Yes / System safety, reliability and risk analysis are important tasks that are performed throughout the system lifecycle to ensure the dependability of safety-critical systems. Probabilistic risk assessment (PRA) approaches are comprehensive, structured and logical methods widely used for this purpose. PRA approaches include, but not limited to, Fault Tree Analysis (FTA), Failure Mode and Effects Analysis (FMEA), and Event Tree Analysis (ETA). Growing complexity of modern systems and their capability of behaving dynamically make it challenging for classical PRA techniques to analyse such systems accurately. For a comprehensive and accurate analysis of complex systems, different characteristics such as functional dependencies among components, temporal behaviour of systems, multiple failure modes/states for components/systems, and uncertainty in system behaviour and failure data are needed to be considered. Unfortunately, classical approaches are not capable of accounting for these aspects. Bayesian networks (BNs) have gained popularity in risk assessment applications due to their flexible structure and capability of incorporating most of the above mentioned aspects during analysis. Furthermore, BNs have the ability to perform diagnostic analysis. Petri Nets are another formal graphical and mathematical tool capable of modelling and analysing dynamic behaviour of systems. They are also increasingly used for system safety, reliability and risk evaluation. This paper presents a review of the applications of Bayesian networks and Petri nets in system safety, reliability and risk assessments. The review highlights the potential usefulness of the BN and PN based approaches over other classical approaches, and relative strengths and weaknesses in different practical application scenarios. / This work was funded by the DEIS H2020 project (Grant Agreement 732242).

In this thesis I develop Bayesian approach to model galaxy surface brightness and apply it to a bulge-disc decomposition analysis of galaxies in near-infrared band, from Two Micron All Sky Survey (2MASS). The thesis has three main parts. First part is a technical development of Bayesian galaxy image decomposition package Galphat based on Markov chain Monte Carlo algorithm. I implement a fast and accurate galaxy model image generation algorithm to reduce computation time and make Bayesian approach feasible for real science analysis using large ensemble of galaxies. I perform a benchmark test of Galphat and demonstrate significant improvement in parameter estimation with a correct statistical confidence. Second part is a performance test for full Bayesian application to galaxy bulgedisc decomposition analysis including not only the parameter estimation but also the model comparison to classify different galaxy population. The test demonstrates that Galphat has enough statistical power to make a reliable model inference using galaxy photometric survey data. Bayesian prior update is also tested for parameter estimation and Bayes factor model comparison and it shows that informative prior significantly improves the model inference in every aspects. Last part is a Bayesian bulge-disc decomposition analysis using 2MASS Ks-band selected samples. I characterise the luminosity distributions in spheroids, bulges and discs separately in the local Universe and study the galaxy morphology correlation, by full utilising the ensemble parameter posterior of the entire galaxy samples. It shows that to avoid a biased inference, the parameter covariance and model degeneracy has to be carefully characterised by the full probability distribution.

Growth plays a key role in regulating ecological and population dynamics. Life history characteristics such as age at maturity, fecundity and age and size at migration are tightly linked to growth rate. In addition, size can often determine survival and individual breeding success. To fully understand the process of growth it is important to understand the mechanisms that drive growth rates. In Atlantic salmon, growth is critical in determining life history pathways. Models to estimate growth could be useful in the broader context of predicting population dynamics. In this dissertation I investigate the growth process in juvenile Atlantic salmon (Salmo salar). I first used basic modeling approaches and data on individually tagged salmon to investigate the assumptions of different growth metrics. I demonstrate the size-dependency in certain growth metrics when assumptions are violated. Next, I assessed the efficacy of linear mixed effects models in modeling length-weight relationships from longitudinal data. I show that combining a random effects approach with third order polynomials can be an effective way to model length-weight relationships with mark-recapture data. I extend this hierarchical modeling approach to develop a Bayesian growth model. With limited assumptions, I derive a relatively simple discrete time model from von Bertalanffy growth that includes a nonparametric seasonal growth function. The linear dynamics of this model allow for efficient estimation of parameters in a Bayesian framework. Finally, I investigated the role of life history in driving compensatory growth patterns in immature Atlantic salmon. This analysis demonstrates the importance of considering life history as a mechanism in compensatory growth. Information provided in this dissertation will help provide ecologists with statistical tools to estimate growth rates, estimate length-weight relationships, and forecast growth from mark-recapture data. In addition, comparisons of seasonal growth within and among life history groups and within and among tributaries should make a valuable contribution to the important literature on growth in Atlantic salmon.

The dissertation presents a method for deriving the shape of a surface from a radar image of the surface. An appropriate model of radar image formation is derived from physical principles. A Bayesian formulation of the inversion problem is developed upon which a computational strategy is based. Theoretical results on random surfaces relevant to the prior distribution are presented, and convergence and optimality properties of a new sampling algorithm are described. The technique is applied to Magellan data of Venus.

