A principal component analysis of gravitational-wave signals from extreme-mass-ratio sources

The Laser Interferometer Space Antenna (LISA) will detect the gravitational wave emissions from a vast number of astrophysical sources, but extracting useful information about individual sources or source types is an extremely challenging prospect; the large number of parameters governing the behaviour of some sources make exhaustively searching this parameter space computationally expensive. We investigate the potential of an alternative approach, with a focus on detecting the presence of particular inspiraling binary source signals within a timeseries of gravitational wave data, and quickly providing estimates of their coalescence times. Specically, we use Principal Component Analysis (PCA) to identify redundancy within the parameter space of Extreme Mass Ratio Inspiral (EMRI) sources and construct a new, smaller parameter space containing only relevant signal information. We then create a simple search method based on how gravitational wave signals project into this new parameter space. Test cases indicate that a small number of principal components span a space occupied by the majority of EMRI spectrograms, but non-EMRI signals (including noise) do not inhabit this space. A PCA-based search method is capable of indicating the presence of gravitational waves from EMRI sources within a new test spectrogram. The results of our PCA-based searches show that the method could be used to provide initial estimates of EMRI coalescence times quickly, to be used as initial data for a more thorough search

Applications of Markov Chain Monte Carlo methods to continuous gravitational wave data analysis

A new algorithm for the analysis of gravitational wave data from rapidly rotating neutron stars has been developed. The work is based on the Markov Chain Monte Carlo algorithm and features enhancements specifically targeted to this problem. The algorithm is tested on both synthetic data and hardware injections in the LIGO Hanford interferometer during its third science run ("S3''). By utilising the features of this probabilistic algorithm a search is performed for a rotating neutron star in the remnant of SN1987A within in frequency window of 4 Hz and a spindown window of 2E-10 Hz/s. A method for setting upper limits is described and used on this data in the absence of a detection setting an upper limit on strain of 7.3E-23. A further application of MCMC methods is made in the area of data analysis for the proposed LISA mission. An algorithm is developed to simultaneously estimate the number of sources and their parameters in a noisy data stream using reversible jump MCMC. An extension is made to estimate the position in the sky of a source and this is further improved by the implementation of a fast approximate calculation of the covariance matrix to enhance acceptance rates. This new algorithm is also tested upon synthetic data and the results are presented here. Conclusions are drawn from the results of this work, and comments are made on the development of MCMC algorithms within the field of gravitational wave data analysis, with a view to their increasing usage

Application of generative models in speech processing tasks

Generative probabilistic and neural models of the speech signal are shown to be effective in speech synthesis and speech enhancement, where generating natural and clean speech is the goal. This thesis develops two probabilistic signal processing algorithms based on the source-filter model of speech production, and two based on neural generative models of the speech signal. They are a model-based speech enhancement algorithm with ad-hoc microphone array, called GRAB; a probabilistic generative model of speech called PAT; a neural generative F0 model called TEReTA; and a Bayesian enhancement network, call BaWN, that incorporates a neural generative model of speech, called WaveNet. PAT and TEReTA aim to develop better generative models for speech synthesis. BaWN and GRAB aim to improve the naturalness and noise robustness of speech enhancement algorithms. Probabilistic Acoustic Tube (PAT) is a probabilistic generative model for speech, whose basis is the source-filter model. The highlights of the model are threefold. First, it is among the very first works to build a complete probabilistic model for speech. Second, it has a well-designed model for the phase spectrum of speech, which has been hard to model and often neglected. Third, it models the AM-FM effects in speech, which are perceptually significant but often ignored in frame-based speech processing algorithms. Experiments show that the proposed model has good potential for a number of speech processing tasks. TEReTA generates pitch contours by incorporating a theoretical model of pitch planning, the piece-wise linear target approximation (TA) model, as the output layer of a deep recurrent neural network. It aims to model semantic variations in the F0 contour, which is challenging for existing network. By combining the TA model, TEReTA is able to memorize semantic context and capture the semantic variations. Experiments on contrastive focus verify TEReTA's ability in semantics modeling. BaWN is a neural network based algorithm for single-channel enhancement. The biggest challenges of the neural network based speech enhancement algorithm are the poor generalizability to unseen noises and unnaturalness of the output speech. By incorporating a neural generative model, WaveNet, in the Bayesian framework, where WaveNet predicts the prior for speech, and where a separate enhancement network incorporates the likelihood function, BaWN is able to achieve satisfactory generalizability and a good intelligibility score of its output, even when the noisy training set is small. GRAB is a beamforming algorithm for ad-hoc microphone arrays. The task of enhancing speech with ad-hoc microphone array is challenging because of the inaccuracy in position and interference calibration. Inspired by the source-filter model, GRAB does not rely on any position or interference calibration. Instead, it incorporates a source-filter speech model and minimizes the energy that cannot be accounted for by the model. Objective and subjective evaluations on both simulated and real-world data show that GRAB is able to suppress noise effectively while keeping the speech natural and dry. Final chapters discuss the implications of this work for future research in speech processing

