Bayesian error bars for regression

Regression problems are concerned with predicting the values of one or more continuous quantities, given the values of a number of input variables. For virtually every application of regression, however, it is also important to have an indication of the uncertainty in the predictions. Such uncertainties are expressed in terms of the error bars, which specify the standard deviation of the distribution of predictions about the mean. Accurate estimate of error bars is of practical importance especially when safety and reliability is an issue. The Bayesian view of regression leads naturally to two contributions to the error bars. The first arises from the intrinsic noise on the target data, while the second comes from the uncertainty in the values of the model parameters which manifests itself in the finite width of the posterior distribution over the space of these parameters. The Hessian matrix which involves the second derivatives of the error function with respect to the weights is needed for implementing the Bayesian formalism in general and estimating the error bars in particular. A study of different methods for evaluating this matrix is given with special emphasis on the outer product approximation method. The contribution of the uncertainty in model parameters to the error bars is a finite data size effect, which becomes negligible as the number of data points in the training set increases. A study of this contribution is given in relation to the distribution of data in input space. It is shown that the addition of data points to the training set can only reduce the local magnitude of the error bars or leave it unchanged. Using the asymptotic limit of an infinite data set, it is shown that the error bars have an approximate relation to the density of data in input space.

Simultaneous measurement of strain and temperature using the first- and second-order diffraction wavelengths of Bragg gratings

A method of discriminating between temperature and strain effects in fibre sensing using a conventionally written, in-fibre Bragg grating is presented. The technique uses wavelength information from the first and second diffraction orders of the grating element to determine the wavelength dependent strain and temperature coefficients, from which independent temperature and strain measurements can be made. The authors present results that validate this matrix inversion technique and quantify the strain and temperature errors which can arise for a given uncertainty in the measurement of the reflected wavelength.

Strategic development of transport systems: a study of the physical constraints on planning processes

Investment in transport infrastructure can be highly sensitive to uncertainty. The scale and lead time of strategic transport programmes are such that they require continuing policy support and accurate forecasting. Delay, cost escalation and abandonment of projects often result if these conditions are not present. In Part One the physical characteristics of infrastructure are identified as a major constraint on planning processes. The extent to which strategies and techniques acknowledge these constraints is examined. A simple simulation model is developed to evaluate the effects on system development of variations in the scale and lead time of investments. In Part Two, two case studies of strategic infrastructure investment are analysed. The absence of a policy consensus for airport location was an important factor in the delayed resolution of the Third London Airport issue. In London itself, the traffic and environmental effects of major highway investment ultimately resulted in the abandonment of plans to construct urban motorways. In both cases, the infrastructure implications of alternative strategies are reviewed with reference to the problems of uncertainty. In conclusion, the scale of infrastructure investment is considered the most important of the constraints on the processes of transport planning. Adequate appraisal of such constraints may best be achieved by evaluation more closely aligned to policy objectives.

Real options and demographic decisions:empirical evidence from East and West Germany

Iyer and Velu (2006) have convincingly argued that contemporary analyses of fertility behaviour fail to explain why a woman (or a couple) will choose to postpone childbirth, and in particular to consider the role of uncertainty in this regard. They have addressed this lacuna in the literature by using a real options approach to model fertility decisions by relating uncertainty experienced by individuals to the likelihood of childbirth. However, they did not present empirical evidence. Since the theory implies the existence of two offsetting effects of uncertainty on fertility decisions, a positive insurance effect and a negative option value effect, it is not easy to reject the theory on the basis of empirical analysis, when one of these effects offsets the other. We construct such a test for East (and also West) Germany during that country's reunification, which takes advantage of the fact that because of the country's strong welfare system, the insurance effect should be dominated by the option value effect, thereby suggesting that the net relationship should be negative. The results provide rather strong support for the real options link, especially for Eastern Germany.

Run-time model evaluation for requirements model-driven self-adaptation

A self-adaptive system adjusts its configuration to tolerate changes in its operating environment. To date, requirements modeling methodologies for self-adaptive systems have necessitated analysis of all potential system configurations, and the circumstances under which each is to be adopted. We argue that, by explicitly capturing and modelling uncertainty in the operating environment, and by verifying and analysing this model at runtime, it is possible for a system to adapt to tolerate some conditions that were not fully considered at design time. We showcase in this paper our tools and research results. © 2012 IEEE.

Tracing requirements for adaptive systems using claims

The complexity of environments faced by dynamically adaptive systems (DAS) means that the RE process will often be iterative with analysts revisiting the system specifications based on new environmental understanding product of experiences with experimental deployments, or even after final deployments. An ability to trace backwards to an identified environmental assumption, and to trace forwards to find the areas of a DAS's specification that are affected by changes in environmental understanding aids in supporting this necessarily iterative RE process. This paper demonstrates how claims can be used as markers for areas of uncertainty in a DAS specification. The paper demonstrates backward tracing using claims to identify faulty environmental understanding, and forward tracing to allow generation of new behaviour in the form of policy adaptations and models for transitioning the running system. © 2011 ACM.

