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In the era of deep and wide-field surveys (e.g. SDSS, LSST, LOFAR, SKA), we have access to an ever-increasing volume of multi-wavelength data for millions of galaxies both locally and at high redshifts. However, inferring the intrinsic properties of the whole population of galaxies requires robust statistical techniques and an understanding of observational bias. In this thesis, I present a study of the Far-Infrared Radio Correlation (FIRC) – a relation which is widely used to infer star-formation rates from otherwise featureless radio sources. Using LOFAR 150MHz, FIRST 1:4GHz, and Herschel infrared luminosities derived from the new LOFAR/H-ATLAS catalogue, we investigate possible variation in the monochromatic (250mm) FIRC at low and high radio frequencies. Although the average FIRC at high radio frequency is consistent with expectations based on a standard power-law radio spectrum, the average correlation at 150MHz is not. We see evidence for redshift evolution of the FIRC at 150MHz, and find that the FIRC varies with stellar mass, dust temperature and specific star formation rate, whether the latter is probed using MAGPHYS fitting, or using mid-infrared colour as a proxy. We can explain the variation, to within σ using a Bayesian partial correlation technique. This work was published as Read et al. (2018) in the Monthly Notices of the Royal Astronomical Society. Identifying an opportunity to increase in the efficiency of black-hole mass estimations, we perform photometric reverberation mapping using the Javelin photometric damped random walk model for the QSO SDSS J144645.44 +625304.0 at ɀ = 0:351 and estimate the Hβ lag of 72 +5-1 days and black hole mass of 108:28 +0.12-0.07 Mʘ. An analysis of the reliability of photometric reverberation mapping conducted using many thousands of simulated light curves shows that we can recover any input lag less than a third of the duration of our observing campaign to within 4per cent on average given our target’s observed signal-to-noise of > 20 and cadence of 14 days. We use our suite of simulated light curves to deconvolve artefacts from the QSO’s posterior lag distribution, increasing the signal-to-noise by a factor of ~3. We exceed the signal-to-noise of the Sloan Digital Sky Survey Reverberation Mapping Project (SDSS-RM) campaign with a quarter of the observing time resulting in a ~310 per cent per cent increase in SNR efficiency over SDSS-RM. Finally, I present a study of the radio luminosity star-formation rate relation directly with the LOFAR Two Metre Sky Survey (LoTSS) DR1, in an effort to understand the mass dependency of the L150MHz - SFR slope reported by Gürkan et al. (2018). Building on our previous study of the FIRC, we develop a fast, generalised algorithm to recover Complete And Noiseless Distributions from Incomplete Data (CANDID). We find that the mass dependency is real and in agreement with previous estimations in the literature when we include the effects of selection biases present in the LoTSS DR1 sample. We also propose that type-Ia supernovae may contribute to a L150MHz excess and construct a joint distribution of our LoTSS observations and the Horizon AGN simulation to test this.

Due to the complexity of the operational design domain of Automated Driving Systems, the industry is trending towards the use of simulation-based methods for their verification and validation (V\&V), which rely on the use of models of the vehicles, sensors, vehicle environments, etc. Depending on the testing requirements, computational capabilities, modeling effort, and other such factors, these models can vary in fidelity. However, this variation in fidelity has an effect on the excitation of the control systems under test, and can therefore affect the results of the tests themselves. Moreover, since every model is an approximation of the actual physical system it represents, there is uncertainty associated with its output. Therefore, we need to be able to compare uncertain system models in order to understand the effect of model fidelity variation on test accuracy. The existing metrics such as Hankel Singular Values compare asymptotic behavior of the models, whereas simulation studies are over finite time. Although some of these metrics may be applied over finite time, they rely on hyper-parameters like weights on time or frequency.In this study, we propose an approach for computing a (pseudo)metric based on the literature for comparing the predictive performance of two models, called finite-time Kullback-Leibler (KL) rate. For any two general state space models with a general additive uncertainty, we first discuss an approach for propagating a general additive uncertainty (represented as a Gaussian Mixture Model (GMM) ) through a linear time-invariant system. We then apply this propagation approach to linear representations of nonlinear systems obtained through Dynamic Mode Decomposition (DMD). We illustrate this combined approach for the comparison of two lateral vehicle dynamics models over an obstacle avoidance maneuver to measure the effect of fidelity on the predictive performance of each model. We also apply this to a \vv problem, wherein we compare the application of the two vehicle dynamics models to reference vehicle trajectories. We see that the KL rate depends not only on the differences in the asymptotic spectral properties of each model, but also on the trajectory being simulated.Through these methods, we illustrate a process for comparing models of different fidelity over relevant trajectories. This enables us to understand which model is most appropriate for a particular scenario in a virtual test. We also show that the variation in the comparison metric can be connected to the phase space of the system. This enables us to use thresholds on the metric to decide when to switch between models of different fidelity.

