Light curves and multidimensional reconstructions of photon observations

Diese Dissertation konzentriert sich auf die Entwicklung und Anwendung von bayesianischen Inferenzmethoden, um physikalisch relevante Informationen aus verrauschten Photonenbeobachtungen zu extrahieren. Des Weiteren wird eine Methode entwickelt, um Beobachtungen von komplexen Systemen, welche sich stochastisch mit der Zeit entwickeln, anhand weniger Trainingsbeispiele in verschiedene Klassen einzuordnen. Zu letztem Zweck entwickeln wir den Dynamic System Classifier (DSC). Dieser basiert auf der grundlegenden Annahme, dass viele komplexe Systeme in einem vereinfachten Rahmen durch stochastische Differentialgleichungen (SDE) mit zeitabhängigen Koeffizienten beschrieben werden können. Diese werden verwendet, um Informationen aus einer Klasse ähnlicher, aber nicht identischer simulierter Systeme zu abstrahieren. Der DSC ist in zwei Phasen unterteilt. In der ersten Lernphase werden die Koeffizienten der SDE aus einem kleinen Trainingsdatensatz gelernt. Sobald diese gelernt wurden, dienen sie für einen kostengünstigen Vergleich von Daten und abstrahierter Information. Wir entwickeln, implementieren und testen beide Schritte in dem Rahmen bayesianischer Logik für kontinuierliche Größen, nämlich der Informationsfeldtheorie. Der zweite Teil dieser Arbeit beschäftigt sich mit astronomischer Bildgebung basierend auf Zählraten von Photonen. Die Notwendigkeit hierfür ergibt sich unter anderem aus der Verfügbarkeit von zahlreichen Satelliten, welche die Röntgen- und γ−Strahlen im Weltraum beobachten. In diesem Zusammenhang entwickeln wir den existierenden D3PO-Algorithmus weiter, hin zu D4PO, um multidimensionale Photonenbeobachtungen zu entrauschen, zu dekonvolvieren und in morphologisch unterschiedliche Komponenten aufzuteilen. Die Zerlegung wird durch ein hierarchisches bayesianisches Parametermodell gesteuert. Dieses erlaubt es, Felder zu rekonstruieren, die über den Produktraum von mehreren Mannigfaltigkeiten definiert sind. D4PO zerlegt den beobachteten Fluss an Photonen in eine diffuse, eine punktförmige und eine Hintergrundkomponente, während er gleichzeitig die Korrelationsstruktur für jede einzelne Komponente in jeder ihrer Mannigfaltigkeiten lernt. Die Funktionsweise von D4PO wird anhand eines simulierten Datensatzes hochenergetischer Photonen demonstriert. Schließlich wenden wir D4PO auf Daten der Magnetar-Flares von SGR 1806-20 und SGR 1900+14 an, um nach deren charakteristischen Eigenschwingungen zu suchen. Der Algorithmus rekonstruierte erfolgreich den logarithmischen Photonenfluss sowie dessen spektrale Leistungsdichte. Im Gegensatz zu früheren Arbeiten anderer Autoren können wir quasi- periodische Oszillationen (QPO) in den abklingenden Enden dieser Ereignisse bei Frequenzen ν > 17 Hz nicht bestätigen. Deren Echtheit ist fraglich, da diese in das von Rauschen dominierende Regime fallen. Dennoch finden wir neue Kandidaten für Oszillationen bei ν ≈ 9.2 Hz (SGR 1806-20) und ν ≈ 7.7 Hz (SGR 1900+14). Für den Fall, dass diese Oszillationen real sind, bevorzugen moderne theoretische Modelle von Magnetaren relativ schwache Magnetfelder im Bereich von B ≈ 6 × 1013 − 3 × 1014 G.This thesis focuses on the development and application of Bayesian inference methods to extract physical relevant information from noise contaminated photon observations and to classify the observations of complex stochastically evolving systems into different classes based on a few training samples of each class. To this latter end we develop the dynamic system classifier (DSC). This is based on the fundamental assumption that many complex systems may be described in a simplified framework by stochastic differential equations (SDE) with time dependent coefficients. These are used to abstract information from a class of similar but not identical simulated systems. The DSC is split into two phases. In the first learning phase the coefficients of the SDE are learned from a small training data set. Once these are obtained, they serve for an inexpensive data - class comparison. We develop, implement, and test both steps in a Bayesian inference framework for continuous quantities, namely information field theory. Astronomical imaging based on photon count data is a challenging task but absolutely necessary due to todays availability of space based X-ray and γ- ray telescopes. In this context we advance the existing D3PO algorithm into D4PO to denoise, denconvolve, and decompose multidimensional photon observations into morphologically different components. The decomposition is driven by a probabilistic hierarchical Bayesian parameter model, allowing us to reconstruct fields, that are defined over the product space of multiple manifolds. Thereby D4PO decomposes the photon count data into a diffuse, point-like, and background component, while it simultaneously learns the correlation structure over each of their manifolds individually. The capabilities of the algorithm are demonstrated by applying it to a simulated high energy photon count data set. Finally we apply D4PO to analyse the giant magnetar flare data of SGR 1806-20 and SGR 1900+14. The algorithm successfully reconstructs the logarithmic photon flux as well as its power spectrum. In contrast to previous findings we cannot confirm quasi periodic oscillations (QPO) in the decaying tails of these events at frequencies ν > 17 Hz. They might not be real as these fall into the noise dominated regime of the spectrum. Nevertheless we find new candidates for oscillations at ν ≈ 9.2 Hz (SGR 1806-20) and ν ≈ 7.7 Hz (SGR 1900+14). In case these oscillations are real, state of the art theoretical models of magnetars favour relatively weak magnetic fields in the range of B ≈ 6×1013−3×1014 G