A central goal of the robotics community is to develop general optimization algorithms for producing high-performance dynamic behaviors in robot systems. This goal is challenging because many robot control tasks are characterized by significant stochasticity, high-dimensionality, expensive evaluations, and unknown or unreliable system models. Despite these challenges, a range of algorithms exist for performing efficient optimization of parameterized control policies with respect to average cost criteria. However, other statistics of the cost may also be important. In particular, for many stochastic control problems, it can be advantageous to select policies based not only on their average cost, but also their variance (or risk). In this thesis, I present new efficient global and local risk-sensitive stochastic optimization algorithms suitable for performing policy search in a wide variety of problems of interest to robotics researchers. These algorithms exploit new techniques in nonparameteric heteroscedastic regression to directly model the policy-dependent distribution of cost. For local search, learned cost models can be used as critics for performing risk-sensitive gradient descent. Alternatively, decision-theoretic criteria can be applied to globally select policies to balance exploration and exploitation in a principled way, or to perform greedy minimization with respect to various risk-sensitive criteria. This separation of learning and policy selection permits variable risk control, where risk sensitivity can be flexibly adjusted and appropriate policies can be selected at runtime without requiring additional policy executions. To evaluate these algorithms and highlight the importance of risk in dynamic control tasks, I describe several experiments with the UMass uBot-5 that include learning dynamic arm motions to stabilize after large impacts, lifting heavy objects while balancing, and developing safe fall bracing behaviors. The results of these experiments suggest that the ability to select policies based on risk-sensitive criteria can lead to greater flexibility in dynamic behavior generation.

Robots exhibit flexible behavior largely in proportion to their degree of semantic knowledge about the world. Such knowledge is often meticulously hand-coded for a narrow class of tasks, limiting the scope of possible robot competencies. Thus, the primary limiting factor of robot capabilities is often not the physical attributes of the robot, but the limited time and skill of expert programmers. One way to deal with the vast number of situations and environments that robots face outside the laboratory is to provide users with simple methods for programming robots that do not require the skill of an expert. For this reason, learning from demonstration (LfD) has become a popular alternative to traditional robot programming methods, aiming to provide a natural mechanism for quickly teaching robots. By simply showing a robot how to perform a task, users can easily demonstrate new tasks as needed, without any special knowledge about the robot. Unfortunately, LfD often yields little semantic knowledge about the world, and thus lacks robust generalization capabilities, especially for complex, multi-step tasks. To address this shortcoming of LfD, we present a series of algorithms that draw from recent advances in Bayesian nonparametric statistics and control theory to automatically detect and leverage repeated structure at multiple levels of abstraction in demonstration data. The discovery of repeated structure provides critical insights into task invariants, features of importance, high-level task structure, and appropriate skills for the task. This culminates in the discovery of semantically meaningful skills that are flexible and reusable, providing robust generalization and transfer in complex, multi-step robotic tasks. These algorithms are tested and evaluated using a PR2 mobile manipulator, showing success on several complex real-world tasks, such as furniture assembly.

A Bayesian network is graphical representation of the probabilistic relationships among set of variables and can be used to encode expert knowledge about uncertain domains. The structure of this model represents the set of conditional independencies among the variables in the data. Bayesian networks are widely applicable, having been used to model domains ranging from monitoring patients in an emergency room to predicting the severity of hailstorms. In this thesis, I focus on the problem of learning the structure of Bayesian networks from data. Under certain assumptions, the learned structure of a Bayesian network can represent causal relationships in the data. Constraint-based algorithms for structure learning are designed to accurately identify the structure of the distribution underlying the data and, therefore, the causal relationships. These algorithms use a series of conditional hypothesis tests to learn independence constraints on the structure of the model. When sample size is limited, these hypothesis tests are prone to errors. I present a comprehensive empirical evaluation of constraint-based algorithms and show that existing constraint-based algorithms are prone to many false negative errors in the constraints due to run- ning hypothesis tests with low statistical power. Furthermore, this analysis shows that many statistical solutions fail to reduce the overall errors of constraint-based algorithms. I show that new algorithms inspired by constraint satisfaction are able to produce significant improvements in structural accuracy. These constraint satisfaction algo- rithms exploit the interaction among the constraints to reduce error. First, I introduce an algorithm based on constraint optimization that is sound in the sample limit, like existing algorithms, but is guaranteed to produce a DAG. This new algorithm learns models with structural accuracy equivalent or better to existing algorithms. Second, I introduce an algorithm based constraint relaxation. Constraint relaxation combines different statistical techniques to identify constraints that are likely to be incorrect, and remove those constraints from consideration. I show that an algorithm combining constraint relaxation with constraint optimization produces Bayesian networks with significantly better structural accuracy when compared to existing structure learning algorithms, demonstrating the effectiveness of constraint satisfaction approaches for learning accurate structure of Bayesian networks.