We propose a new algorithm for tensor decomposition, based on \algname~algorithm, and apply our new algorithmic ideas to blind deconvolution and Gaussian mixture models.Our first contribution is a simple and efficient algorithm to decompose certain symmetric overcomplete order-3 tensors, that is, three dimensional arrays of the form $\tensor T = \sum_{i=1}^n \vm a_i \otimes \vm a_i \otimes \vm a_i$ where the $\vm a_i$s are not linearly independent. Our algorithm comes with a detailed robustness analysis. Our second contribution builds on top of our tensor decomposition algorithm to expand the family of Gaussian mixture models whose parameters can be estimated efficiently. These ideas are also presented in a more general framework of blind deconvolution that makes them applicable to mixture models of identical but very general distributions, including all centrally symmetric distributions with finite 6th moment.

The use of Gaussian mixture model representations for nonlinear estimation is an attractive tool for object tracking and orbit determination. It is the potential for a reasonable balance between algorithm speed and estimator performance that lends these models to applications which necessitate consistent effectiveness in both. Performance of such filters relies on the ability to intelligently manage the number of mixture components, a notion equivalent to model selection among the class of approximating mixtures. The purpose of replacing a state density with a mixture approximation is clearly not better representation of this original density, which by definition is now only approximately represented. Rather, the goal is better representation of the mixture-generated density resulting from a nonlinear transformation of the state. Knowing that use of a compact, linearized estimator is typically desired, successful approximation of the transformed density is accomplished via anticipating and mitigating linearized solution weaknesses while still substantially capturing the original density. A popular method for re-approximation is the act of splitting individual Gaussian components into sub-mixtures. The current work first offers an automated splitting algorithm to address the less investigated measurement update step. A key aspect of the solution is quantification of not only prior uncertainty but also nonlinearity associated with particular regions of the state-space. Via these direct quantifications we pose and solve an optimization problem that yields a simple, optimal splitting direction, i.e., the dimension along which sub-mixture components are added. Automation of the scheme allows recursive splitting until a measure of information content loss signals acceptable error. We extend this new method from nonlinear inference to nonlinear prediction for coverage of both filtering phases. It is demonstrated via numerical simulations that this method automatically refines the number of components to better encompass the effects of the nonlinear transformations. The second model selection domain in this dissertation is sensor scheduling. Many applications have emerged with a significant need for configurability of rapid, real-time, plug-and-play sensing systems. Even with modern computational power, the underlying guidance, navigation, and control tasks can quickly overwhelm processing ability as the problem complexity increases over time and/or degrees of freedom. This dissertation offers an efficient algorithm when selections must be made among multiple sensors at each time-step of a general dynamic linear system. To the author's knowledge, this algorithm is the first in the literature to address the case of time-correlated measurement or process noises and one of the first for spatially-correlated sensors. By deriving an expression of the true scheduling objective explicit in all schedules (which was previously considered infeasible), this method efficiently approximates the effects of accepting or rejecting each measurement on the basis of the underlying estimation and/or control problem.

As the number of Resident Space Objects (RSOs) in Earth Orbit continues to rise by not only increased trackability but also an unprecedented number of commercial launches, conjunction assessment (CA) remains a paramount issue. Maintaining accuracy in probability of collision calculations is specifically of interest because any disparity will cause operators and analysts to lose trust, dismantling the entire CA system. Methods of state uncertainty propagation remain the most tractable way of controlling computational efficiency vs. accuracy. Gaussian Mixture Models (GMMs) have recently been used as an approach to maintain accuracy while decreasing the amount of computation time when compared to a Monte Carlo approach. These GMMs are able to represent the initial probability distribution function (pdf) as a weighted combination of individual Gaussian distributions. When propagated through a nonlinear function, such as the orbital equations of motion, higher order effects are maintained. How that initial pdf is split into a convolution of pdfs is the focus of this and current research. Multidirectional GMMs allow for the pdf to be split along directions of highest nonlinearity in a recursive manner. This study improves on this method by evaluating the directions at every split of every Gaussian mixture and also taking into account the weight of that Gaussian mixture. Equinoctial elements are also explored as a potential element space to perform the splitting due their ability to maintain linearity during propagation. Results show that these improved methods are able to capture the majority of the nonlinear effects very well with relatively few GMs, and therefore can generate accurate Pc calculations, but fail to converge to the exact Monte Carlo value as more mixtures are added in a reasonable time. This is still of use to get within 5% of the Monte Carlo value with very few propagations in highly nonlinear encounters

