We address the problem of learning discrete hidden Markov models from very long sequences of observations. Incremental versions of the Baum-Welch algorithm that approximate the beta-values used in the backward procedure are commonly used for this problem since their memory complexity is independent of the sequence length. However, traditional approaches have two main disadvantages: the approximation of the beta-values deviates far from the real values, and the learning algorithm requires previous knowledge of the topology of the model. This dissertation describes a new incremental Baum-Welch algorithm with a novel backward procedure that improves the approximation of the â-values based on a one-step lookahead in the training sequence and investigates heuristics to prune unnecessary states from an initial complex model. Two new approaches for pruning, greedy and controlled, are introduced and a novel method for identification of ill-conditioned models is presented. Incremental learning of multiple independent observations is also investigated. We justify the new approaches analytically and report empirical results that show they converge faster than the traditional Baum-Welch algorithm using fewer computer resources. Furthermore, we demonstrate that the new learning algorithms converge faster than the previous incremental approaches and can be used to perform online learning of high-quality models useful for classification tasks. Finally, this dissertation explores the use of the new algorithms for anomaly detection in computer systems, that improve our previous research work on detectors based on hidden Markov models integrated into real-world monitoring systems of high-performance computers.

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This thesis consists of four papers dealing with the futures price process. In the first paper, we propose a two-factor futures volatility model designed for the US natural gas market, but applicable to any futures market where volatility decreases with maturity and varies with the seasons. A closed form analytical expression for European call options is derived within the model and used to calibrate the model to implied market volatilities. The result is used to price swaptions and calendar spread options on the futures curve. In the second paper, a financial market is specified where the underlying asset is driven by a d-dimensional Wiener process and an M dimensional Markov process. On this market, we provide necessary and, in the time homogenous case, sufficient conditions for the futures price to possess a semi-affine term structure. Next, the case when the Markov process is unobservable is considered. We show that the pricing problem in this setting can be viewed as a filtering problem, and we present explicit solutions for futures. Finally, we present explicit solutions for options on futures both in the observable and unobservable case. The third paper is an empirical study of the SABR model, one of the latest contributions to the field of stochastic volatility models. By Monte Carlo simulation we test the accuracy of the approximation the model relies on, and we investigate the stability of the parameters involved. Further, the model is calibrated to market implied volatility, and its dynamic performance is tested. In the fourth paper, co-authored with Tomas Björk and Camilla Landén, we consider HJM type models for the term structure of futures prices, where the volatility is allowed to be an arbitrary smooth functional of the present futures price curve. Using a Lie algebraic approach we investigate when the infinite dimensional futures price process can be realized by a finite dimensional Markovian state space model, and we give general necessary and sufficient conditions, in terms of the volatility structure, for the existence of a finite dimensional realization. We study a number of concrete applications including the model developed in the first paper of this thesis. In particular, we provide necessary and sufficient conditions for when the induced spot price is a Markov process. We prove that the only HJM type futures price models with spot price dependent volatility structures, generically possessing a spot price realization, are the affine ones. These models are thus the only generic spot price models from a futures price term structure point of view. / Diss. Stockholm : Handelshögskolan, 2004

The field of speech recognition has during the last decade left the re- search stage and found its way in to the public market. Most computers and mobile phones sold today support dictation and transcription in a number of chosen languages.  Swedish is often not one of them. In this thesis, which is executed on behalf of the Swedish Radio, an Automatic Speech Recognition model for Swedish is trained and the performance evaluated. The model is built using the open source toolkit Kaldi.  Two approaches of training the acoustic part of the model is investigated. Firstly, using Hidden Markov Model and Gaussian Mixture Models and secondly, using Hidden Markov Models and Deep Neural Networks. The later approach using deep neural networks is found to achieve a better performance in terms of Word Error Rate. / De senaste åren har olika tillämpningar inom människa-dator interaktion och främst taligenkänning hittat sig ut på den allmänna marknaden. Många system och tekniska produkter stöder idag tjänsterna att transkribera tal och diktera text. Detta gäller dock främst de större språken och sällan finns samma stöd för mindre språk som exempelvis svenskan. I detta examensprojekt har en modell för taligenkänning på svenska ut- vecklas. Det är genomfört på uppdrag av Sveriges Radio som skulle ha stor nytta av en fungerande taligenkänningsmodell på svenska. Modellen är utvecklad i ramverket Kaldi. Två tillvägagångssätt för den akustiska träningen av modellen är implementerade och prestandan för dessa två är evaluerade och jämförda. Först tränas en modell med användningen av Hidden Markov Models och Gaussian Mixture Models och slutligen en modell där Hidden Markov Models och Deep Neural Networks an- vänds, det visar sig att den senare uppnår ett bättre resultat i form av måttet Word Error Rate.