Classical models for multivariate or spatial extremes are mainly based upon the asymptotically justified max-stable or generalized Pareto processes. These models are suitable when asymptotic dependence is present. However, recent environmental data applications suggest that asymptotic independence is equally important. Therefore, development of flexible subasymptotic models is in pressing need. This dissertation consists of four major contributions to subasymptotic modeling of multivariate and spatial extremes. Firstly, the dissertation proposes a new spatial copula model for extremes based on the multivariate generalized hyperbolic distribution. The extremal dependence of this distribution is revisited and a corrected theoretical description is provided. Secondly, the dissertation thoroughly investigates the extremal dependence of stochastic processes driven by exponential-tailed Lévy noise. It shows that the discrete approximation models, which are linear transformations of a random vector with independent components, bridge asymptotic independence and asymptotic dependence in a novel way, whilst the exact stochastic processes exhibit only asymptotic independence. Thirdly, the dissertation explores two different notions of optimal prediction for extremes, and compares the classical linear kriging predictor and the conditional mean predictor for certain non-Gaussian models. Finally, the dissertation proposes a multivariate skew-elliptical link model for correlated highly-imbalanced (extreme) binary responses, and shows that the regression coefficients have a closed-form unified skew-elliptical posterior with an elliptical prior.

The remarkable ability of the human brain to draw an accurate percept from imprecise sensory information is not well understood. Bayesian inference provides an optimal means for drawing perceptual conclusions from sensorineural activity. This approach has frequently been applied to visual and auditory studies but only rarely to studies of tactile perception. We explored whether a Bayesian observer model could replicate fundamental aspects of human tactile spatial perception. The model consisted of an encoder that simulated sensorineural responses with Poisson statistics followed by a decoder that interpreted the observed firing rates. We compared the performance of our Bayesian observer on a battery of tactile tasks to human participant data collected previously by our laboratory and others. The Bayesian observer replicated human performance trends on three spatial acuity tasks: classic two-point discrimination (C2PD), sequential two-point discrimination (S2PD), and two-point orientation discrimination (2POD). We confirmed the widely reported observation that C2PD is the least reliable method of assessing tactile acuity due presumably to the presence of non-spatial cues. Additionally, the Bayesian observer performed similarly to humans on raised letter and Braille character-recognition tasks. The Bayesian observer further replicated two illusions previously reported in humans: an adaptation-induced repulsion illusion and an orientation anisotropy illusion. Taken together, these results suggest that human tactile spatial perception may arise from a Bayesian-like decoder that is unaware of the precise characteristics of its inputs. / Thesis / Master of Science (MSc)

Patients with a history of lateral ankle sprain (LAS) may experience different levels of mechanical and/or sensorimotor deficits following their injuries. Although various factors, such as structural damage, sensorimotor adaptation, perceived instability, swelling and/or pain, can develop and perpetuate the condition of chronic ankle instability (CAI), most previous CAI research on biomechanics has considered all patients with CAI as a homogeneous group. Recent research has clustered patients with CAI into six distinct movement patterns during a maximal jump-landing/cutting task. This approach could motivate clinicians to develop appropriate rehabilitation programs for each patient with CAI depending on their movement patterns. However, evaluating patients with CAI for the quality of movement and sensorimotor deficits using a 3D motion capture system and a force plate is not easily accessible in clinical settings. PURPOSE: (i) to identify subgroups within the CAI population based on their movement patterns using inertial measurement unit (IMU) devices and (ii) to characterize each subgroup's functional movement patterns during maximal jump-landing/cutting relative to the uninjured controls. METHODS: A total of 100 patients with CAI (height = 1.76 ± 0.1 m, mass = 74.0 ± 14.9 kg) were assessed according to the Foot and Ankle Ability Measure (FAAM) (ADL: 84.3 ± 7.6%, Sport: 63.6 ± 8.6%) and the Ankle Instability Instrument (AII) (6.7 ± 1.2) and were fit into clusters based on their movement strategy during the maximal jump-landing/cutting task. A total of 21 uninjured controls (height = 1.74 ± 0.1 m, mass = 70.7 ± 13.4 kg) were compared with each cluster. Seven IMU sensors were placed on the base of the lumbar spine, lower and upper legs, and feet and participants performed 5 trials of the maximal jump-landing/cutting test. Joint kinematics in the lower extremity were collected during the task using IMU sensors. Data were reduced to functional curves; kinematic data from the sagittal and frontal planes were reduced to a single representative curve for each plane. Then, representative curves were clustered using a Bayesian clustering technique. Functional analyses of variance were used to identify between-group differences for outcome measures and describe specific movement characteristics of each subgroup. Pairwise comparison functions as well as 95% confidence interval (CI) bands were plotted to determine specific differences. If 95% CI bands did not cross the zero line, we considered the difference significant. RESULTS: Four distinct clusters were identified from the sagittal- and frontal-plane kinematic data. Specific movement patterns in each cluster compared to either uninjured controls or rest of patients with CAI were also identified. CONCLUSION: The IMUs were able to distinguish 4 clusters within the CAI population based on distinct movement patterns during a maximal jump-landing/cutting task. Thus, IMUs can be effective measuring devices to distinguish and characterize multiple distinct movement patterns without relying on a traditional 3D motion capture system. Clinicians should consider utilizing IMU devices to measure and evaluate specific movement patterns in the CAI population during multiplanar demanding tests before developing appropriate treatment interventions in clinical settings.