Clustering analysis is a popular technique in statistics and machine learning. Despite its wide use, certain theoretical properties of clustering algorithms are not well-understood. In this dissertation, we investigate two problems concerning the convergence and consistency of clustering algorithms. The first problem is on the uniform consistency of spectral embeddings in spectral clustering and in, more generally, spectral methods. The second problem is on the statistical convergence of the Expectation Maximization (EM) algorithm on Gaussian mixture models. Specifically, in the first problem, we study the convergence of the spectral embeddings obtained from the leading eigenvectors of certain similarity matrices to their population counterparts. We opt to study this convergence in a uniform (instead of average) sense and highlight the benefits of this choice. Using the Newton-Kantorovich Theorem and other tools from functional analysis, we first establish a general perturbation result for orthonormal bases of invariant subspaces. We then apply this general result to normalized spectral clustering. By tapping into the rich literature of Sobolev spaces and exploiting some concentration results in Hilbert spaces, we are able to prove a finite sample error bound on the uniform consistency error of the spectral embeddings in normalized spectral clustering. In the second problem, we study the convergence behavior of the EM algorithm on Gaussian mixture models with an arbitrary number of mixture components and mixing weights. We show that as long as the means of the components are separated by an amount proportional to the square root of the smaller of the number of components and the dimension, the EM algorithm converges locally to the global optimum of the log-likelihood. Further, we show that the convergence rate is linear and characterize the size of the basin of attraction to the global optimum.

Player tracking data has previously been used to quantify movement profiles in the Australian Football League (AFL), however little research exists into its use to measure the spatial interactions of players. This thesis presents new methodologies for measuring the spatial interactions and occupancy of players in team sports. Global positioning systems (GPS) and local positioning systems (LPS) spatiotemporal datasets were sourced from training sessions, Under-18s matches and elite-level AFL matches. Datasets were consolidated with play-by-play transactions to infer ball position. An initial pilot study investigated the relative importance of traditional performance indicators to inform the focus of later studies. Subsequent chapters investigated the relative phase of inter- and intra-team player couples and multiple approaches to the measurement of the spatial control of individuals. Gaussian mixture models (GMM) were used to estimate the density of player groups in order to analyse changes in congestion throughout a match. Player motion models fit on player displacements were combined with a measure of field equity to value the passing decisions of players. A new approach to player motion models was developed by fitting the weighted distributions of player commitment to contest events. The resultant models more realistically explain player behaviour in proximity to the ball. The models were used to measure the spatial control of teams, from which the spatial characteristics of passes in the AFL were extracted. Passes were clustered into three distinct styles. In the final chapter of this thesis, the models developed in the preceding sections are used to develop a new decision-making model. The expected outcomes of a player’s passing options are modelled through consideration of field equity, spatial control, kicking variance and possession outcomes. Using this model, passing decisions from the 2017 and 2018 AFL seasons were analysed. In contrast to previous studies, the value of a player’s decision is measured relative to their options, rather than to an increase in possession expectation. This thesis aims to derive insights into player movement behaviour in Australian football. Furthermore, the novel spatial metrics developed in this thesis have applications in player recruitment, coaching, and performance analysis.