Proteins are the fundamental unit of computation and signal processing in biological systems. A quantitative understanding of protein biophysics is of paramount importance, since even slight malfunction of proteins can lead to diverse and severe disease states. However, developing accurate and useful mechanistic models of protein function can be strikingly elusive. I demonstrate that the adoption of Bayesian statistical methods can greatly aid in modeling protein systems. I first discuss the pitfall of parameter non-identifiability and how a Bayesian approach to modeling can yield reliable and meaningful models of molecular systems. I then delve into a particular case of non-identifiability within the context of an emerging experimental technique called single molecule photobleaching. I show that the interpretation of this data is non-trivial and provide a rigorous inference model for the analysis of this pervasive experimental tool. Finally, I introduce the use of nonparametric Bayesian inference for the analysis of single molecule time series. These methods aim to circumvent problems of model selection and parameter identifiability and are demonstrated with diverse applications in single molecule biophysics. The adoption of sophisticated inference methods will lead to a more detailed understanding of biophysical systems. / text

Explorations into the organisation of spontaneous activity within the brain have demonstrated the existence of networks of temporally correlated activity, consisting of brain areas that share similar cognitive or sensory functions. These so-called resting state networks (RSNs) emerge spontaneously during rest and disappear in response to overt stimuli or cognitive demands. In recent years, the study of RSNs has emerged as a valuable tool for probing brain function, both in the healthy brain and in disorders such as schizophrenia, Alzheimer’s disease and Parkinson’s disease. However, analyses of these networks have so far been limited, in part due to assumptions that the patterns of neuronal activity that underlie these networks remain constant over time. Moreover, the majority of RSN studies have used functional magnetic resonance imaging (fMRI), in which slow fluctuations in the level of oxygen in the blood are used as a proxy for the activity within a given brain region. In this thesis we develop the use of magnetoencephalography (MEG) to study resting state functional connectivity. Unlike fMRI, MEG provides a direct measure of neuronal activity and can provide novel insights into the temporal dynamics that underlie resting state activity. In particular, we focus on the application of non- stationary analysis methods, which are able to capture fast temporal changes in activity. We first develop a framework for preprocessing MEG data and measuring interactions within different RSNs (Chapter 3). We then extend this framework to assess temporal variability in resting state functional connectivity by applying time- varying measures of interactions and show that within-network functional connectivity is underpinned by non-stationary temporal dynamics (Chapter 4). Finally we develop a data driven approach based on a hidden Markov model for inferring short lived connectivity states from resting state and task data (Chapter 5). By applying this approach to data from multiple subjects we reveal transient states that capture short lived patterns of neuronal activity (Chapter 6).