Multilevel Bayesian framework for modeling the production, propagation and detection of ultra-high energy cosmic rays

Ultra-high energy cosmic rays (UHECRs) are atomic nuclei with energies over ten million times energies accessible to human-made particle accelerators. Evidence suggests that they originate from relatively nearby extragalactic sources, but the nature of the sources is unknown. We develop a multilevel Bayesian framework for assessing association of UHECRs and candidate source populations, and Markov chain Monte Carlo algorithms for estimating model parameters and comparing models by computing, via Chib's method, marginal likelihoods and Bayes factors. We demonstrate the framework by analyzing measurements of 69 UHECRs observed by the Pierre Auger Observatory (PAO) from 2004-2009, using a volume-complete catalog of 17 local active galactic nuclei (AGN) out to 15 megaparsecs as candidate sources. An early portion of the data ("period 1," with 14 events) was used by PAO to set an energy cut maximizing the anisotropy in period 1; the 69 measurements include this "tuned" subset, and subsequent "untuned" events with energies above the same cutoff. Also, measurement errors are approximately summarized. These factors are problematic for independent analyses of PAO data. Within the context of "standard candle" source models (i.e., with a common isotropic emission rate), and considering only the 55 untuned events, there is no significant evidence favoring association of UHECRs with local AGN vs. an isotropic background. The highest-probability associations are with the two nearest, adjacent AGN, Centaurus A and NGC 4945. If the association model is adopted, the fraction of UHECRs that may be associated is likely nonzero but is well below 50%. Our framework enables estimation of the angular scale for deflection of cosmic rays by cosmic magnetic fields; relatively modest scales of $\approx\!3^{\circ}$ to $30^{\circ}$ are favored. Models that assign a large fraction of UHECRs to a single nearby source (e.g., Centaurus A) are ruled out unless very large deflection scales are specified a priori, and even then they are disfavored. However, including the period 1 data alters the conclusions significantly, and a simulation study supports the idea that the period 1 data are anomalous, presumably due to the tuning. Accurate and optimal analysis of future data will likely require more complete disclosure of the data.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS654 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Probabilistic Modelling of Morphologically Rich Languages