Contributions to MCMC Methods in Constrained Domains with Applications to Neuroimaging

Markov chain Monte Carlo (MCMC) methods form a rich class of computational techniques that help its user ascertain samples from target distributions when direct sampling is not possible or when their closed forms are intractable. Over the years, MCMC methods have been used in innumerable situations due to their flexibility and generalizability, even in situations involving nonlinear and/or highly parametrized models. In this dissertation, two major works relating to MCMC methods are presented. The first involves the development of a method to identify the number and directions of nerve fibers using diffusion-weighted MRI measurements. For this, the biological problem is first formulated as a model selection and estimation problem. Using the framework of reversible jump MCMC, a novel Bayesian scheme that performs both the above tasks simultaneously using customizable priors and proposal distributions is proposed. The proposed method allows users to set a prior level of spatial separation between the nerve fibers, allowing more crossing paths to be detected when desired or a lower number to potentially only detect robust nerve tracts. Hence, estimation that is specific to a given region of interest within the brain can be performed. In simulated examples, the method has been shown to resolve up to four fibers even in instances of highly noisy data. Comparative analysis with other state-of-the-art methods on in-vivo data showed the method\u27s ability to detect more crossing nerve fibers. The second work involves the construction of an MCMC algorithm that efficiently performs (Bayesian) sampling of parameters with support constraints. The method works by embedding a transformation called inversion in a sphere within the Metropolis-Hastings sampler. This creates an image of the constrained support that is amenable to sampling using standard proposals such as Gaussian. The proposed strategy is tested on three domains: the standard simplex, a sector of an n-sphere, and hypercubes. In each domain, a comparison is made with existing sampling techniques