Millions of people around the world are diagnosed with neurological disorders like Parkinson’s, Cerebral Palsy or Amyotrophic Lateral Sclerosis. Due to the neurological damage as the disease progresses, the person suffering from the disease loses control of muscles, along with speech deterioration. Speech deterioration is due to neuro motor condition that limits manipulation of the articulators of the vocal tract, the condition collectively called as dysarthria. Even though dysarthric speech is grammatically and syntactically correct, it is difficult for humans to understand and for Automatic Speech Recognition (ASR) systems to decipher. With the emergence of deep learning, speech recognition systems have improved a lot compared to traditional speech recognition systems, which use sophisticated preprocessing techniques to extract speech features. In this digital era there are still many documents that are handwritten many of which need to be digitized. Offline handwriting recognition involves recognizing handwritten characters from images of handwritten text (i.e. scanned documents). This is an interesting task as it involves sequence learning with computer vision. The task is more difficult than Optical Character Recognition (OCR), because handwritten letters can be written in virtually infinite different styles. This thesis proposes exploiting deep learning techniques like Convolutional Neural Networks (CNN) and Recurrent Neural Networks (RNN) for offline handwriting recognition. For speech recognition, we compare traditional methods for speech recognition with recent deep learning methods. Also, we apply speaker adaptation methods both at feature level and at parameter level to improve recognition of dysarthric speech.

Presented is an Online Novelty Detection System (ONDS) that uses Gaussian Mixture Models (GMMs) and one-class classification techniques to identify novel information from multivariate times-series data. Multiple data preprocessing methods are explored and features vectors formed from frequency components obtained by the Fast Fourier Transform (FFT) and Welch's method of estimating Power Spectral Density (PSD). The number of features are reduced by using bandpower schemes and Principal Component Analysis (PCA). The Expectation Maximization (EM) algorithm is used to learn parameters for GMMs on feature vectors collected from only normal operational conditions. One-class classification is achieved by thresholding likelihood values relative to statistical limits. The ONDS is applied to two different applications from different application domains. The first application uses the ONDS to evaluate systemic health of Radio Frequency (RF) power generators. Four different models of RF power generators and over 400 unique units are tested, and the average robust true positive rate of 94.76% is achieved and the best specificity reported as 86.56%. The second application uses the ONDS to identify novel events from equine motion data and assess equine distress. The ONDS correctly identifies target behaviors as novel events with 97.5% accuracy. Algorithm implementation for both methods is evaluated within embedded systems and demonstrates execution times appropriate for online use.

In the oil industry, underground pipelines are the most preferred means of transporting a large amount of liquid product. However, a considerable number of unforeseen incidents due to corrosion failure are reported each year. Since corrosion in underground pipelines is caused by physicochemical interactions between the material (steel pipeline) and the environment (soil), the assessment of soil as a corrosive environment is indispensable. Because of the complex characteristics of soil as a corrosion precursor influencing the dissolution process, soil cannot be explained fully by conventional semi-empirical methodologies defined in controlled settings. The uncertainties inherited from the dynamic and heterogeneous underground environment should be considered.Therefore, this work presents the unification of direct assessment of soil and in-line inspection (ILI) with a probabilistic model to categorize soil corrosion. To pursue this task, we employed a model-based clustering analysis via Gaussian mixture models. The analysis was performed on data collected from southeastern Mexico. The clustering approach helps to prioritize areas to be inspected in terms of underground conditions and can improve repair decision making beyond what is offered by current assessment methodologies. This study also addresses two important issues related to in-situ data: missing data and truncated data. The typical approaches for treating missing data utilized in civil engineering are ad hoc methods. However, these conventional approaches may cause several critical problems such as biased estimates, artificially reduced variance, and loss of statistical power. Therefore, this study presents a variant of EM algorithms called Informative EM (IEM) to perform clustering analysis without filling in missing values prior to the analysis. This model-based method introduces additional cluster-specific Bernoulli parameters to exploit the nonuniformity of the frequency of missing values across clusters.In-line inspection tools (ILI) are commonly used for pipeline defect detection and characterization with advanced technologies such as magnetic flux leakage (MFL) and ultrasonic tools (UT). Each technology has its limitation for minimum detectable defect size. As a result, the data measured by different technologies are difficult to compare under the same modeling framework. In the present study, this problem will be addressed, considering two datasets measured by MFL and UT. Moreover, a truncated generalized exponential (TGE) distribution is introduced to describe the observed data. The non-informative Jeffreys’ prior is used to establish the Bayesian updating algorithm, and the Markov chain Monte Carlo (MCMC) method is adopted to estimate the posterior distribution of model.