This thesis investigates how the sub-structure of words can be accounted for in probabilistic models of language. Such models play an important role in natural language processing tasks such as translation or speech recognition, but often rely on the simplistic assumption that words are opaque symbols. This assumption does not fit morphologically complex language well, where words can have rich internal structure and sub-word elements are shared across distinct word forms. Our approach is to encode basic notions of morphology into the assumptions of three different types of language models, with the intention that leveraging shared sub-word structure can improve model performance and help overcome data sparsity that arises from morphological processes. In the context of n-gram language modelling, we formulate a new Bayesian model that relies on the decomposition of compound words to attain better smoothing, and we develop a new distributed language model that learns vector representations of morphemes and leverages them to link together morphologically related words. In both cases, we show that accounting for word sub-structure improves the models' intrinsic performance and provides benefits when applied to other tasks, including machine translation. We then shift the focus beyond the modelling of word sequences and consider models that automatically learn what the sub-word elements of a given language are, given an unannotated list of words. We formulate a novel model that can learn discontiguous morphemes in addition to the more conventional contiguous morphemes that most previous models are limited to. This approach is demonstrated on Semitic languages, and we find that modelling discontiguous sub-word structures leads to improvements in the task of segmenting words into their contiguous morphemes.Comment: DPhil thesis, University of Oxford, submitted and accepted 2014. http://ora.ox.ac.uk/objects/uuid:8df7324f-d3b8-47a1-8b0b-3a6feb5f45c

Light curves and multidimensional reconstructions of photon observations

Diese Dissertation konzentriert sich auf die Entwicklung und Anwendung von bayesianischen Inferenzmethoden, um physikalisch relevante Informationen aus verrauschten Photonenbeobachtungen zu extrahieren. Des Weiteren wird eine Methode entwickelt, um Beobachtungen von komplexen Systemen, welche sich stochastisch mit der Zeit entwickeln, anhand weniger Trainingsbeispiele in verschiedene Klassen einzuordnen. Zu letztem Zweck entwickeln wir den Dynamic System Classifier (DSC). Dieser basiert auf der grundlegenden Annahme, dass viele komplexe Systeme in einem vereinfachten Rahmen durch stochastische Differentialgleichungen (SDE) mit zeitabhängigen Koeffizienten beschrieben werden können. Diese werden verwendet, um Informationen aus einer Klasse ähnlicher, aber nicht identischer simulierter Systeme zu abstrahieren. Der DSC ist in zwei Phasen unterteilt. In der ersten Lernphase werden die Koeffizienten der SDE aus einem kleinen Trainingsdatensatz gelernt. Sobald diese gelernt wurden, dienen sie für einen kostengünstigen Vergleich von Daten und abstrahierter Information. Wir entwickeln, implementieren und testen beide Schritte in dem Rahmen bayesianischer Logik für kontinuierliche Größen, nämlich der Informationsfeldtheorie. Der zweite Teil dieser Arbeit beschäftigt sich mit astronomischer Bildgebung basierend auf Zählraten von Photonen. Die Notwendigkeit hierfür ergibt sich unter anderem aus der Verfügbarkeit von zahlreichen Satelliten, welche die Röntgen- und γ−Strahlen im Weltraum beobachten. In diesem Zusammenhang entwickeln wir den existierenden D3PO-Algorithmus weiter, hin zu D4PO, um multidimensionale Photonenbeobachtungen zu entrauschen, zu dekonvolvieren und in morphologisch unterschiedliche Komponenten aufzuteilen. Die Zerlegung wird durch ein hierarchisches bayesianisches Parametermodell gesteuert. Dieses erlaubt es, Felder zu rekonstruieren, die über den Produktraum von mehreren Mannigfaltigkeiten definiert sind. D4PO zerlegt den beobachteten Fluss an Photonen in eine diffuse, eine punktförmige und eine Hintergrundkomponente, während er gleichzeitig die Korrelationsstruktur für jede einzelne Komponente in jeder ihrer Mannigfaltigkeiten lernt. Die Funktionsweise von D4PO wird anhand eines simulierten Datensatzes hochenergetischer Photonen demonstriert. Schließlich wenden wir D4PO auf Daten der Magnetar-Flares von SGR 1806-20 und SGR 1900+14 an, um nach deren charakteristischen Eigenschwingungen zu suchen. Der Algorithmus rekonstruierte erfolgreich den logarithmischen Photonenfluss sowie dessen spektrale Leistungsdichte. Im Gegensatz zu früheren Arbeiten anderer Autoren können wir quasi- periodische Oszillationen (QPO) in den abklingenden Enden dieser Ereignisse bei Frequenzen ν > 17 Hz nicht bestätigen. Deren Echtheit ist fraglich, da diese in das von Rauschen dominierende Regime fallen. Dennoch finden wir neue Kandidaten für Oszillationen bei ν ≈ 9.2 Hz (SGR 1806-20) und ν ≈ 7.7 Hz (SGR 1900+14). Für den Fall, dass diese Oszillationen real sind, bevorzugen moderne theoretische Modelle von Magnetaren relativ schwache Magnetfelder im Bereich von B ≈ 6 × 1013 − 3 × 1014 G.This thesis focuses on the development and application of Bayesian inference methods to extract physical relevant information from noise contaminated photon observations and to classify the observations of complex stochastically evolving systems into different classes based on a few training samples of each class. To this latter end we develop the dynamic system classifier (DSC). This is based on the fundamental assumption that many complex systems may be described in a simplified framework by stochastic differential equations (SDE) with time dependent coefficients. These are used to abstract information from a class of similar but not identical simulated systems. The DSC is split into two phases. In the first learning phase the coefficients of the SDE are learned from a small training data set. Once these are obtained, they serve for an inexpensive data - class comparison. We develop, implement, and test both steps in a Bayesian inference framework for continuous quantities, namely information field theory. Astronomical imaging based on photon count data is a challenging task but absolutely necessary due to todays availability of space based X-ray and γ- ray telescopes. In this context we advance the existing D3PO algorithm into D4PO to denoise, denconvolve, and decompose multidimensional photon observations into morphologically different components. The decomposition is driven by a probabilistic hierarchical Bayesian parameter model, allowing us to reconstruct fields, that are defined over the product space of multiple manifolds. Thereby D4PO decomposes the photon count data into a diffuse, point-like, and background component, while it simultaneously learns the correlation structure over each of their manifolds individually. The capabilities of the algorithm are demonstrated by applying it to a simulated high energy photon count data set. Finally we apply D4PO to analyse the giant magnetar flare data of SGR 1806-20 and SGR 1900+14. The algorithm successfully reconstructs the logarithmic photon flux as well as its power spectrum. In contrast to previous findings we cannot confirm quasi periodic oscillations (QPO) in the decaying tails of these events at frequencies ν > 17 Hz. They might not be real as these fall into the noise dominated regime of the spectrum. Nevertheless we find new candidates for oscillations at ν ≈ 9.2 Hz (SGR 1806-20) and ν ≈ 7.7 Hz (SGR 1900+14). In case these oscillations are real, state of the art theoretical models of magnetars favour relatively weak magnetic fields in the range of B ≈ 6×1013−3×1014 G