Observational tests of fundamental physics from gravitational wave detections

With the detection of the signal GW150914 from the collision of two black holes in 2015, observational gravitational wave physics has begun. Many more signals have since been recorded, and new detections are now becoming routine. These observations offer a new window to probe fundamental physics in thus far inaccessible regimes of strong gravity, such as in the regions near black hole horizons. The work presented here pursues this through two approaches, studying predicted signals of either black holes of general relativity, or of proposed alternative objects without horizons. A binary black hole collision creates a single perturbed black hole, which settles to its final state through the ringdown gravitational wave emission. The ringdown consists of a spectrum of modes, which the no-hair theorem in General Relativity predicts to be determined entirely by the black hole mass and angular momentum. Measurement of multiple modes allows to test this prediction but is challenging due to the weak and short-lived nature of the ringdown signal. Two studies are presented on the feasibility of such tests using current and near-future de- tector sensitivities. Large populations of simulated ringdown signals are constructed based on observational models of the binary black hole population. Bayesian parameter estimation techniques are applied to these signals to place bounds on deviations from the no-hair prediction. Detections leading to stringent bounds are unlikely to occur for current instruments but can be found during a few years of operation at their planned future sensitivities. The prospects improve when extending the analysis to combine data from multiple detections into a single bound on deviations. At the sensitivity planned for the next observation run of current instruments, the detections from one year of data can be combined into stringent bounds. Solutions are provided to limitations uncovered for this type of study. In a further study, strong evidence is found for the presence of a subdominant mode in the data of the event GW190521. A new method is employed to allow the analysis of only the ringdown part of the signal, without contamination from outside the analysis window and preventing windowing artefacts and signal loss. Tests of the no-hair theorem are performed, yielding unexpectedly tight constraints on deviations. Two phenomenologically distinct signals from horizonless compact objects are studied, both following after the primary signal which is otherwise unchanged compared to that of a black hole binary. One takes the form of repeated pulses after the ringdown, called gravitational wave echoes, while the other consists of a very long-lived damped sinusoid with a small amplitude. Using a simplified waveform model for echoes, evidence for such signals in the data of several detections is evaluated. Previous results from the first search for these are replicated, and the methods tested thoroughly. Through improved estimation methods, low statistical significance is established for these results, yet the presence of such signals cannot be ruled out by the analysis. An independent Bayesian analysis is performed for the same waveform model, with results for each event either preferring the absence of echoes in the data or being consistent with it. Bounds on the echo amplitudes ruled out by the data are produced. The long-lived mode signal for a broad class of horizonless objects is considered in a Bayesian analysis. Methods are developed to accommodate the long duration of the signal, and their performance is tested with simulated signals and off-source data. They are then applied to the data of the event GW150914, yielding stringent bounds on the deviations from the Kerr geometry exhibited by such objects.Mit der Detektion des Signals GW150914 von der Kollision zweier schwarzer Löcher im Jahr 2015 begann die beobachtungsbasierte Gravitationswellenphysik. Viele weitere Signale wurden seither aufgezeichnet und neue Detektionen werden zur Routine. Diese Beobachtungen eröffnen einen neuen Weg, fundamentale Physik im bisher unzugänglichen Regime starker Gravitation zu untersuchen, zum Beispiel in der Umgebung der Horizonte schwarzer Löcher. Die hier präsentierten Studien verfolgen dies durch zwei Ansätze, indem sie entweder die vorhergesagten Signale schwarzer Löcher in der Allgemeinen Relativitätstheorie oder vorgeschlagener alternativer Objekte ohne Horizonte untersuchen. Die Kollision zweier schwarzer Löcher erzeugt ein einzelnes gestörtes schwarzes Loch, welches durch Emission der Abkling-Gravitationswellen schließlich in einen ungestörten Zustand übergeht. Die Abkling-Strahlung besteht aus einem Spektrum von Moden, welche dem Keine- Haare-Theorem der Allgemeinen Relativitätstheorie nach gänzlich durch Masse und Drehimpuls des schwarzen Loches bestimmt werden. Die Messung mehrerer Moden ermöglicht die Prüfung dieser Vorhersage, ist jedoch wegen des schwachen und kurzlebigen Abklingsignals schwierig. Zwei Studien zur Durchführbarkeit solcher Tests mithilfe aktuell und in naher Zukunft verfügbarer Detektor-Empfindlichkeiten werden dargelegt. Große Populationen simulierter Abklingsignale werden konstruiert, basierend auf beobachtungsgestützten Modellen der Population von Binärsystemen schwarzer Löcher. Bayessche Parameterabschätzung wird auf diese Signale angewendet, um Abweichungen von der Keine-Haare-Vorhersage zu beschränken. Detektionen, die zu strikter Begrenzung führen, sind mit aktuellen Instrumenten unwahrscheinlich, können aber innerhalb weniger Jahre des Betriebs mit ihren geplanten zukünftigen Empfindlichkeiten erreicht werden. Diese Aussichten verbessern sich, wenn Daten mehrerer Detektionen in der Begrenzung kombiniert werden. Mit der geplanten Empfindlichkeit aktueller Instrumente im nächsten Beobachtungslauf können die in einem Jahr gesammelten Daten zu strikten Begrenzungen kombiniert werden. Lösungen für die entdeckten Limitationen dieser Art Analyse werden vorgestellt. In einer weiteren Studie wird starke Evidenz für die Existenz einer subdominanten Mode in den Daten des Signals GW190521 gefunden. Eine neue Methode wird eingesetzt, welche die Analyse des Abkling-Signals ermöglicht, ohne Kontamination von außerhalb des Analyse- Fensters, Artefakte oder Signalverlust zu verursachen. Tests des Keine-Haare-Theorems werden durchgeführt und liefern unerwartet strikte Beschränkungen für Abweichungen. Zwei phänomenologisch verschiedene Signale horizontfreier kompakter Objekte werden untersucht. Beide folgen dem Primärsignal, das ansonsten gegenüber dem schwarzer Löcher un- verändert ist. Eines besteht aus wiederholten Pulsen, als Gravitationswellen-Echos bezeichnet, während das zweite die Form einer langlebigen, gedämpften Sinuswelle geringer Amplitude hat. Anhand eines vereinfachten Modells der Echo-Wellenform wird die Evidenz solcher Signale in den Daten mehrerer Detektionen bewertet. Frühere Ergebnisse der ersten Suche nach Echos werden repliziert und die Methoden ausführlich geprüft. Durch verbesserte Abschätzungsmethoden wird eine geringe statistische Signifikanz der Ergebnisse etabliert, allerdings kann die Anwesenheit solcher Signale nicht durch diese Untersuchung ausgeschlossen werden. Eine unabhängige Bayessche Analyse wird mit derselben Wellenform durchgeführt, wobei die Ergebnisse die Abwesenheit des Signals bevorzugen oder mit Rauschen vereinbar sind. Grenzen für die von den Daten ausgeschlossenen Amplituden der Echos werden gefunden. Das Signal einer langlebigen Mode von einer großen Klasse horizontfreier Objekte wird in einer Bayesschen Analyse betrachtet. Methoden werden entwickelt, um die lange Dauer des Signals handhaben zu können, und ihre Leistungsfähigkeit wird an simulierten Signalen und signalfreien Daten getestet. Auf die Daten des Signals GW150914 angewendet, liefern sie strikte Beschränkungen für die Abweichungen solcher Objekte von der Kerr-Geometrie