A new method for predicting the uncertainty in a nonlinear dynamical system is developed and analyzed in the context of uncertainty evolution for resident space objects (RSOs) in the near-geosynchronous orbit regime under the influence of central body gravitational acceleration, third body perturbations, and attitude-dependent solar radiation pressure (SRP) accelerations and torques. The new method, termed the splitting Gaussian mixture unscented Kalman filter (SGMUKF), exploits properties of the differential entropy or Renyi entropy for a linearized dynamical system to determine when a higher-order prediction of uncertainty reaches a level of disagreement with a first-order prediction, and then applies a multivariate Gaussian splitting algorithm to reduce the impact of induced nonlinearity. In order to address the relative accuracy of the new method with respect to the more traditional approaches of the extended Kalman filter (EKF) and unscented Kalman filter (UKF), several concepts regarding the comparison of probability density functions (pdfs) are introduced and utilized in the analysis. The research also describes high-fidelity modeling of the nonlinear dynamical system which drives the motion of an RSO, and includes models for evaluation of the central body gravitational acceleration, the gravitational acceleration due to other celestial bodies, and attitude-dependent SRP accelerations and torques when employing a macro plate model of an RSO. Furthermore, a high-fidelity model of the measurement of the line-of-sight of a spacecraft from a ground station is presented, which applies light-time and stellar aberration corrections, and accounts for observer and target lighting conditions, as well as for the sensor field of view. The developed algorithms are applied to the problem of forward predicting the time evolution of the region of uncertainty for RSO tracking, and uncertainty rectification via the fusion of incoming measurement data with prior knowledge. It is demonstrated that the SGMUKF method is significantly better able to forward predict the region of uncertainty and is subsequently better able to utilize new measurement data.

This work presents an approach to visual tracking based on dividing a target into multiple regions, or fragments. The target is represented by a Gaussian mixture model in a joint feature-spatial space, with each ellipsoid corresponding to a different fragment. The fragment set and its cardinality are automatically adapted to the image data using an efficient region-growing procedure and updated according to a weighted average of the past and present image statistics. The fragment modeling is used to generate a strength map indicating the probability of each pixel belonging to the foreground. The strength map provides vital information about new fragments appearing in the scene, thereby assisting in addressing problematic cases like self-occlusion. The strength map is used by the region growing formulation, reminiscent of discrete level set implementation, to extract accurate boundaries of the target. Significant speedup is achieved using the region growing procedure over traditional level set based methods. The joint Lucas-Kanade feature tracking approach is also incorporated for handling large unpredictable motions even in untextured regions. Experimental results on a number of challenging sequences demonstrate the effectiveness of the technique.

Of the many existing eukaryotic gene finding software programs, none are able to guarantee accurate identification of genomic protein coding regions and other biological signals central to pathway from DNA to the protein. Eukaryotic gene finding is difficult mainly due to noncontiguous and non-continuous nature of genes. Existing approaches are heavily dependent on the compositional statistics of the sequences they learn from and are not equally suitable for all types of sequences. This thesis firstly develops efficient digital signal processing-based methods for the identification of genomic protein coding regions, and then combines the optimum signal processing-based non-data-driven technique with an existing data-driven statistical method in a novel system demonstrating improved identification of acceptor splice sites. Most existing well-known DNA symbolic-to-numeric representations map the DNA information into three or four numerical sequences, potentially increasing the computational requirement of the sequence analyzer. Proposed mapping schemes, to be used for signal processing-based gene and exon prediction, incorporate DNA structural properties in the representation, in addition to reducing complexity in subsequent processing. A detailed comparison of all DNA representations, in terms of computational complexity and relative accuracy for the gene and exon prediction problem, reveals the newly proposed ?paired numeric? to be the best DNA representation. Existing signal processing-based techniques rely mostly on the period-3 behaviour of exons to obtain one dimensional gene and exon prediction features, and are not well equipped to capture the complementary properties of exonic / intronic regions and deal with the background noise in detection of exons at their nucleotide levels. These issues have been addressed in this thesis, by proposing six one-dimensional and three multi-dimensional signal processing-based gene and exon prediction features. All one-dimensional and multi-dimensional features have been evaluated using standard datasets such as Burset/Guigo1996, HMR195, and the GENSCAN test set. This is the first time that different gene and exon prediction features have been compared using substantial databases and using nucleotide-level metrics. Furthermore, the first investigation of the suitability of different window sizes for period-3 exon detection is performed. Finally, the optimum signal processing-based gene and exon prediction scheme from our evaluations is combined with a data-driven statistical technique for the recognition of acceptor splice sites. The proposed DSP-statistical hybrid is shown to achieve 43% reduction in false positives over WWAM, as used in GENSCAN.