Weakly supervised POS tagging without disambiguation

Weakly supervised part-of-speech (POS) tagging is to learn to predict the POS tag for a given word in context by making use of partial annotated data instead of the fully tagged corpora. Weakly supervised POS tagging would benefit various natural language processing applications in such languages where tagged corpora are mostly unavailable. In this article, we propose a novel framework for weakly supervised POS tagging based on a dictionary of words with their possible POS tags. In the constrained error-correcting output codes (ECOC)-based approach, a unique L-bit vector is assigned to each POS tag. The set of bitvectors is referred to as a coding matrix with value { 1, -1}. Each column of the coding matrix specifies a dichotomy over the tag space to learn a binary classifier. For each binary classifier, its training data is generated in the following way: each pair of words and its possible POS tags are considered as a positive training example only if the whole set of its possible tags falls into the positive dichotomy specified by the column coding and similarly for negative training examples. Given a word in context, its POS tag is predicted by concatenating the predictive outputs of the L binary classifiers and choosing the tag with the closest distance according to some measure. By incorporating the ECOC strategy, the set of all possible tags for each word is treated as an entirety without the need of performing disambiguation. Moreover, instead of manual feature engineering employed in most previous POS tagging approaches, features for training and testing in the proposed framework are automatically generated using neural language modeling. The proposed framework has been evaluated on three corpora for English, Italian, and Malagasy POS tagging, achieving accuracies of 93.21%, 90.9%, and 84.5% individually, which shows a significant improvement compared to the state-of-the-art approaches