Advances in Trans-dimensional Geophysical Inference

This research presents a series of novel Bayesian trans-dimensional methods for geophysical inversion. A first example illustrates how Bayesian prior information obtained from theory and numerical experiments can be used to better inform a difficult multi-modal inversion of dispersion information from empirical Greens functions obtained from ambient noise cross-correlation. This approach is an extension of existing partition modeling schemes. An entirely new class of trans-dimensional algorithm, called the trans-dimensional tree method is introduced. This new method is shown to be more efficient at coupling to a forward model, more efficient at convergence, and more adaptable to different dimensions and geometries than existing approaches. The efficiency and flexibility of the trans-dimensional tree method is demonstrated in two different examples: (1) airborne electromagnetic tomography (AEM) in a 2D transect inversion, and (2) a fully non-linear inversion of ambient noise tomography. In this latter example the resolution at depth has been significantly improved by inverting a contiguous band of frequencies jointly rather than as independent phase velocity maps, allowing new insights into crustal architecture beneath Iceland. In a first test case for even larger scale problems, an application of the trans-dimensional tree approach to large global data set is presented. A global database of nearly 5 million multi-model path average Rayleigh wave phase velocity observations has been used to construct global phase velocity maps. Results are comparable to existing published phase velocity maps, however, as the trans-dimensional approach adapts the resolution appropriate to the data, rather than imposing damping or smoothing constraints to stabilize the inversion, the recovered anomaly magnitudes are generally higher with low uncertainties. While further investigation is needed, this early test case shows that trans-dimensional sampling can be applied to global scale seismology problems and that previous analyses may, in some locales, under estimate the heterogeneity of the Earth. Finally, in a further advancement of partition modelling with variable order polynomials, a new method has been developed called trans-dimensional spectral elements. Previous applications involving variable order polynomials have used polynomials that are both difficult to work with in a Bayesian framework and unstable at higher orders. By using the orthogonal polynomials typically used in modern full-waveform solvers, the useful properties of this type of polynomial and its application in trans-dimensional inversion are demonstrated. Additionally, these polynomials can be directly used in complex differential solvers and an example of this for 1D inversion of surface wave dispersion curves is given