A demanda por abordagens eficientes para o problema de reconhecer a estrutura de cada gene numa sequência genômica motivou a implementação de um grande número de programas preditores de genes. Fizemos uma análise dos programas de sucesso com abordagem probabilística e reconhecemos semelhanças na implementação dos mesmos. A maior parte desses programas utiliza a cadeia oculta generalizada de Markov (GHMM - generalized hiddenMarkov model) como um modelo de gene. Percebemos que muitos preditores têm a arquitetura da GHMM fixada no código-fonte, dificultando a investigação de novas abordagens. Devido a essa dificuldade e pelas semelhanças entre os programas atuais, implementamos o sistema MYOP (Make Your Own Predictor) que tem como objetivo fornecer um ambiente flexível o qual permite avaliar rapidamente cada modelo de gene. Mostramos a utilidade da ferramenta através da implementação e avaliação de 96 modelos de genes em que cada modelo é formado por um conjunto de estados e cada estado tem uma distribuição de duração e um outro modelo probabilístico. Verificamos que nem sempre um modelo probabilísticomais sofisticado fornece um preditor melhor, mostrando a relevância das experimentações e a importância de um sistema como o MYOP. / The demand for efficient approaches for the gene structure prediction has motivated the implementation of different programs. In this work, we have analyzed successful programs that apply the probabilistic approach. We have observed similarities between different implementations, the same mathematical framework called generalized hidden Markov chain (GHMM) is applied. One problem with these implementations is that they maintain fixed GHMM architectures that are hard-coded. Due to this problem and similarities between the programs, we have implemented the MYOP framework (Make Your Own Predictor) with the objective of providing a flexible environment that allows the rapid evaluation of each gene model. We have demonstrated the utility of this tool through the implementation and evaluation of 96 gene models in which each model has a set of states and each state has a duration distribution and a probabilistic model. We have shown that a sophisticated probabilisticmodel is not sufficient to obtain better predictor, showing the experimentation relevance and the importance of a system as MYOP.

For young animals, surviving the first year of nutritional independence requires rapid development of effective foraging behaviour before the onset of terminal starvation. Grey seal (Halichoerus grypus) pups are abandoned on the natal colony after a brief (15-21 days) suckling period and must learn to dive and forage without parental instruction. Regional and sex-specific differences in diet and foraging behaviour have been described for adults and juveniles, but the early-life behaviour of pups during the critical first months at sea remains poorly understood. This thesis investigates sources of intrinsic and extrinsic variation in the development of foraging behaviour and resource selection in grey seal pups. The studies presented here feature tracking and dive data collected from 52 recently-weaned pups, tagged at six different breeding colonies in two geographically-distinct regions of the United Kingdom (UK). Original aspects of this thesis include: (Chapter I) a comprehensive review of analytical methods for inferring foraging behaviour from tracking and dive data in pinnipeds; (Chapter II) description and comparison of regional and sex differences in movements and diving characteristics of recently-weaned pups during their first trips at sea; (Chapter III) implementation of a novel generalized hidden Markov modelling (HMM) technique to investigate the development of foraging movement patterns whilst accounting for sources of intrinsic (age, sex) and extrinsic (regional) variation; and (Chapter IV) the first analysis of grey seal pup foraging habitat preference, incorporating behavioural inferences from HMMs and investigating changes in preference through time.

Distance sampling and spatial capture-recapture are statistical methods to estimate the number of animals in a wild population based on encounters between these animals and scientific detectors. Both methods estimate the probability an animal is detected during a survey, but do not explicitly model animal movement. The primary challenge is that animal movement in these surveys is unobserved; one must average over all possible paths each animal could have travelled during the survey. In this thesis, a general statistical model, with distance sampling and spatial capture-recapture as special cases, is presented that explicitly incorporates animal movement. An efficient algorithm to integrate over all possible movement paths, based on quadrature and hidden Markov modelling, is given to overcome the computational obstacles. For distance sampling, simulation studies and case studies show that incorporating animal movement can reduce the bias in estimated abundance found in conventional models and expand application of distance sampling to surveys that violate the assumption of no animal movement. For spatial capture-recapture, continuous-time encounter records are used to make detailed inference on where animals spend their time during the survey. In surveys conducted in discrete occasions, maximum likelihood models that allow for mobile activity centres are presented to account for transience, dispersal, and heterogeneous space use. These methods provide an alternative when animal movement causes bias in standard methods and the opportunity to gain richer inference on how animals move, where they spend their time, and how they interact.