and tested with the technology of targeted energy transfer. Series connection and parallel connection structure systems have been designed to run the tests. Genetic algorithm has been used and presented in the thesis for searching the fit components. One more experiment has been tested with the final components. The results have been compared to find out most efficiency structure and components for the theoretic model. A tremor reduction experiment has been designed and presented in the thesis. The experiment is for designing an application for reducing human body tremor. By using the theoretic method earlier, the experiment has been designed and tested with a tremor reduction model. The experiment includes several tests, one single NES attached system and two NESs attached systems with different structures. The results of theoretic models and experiment models have been compared. The discussion has been made in the end. At the end of the thesis, some further work has been considered to designing the device of the tremor reduction.

Exploring the integration of data mining and data visualization

Due to the rapid advances in computing and sensing technologies, enormous amounts of data are being generated everyday in various applications. The integration of data mining and data visualization has been widely used to analyze these massive and complex data sets to discover hidden patterns. For both data mining and visualization to be effective, it is important to include the visualization techniques in the mining process and to generate the discovered patterns for a more comprehensive visual view. In this dissertation, four related problems: dimensionality reduction for visualizing high dimensional datasets, visualization-based clustering evaluation, interactive document mining, and multiple clusterings exploration are studied to explore the integration of data mining and data visualization. In particular, we 1) propose an efficient feature selection method (reliefF + mRMR) for preprocessing high dimensional datasets; 2) present DClusterE to integrate cluster validation with user interaction and provide rich visualization tools for users to examine document clustering results from multiple perspectives; 3) design two interactive document summarization systems to involve users efforts and generate customized summaries from 2D sentence layouts; and 4) propose a new framework which organizes the different input clusterings into a hierarchical tree structure and allows for interactive exploration of multiple clustering solutions.

LCD-OpenPACS: sistema integrado de telerradiologia com auxílio ao diagnóstico de nódulos pulmonares em exames de tomografia computadorizada

Lung cancer is one of the most common types of cancer and has the highest mortality rate. Patient survival is highly correlated with early detection. Computed Tomography technology services the early detection of lung cancer tremendously by offering aminimally invasive medical diagnostic tool. However, the large amount of data per examination makes the interpretation difficult. This leads to omission of nodules by human radiologist. This thesis presents a development of a computer-aided diagnosis system (CADe) tool for the detection of lung nodules in Computed Tomography study. The system, called LCD-OpenPACS (Lung Cancer Detection - OpenPACS) should be integrated into the OpenPACS system and have all the requirements for use in the workflow of health facilities belonging to the SUS (Brazilian health system). The LCD-OpenPACS made use of image processing techniques (Region Growing and Watershed), feature extraction (Histogram of Gradient Oriented), dimensionality reduction (Principal Component Analysis) and classifier (Support Vector Machine). System was tested on 220 cases, totaling 296 pulmonary nodules, with sensitivity of 94.4% and 7.04 false positives per case. The total time for processing was approximately 10 minutes per case. The system has detected pulmonary nodules (solitary, juxtavascular, ground-glass opacity and juxtapleural) between 3 mm and 30 mm.

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.

Continuous statistical modelling for rapid detection of adulteration of extra virgin olive oil using mid infrared and Raman spectroscopic data

The main objective of this work was to develop a novel dimensionality reduction technique as a part of an integrated pattern recognition solution capable of identifying adulterants such as hazelnut oil in extra virgin olive oil at low percentages based on spectroscopic chemical fingerprints. A novel Continuous Locality Preserving Projections (CLPP) technique is proposed which allows the modelling of the continuous nature of the produced in-house admixtures as data series instead of discrete points. The maintenance of the continuous structure of the data manifold enables the better visualisation of this examined classification problem and facilitates the more accurate utilisation of the manifold for detecting the adulterants. The performance of the proposed technique is validated with two different spectroscopic techniques (Raman and Fourier transform infrared, FT-IR). In all cases studied, CLPP accompanied by k-Nearest Neighbors (kNN) algorithm was found to outperform any other state-of-the-art pattern recognition techniques.