BeyondPlanck I. Global Bayesian analysis of the Planck Low Frequency Instrument data

We describe the BeyondPlanck project in terms of motivation, methodology and main products, and provide a guide to a set of companion papers that describe each result in fuller detail. Building directly on experience from ESA's Planck mission, we implement a complete end-to-end Bayesian analysis framework for the Planck Low Frequency Instrument (LFI) observations. The primary product is a joint posterior distribution P(omega|d), where omega represents the set of all free instrumental (gain, correlated noise, bandpass etc.), astrophysical (synchrotron, free-free, thermal dust emission etc.), and cosmological (CMB map, power spectrum etc.) parameters. Some notable advantages of this approach are seamless end-to-end propagation of uncertainties; accurate modeling of both astrophysical and instrumental effects in the most natural basis for each uncertain quantity; optimized computational costs with little or no need for intermediate human interaction between various analysis steps; and a complete overview of the entire analysis process within one single framework. As a practical demonstration of this framework, we focus in particular on low-l CMB polarization reconstruction, paying special attention to the LFI 44 GHz channel. We find evidence of significant residual systematic effects that are still not accounted for in the current processing, but must be addressed in future work. These include a break-down of the 1/f correlated noise model at 30 and 44 GHz, and scan-aligned stripes in the Southern Galactic hemisphere at 44 GHz. On the Northern hemisphere, however, we find that all results are consistent with the LCDM model, and we constrain the reionization optical depth to tau = 0.067 +/- 0.016, with a low-resolution chi-squared probability-to-exceed of 16%. The marginal CMB dipole amplitude is 3359.5 +/- 1.9 uK. (Abridged.)Comment: 77 pages, 46 figures. All BeyondPlanck products and software will be released publicly at http://beyondplanck.science during the online release conference (November 18-20, 2020). Connection details will be made available at the same website. Registration is mandatory for the online tutorial, but optional for the conferenc

Facial soft tissue segmentation

The importance of the face for socio-ecological interaction is the cause for a high demand on any surgical intervention on the facial musculo-skeletal system. Bones and soft-tissues are of major importance for any facial surgical treatment to guarantee an optimal, functional and aesthetical result. For this reason, surgeons want to pre-operatively plan, simulate and predict the outcome of the surgery allowing for shorter operation times and improved quality. Accurate simulation requires exact segmentation knowledge of the facial tissues. Thus semi-automatic segmentation techniques are required. This thesis proposes semi-automatic methods for segmentation of the facial soft-tissues, such as muscles, skin and fat, from CT and MRI datasets, using a Markov Random Fields (MRF) framework. Due to image noise, artifacts, weak edges and multiple objects of similar appearance in close proximity, it is difficult to segment the object of interest by using image information alone. Segmentations would leak at weak edges into neighboring structures that have a similar intensity profile. To overcome this problem, additional shape knowledge is incorporated in the energy function which can then be minimized using Graph-Cuts (GC). Incremental approaches by incorporating additional prior shape knowledge are presented. The proposed approaches are not object specific and can be applied to segment any class of objects be that anatomical or non-anatomical from medical or non-medical image datasets, whenever a statistical model is present. In the first approach a 3D mean shape template is used as shape prior, which is integrated into the MRF based energy function. Here, the shape knowledge is encoded into the data and the smoothness terms of the energy function that constrains the segmented parts to a reasonable shape. In the second approach, to improve handling of shape variations naturally found in the population, the fixed shape template is replaced by a more robust 3D statistical shape model based on Probabilistic Principal Component Analysis (PPCA). The advantages of using the Probabilistic PCA are that it allows reconstructing the optimal shape and computing the remaining variance of the statistical model from partial information. By using an iterative method, the statistical shape model is then refined using image based cues to get a better fitting of the statistical model to the patient's muscle anatomy. These image cues are based on the segmented muscle, edge information and intensity likelihood of the muscle. Here, a linear shape update mechanism is used to fit the statistical model to the image based cues. In the third approach, the shape refinement step is further improved by using a non-linear shape update mechanism where vertices of the 3D mesh of the statistical model incur the non-linear penalty depending on the remaining variability of the vertex. The non-linear shape update mechanism provides a more accurate shape update and helps in a finer shape fitting of the statistical model to the image based cues in areas where the shape variability is high. Finally, a unified approach is presented to segment the relevant facial muscles and the remaining facial soft-tissues (skin and fat). One soft-tissue layer is removed at a time such as the head and non-head regions followed by the skin. In the next step, bones are removed from the dataset, followed by the separation of the brain and non-brain regions as well as the removal of air cavities. Afterwards, facial fat is segmented using the standard Graph-Cuts approach. After separating the important anatomical structures, finally, a 3D fixed shape template mesh of the facial muscles is used to segment the relevant facial muscles. The proposed methods are tested on the challenging example of segmenting the masseter muscle. The datasets were noisy with almost all possessing mild to severe imaging artifacts such as high-density artifacts caused by e.g. dental fillings and dental implants. Qualitative and quantitative experimental results show that by incorporating prior shape knowledge leaking can be effectively constrained to obtain better segmentation results