Inference Algorithms and Sensorimotor Representations in Brains and Machines

Animals function in a 3D world in which survival depends on robust, well-controlled actions. Historically, researchers in Artificial Intelligence (AI) and neuroscience have explored sensory and motor systems independently. There is a growing body of literature in AI and neuroscience to suggest that they actually work in tandem. While there has been a great deal of work on vision and audition as sensory modalities in these fields, one could argue that a more fundamental modality in biology is haptics, or the sense of touch. In this thesis, we will look at building computational models that integrate tactile sensing with other sensory modalities to perform manipulation-like tasks in robots and discrimination tasks in mice. We will also explore the problem of inference through the lens of Markov Chain Monte Carlo methods (MCMC). We elaborate on the ideas discussed in this thesis in the introduction presented in Chapter 1. A challenging problem one often faces when applying probabilistic mathematical models to the study of sensory-motor systems and other problems involving learning of inference is sampling. Hamiltonian Markov Chain Monte Carlo (HMC) algorithms can efficiently draw representative samples from complex probabilistic models. Most MCMC methods rely on detailed balance to ensure that we can sample from the correct distribution. This constraint can be relaxed in discrete state spaces such as those employed by HMC type methods. In Chapter 2, we study HMC methods without detailed balance to explore faster convergence. Markov jump processes are stochastic processes on discrete state space but continuous in time. In Chapter 3, we use Markov Jump Processes to simulate waiting times along with generalized detailed balance. This waiting time ,we show, helps generate samples faster. Most MCMC methods are plagued by slow simulation times on discrete computing systems. In Chapter 4, we explore HMC in analog circuits where the problem of generating samples from a distribution is mapped to the problem of sampling charge in a capacitor.The second half of this dissertation focuses on the role of haptics in perception and action. Manipulation is a fundamental problem for artificial and biological agents. High dimensional actuators (say, fingers, trunks,etc) are really hard to control. In Chapter 5, we present an approach to learn to actuate dexterous manipulators to grasp objects in simulation. Haptics as a sensory modality is critical to many manipulation tasks. Employing haptics in high dimensional dextrous actuators is challenging. In Chapter 6, we explore how intrinsic curiosity and haptics can be used to learn exploration strategies for discrimination of objects with dextrous hands. A key component to make tactile sensing a possibility is the availability of cheap, efficient, scalable hardware. Chapter 7 presents results for tactile servoing using a physical gelsight sensor. Traditional neuroscience texts delineate sensory and motor systems as two independent systems yet recent results suggest that this may not be entirely complete. That is, there is evidence to suggest that the representations in the cortex is more distributed than is accepted. Finally in Chapter 8, we explore building a computational model of spiking neural data collected from both the barrel and motor cortices during free and active whisking. These works help towards understanding sensorimotor representations in the context of haptics and high dimensional controls. We conclude with a discussion on future directions in Chapter 9

The impact of terrestrial noise on the detectability and reconstruction of gravitational wave signals from core-collapse supernovae

Among of the wide range of potentially interesting astrophysical sources for gravitational wave detectors Advanced LIGO and Advanced Virgo are galactic core-collapse supernovae. Although detectable core-collapse supernovae have a low expected rate (a few per century, or less) these signals would yield a wealth of new physics. Of particular interest is the insight into the explosion mechanism driving core-collapse supernovae that can be gleaned from the reconstructed gravitational wave signal. A well-reconstructed waveform will allow us to assess the likelihood of different explosion models, perform model selection, and potentially map unexpected features to new physics. This dissertation presents a series of studies evaluating the current performance of burst parameter estimation algorithms in reconstructing core-collapse supernovae gravitational wave signals in both simple Gaussian noise and realistic non-Gaussian detector noise. The introduction of non-Gaussian noise has a significant impact on the recovery of core-collapse supernova models from the data. Terrestrial noise is also an important factor in the recovery of any gravitational wave search. This work also details a series of studies that enable the characterization of ground motion local to the Advanced LIGO inteferometers and the ability of the installed active seismic isolation to mitigate it