Early Form Based Morphological Decomposition in Tagalog: MEG Evidence from Reduplication, Infixation and Circumfixation

Neuro-and psycholinguistic experimentation supports the early decomposition of morphologically complex words within the ventral processing stream, which MEG has localized to the M170 response in the (left) visual word form area ( VWFA). Decomposition into an exhaustive parse of visual morpheme forms extends beyond words like farmer to those imitating complexity (e.g., brother; Lewis et al., 2011), and to “unique” stems occurring in only one word but following the syntax and semantics of their affix (e.g., vulnerable; Gwilliams & Marantz, 2018). Evidence comes primarily from suffixation; other morphological processes have been under-investigated. This study explores circumfixation, infixation, and reduplication in Tagalog. In addition to investigating whether these are parsed like suffixation, we address an outstanding question concerning semantically empty morphemes. Some words in Tagalog resemble English winter as decomposition is not supported (wint-er); these apparently reduplicated pseudoreduplicates lack the syntactic and semantic features of reduplicated forms. However, unlike winter, these words exhibit phonological behavior predicted only if they involve a reduplicating morpheme. If these are decomposed, this provides evidence that words are analyzed as complex, like English vulnerable, when the grammar demands it. In a lexical decision task with MEG, we find that VWFA activity correlates with stem:word transition probability for circumfixed, infixed, and reduplicated words. Furthermore, a Bayesian analysis suggests that pseudoreduplicates with reduplicate-like phonology are also decomposed; other pseudoreduplicates are not. These findings are consistent with an interpretation that decomposition is modulated by phonology in addition to syntax and semantics

Two and three dimensional segmentation of multimodal imagery

The role of segmentation in the realms of image understanding/analysis, computer vision, pattern recognition, remote sensing and medical imaging in recent years has been significantly augmented due to accelerated scientific advances made in the acquisition of image data. This low-level analysis protocol is critical to numerous applications, with the primary goal of expediting and improving the effectiveness of subsequent high-level operations by providing a condensed and pertinent representation of image information. In this research, we propose a novel unsupervised segmentation framework for facilitating meaningful segregation of 2-D/3-D image data across multiple modalities (color, remote-sensing and biomedical imaging) into non-overlapping partitions using several spatial-spectral attributes. Initially, our framework exploits the information obtained from detecting edges inherent in the data. To this effect, by using a vector gradient detection technique, pixels without edges are grouped and individually labeled to partition some initial portion of the input image content. Pixels that contain higher gradient densities are included by the dynamic generation of segments as the algorithm progresses to generate an initial region map. Subsequently, texture modeling is performed and the obtained gradient, texture and intensity information along with the aforementioned initial partition map are used to perform a multivariate refinement procedure, to fuse groups with similar characteristics yielding the final output segmentation. Experimental results obtained in comparison to published/state-of the-art segmentation techniques for color as well as multi/hyperspectral imagery, demonstrate the advantages of the proposed method. Furthermore, for the purpose of achieving improved computational efficiency we propose an extension of the aforestated methodology in a multi-resolution framework, demonstrated on color images. Finally, this research also encompasses a 3-D extension of the aforementioned algorithm demonstrated on medical (Magnetic Resonance Imaging / Computed Tomography) volumes