Creating resilient SMEs:why one size might not fit all

This article is a first step towards addressing a gap in the field of organisational resilience research by examining how small and medium enterprises (SME) manage the threat and actuality of extreme events. Pilot research found that the managerial framing of extreme events varied by a range of organisational factors. This finding informed further examination of the contextual nature of the resilience concept. To date, large organisations have been the traditional focus of empirical work and theorising in this area; yet the heterogeneous SME sector makes up approximately 99% of UK industry and routinely operates under conditions of uncertainty. In a comparative study examining UK organisational resilience, it emerged that SME participants had both a distinctive perspective and approach to resilience when compared to participants from larger organisations. This article presents a subset of data from 11 SME decision-makers. The relationship between resilience capabilities, such as flexibility and adaptation, is interrogated in relation to organisational size. The data suggest limitations of applying a one-size-fits-all organisation solution (managerial or policy) to creating resilience. This study forms the basis for survey work examining the extent to which resilience is an organisationally contingent concept in practice.

Simultaneous measurement of strain and temperature using the first- and second-order diffraction wavelengths of Bragg gratings

A method of discriminating between temperature and strain effects in fibre sensing using a conventionally written, in-fibre Bragg grating is presented. The technique uses wavelength information from the first and second diffraction orders of the grating element to determine the wavelength dependent strain and temperature coefficients, from which independent temperature and strain measurements can be made. The authors present results that validate this matrix inversion technique and quantify the strain and temperature errors which can arise for a given uncertainty in the measurement of the reflected wavelength.

An operational research-based integrated approach for mass evacuation planning of a city

Large-scale disasters are constantly occurring around the world, and in many cases evacuation of regions of city is needed. ‘Operational Research/Management Science’ (OR/MS) has been widely used in emergency planning for over five decades. Warning dissemination, evacuee transportation and shelter management are three ‘Evacuation Support Functions’ (ESF) generic to many hazards. This thesis has adopted a case study approach to illustrate the importance of integrated approach of evacuation planning and particularly the role of OR/MS models. In the warning dissemination phase, uncertainty in the household’s behaviour as ‘warning informants’ has been investigated along with uncertainties in the warning system. An agentbased model (ABM) was developed for ESF-1 with households as agents and ‘warning informants’ behaviour as the agent behaviour. The model was used to study warning dissemination effectiveness under various conditions of the official channel. In the transportation phase, uncertainties in the household’s behaviour such as departure time (a function of ESF-1), means of transport and destination have been. Households could evacuate as pedestrians, using car or evacuation buses. An ABM was developed to study the evacuation performance (measured in evacuation travel time). In this thesis, a holistic approach for planning the public evacuation shelters called ‘Shelter Information Management System’ (SIMS) has been developed. A generic allocation framework of was developed to available shelter capacity to the shelter demand by considering the evacuation travel time. This was formulated using integer programming. In the sheltering phase, the uncertainty in household shelter choices (either nearest/allocated/convenient) has been studied for its impact on allocation policies using sensitivity analyses. Using analyses from the models and detailed examination of household states from ‘warning to safety’, it was found that the three ESFs though sequential in time, however have lot of interdependencies from the perspective of evacuation planning. This thesis has illustrated an OR/MS based integrated approach including and beyond single ESF preparedness. The developed approach will help in understanding the inter-linkages of the three evacuation phases and preparing a multi-agency-based evacuation planning evacuation

Humidity responsivity of poly(methyl methacrylate)-based optical fiber Bragg grating sensors

The humidity response of poly(methyl methacrylate) (PMMA)-based optical fiber Bragg gratings (POFBGs) has been studied. The characteristic wavelength of the grating is modulated by water absorption-induced swelling and refractive index change in the fiber. This work indicates that anisotropic expansion may exist in PMMA optical fiber, reducing the humidity responsivity of the grating and introducing uncertainty in the responsivity from fiber to fiber. By pre-straining a grating, one can get rid of this uncertainty and simultaneously improve the POFBG response time. © 2014 Optical Society of America.

Investigating the influence of African American and African Caribbean race on primary care doctors' decision making about depression

This paper explores differences in how primary care doctors process the clinical presentation of depression by African American and African-Caribbean patients compared with white patients in the US and the UK. The aim is to gain a better understanding of possible pathways by which racial disparities arise in depression care. One hundred and eight doctors described their thought processes after viewing video recorded simulated patients presenting with identical symptoms strongly suggestive of depression. These descriptions were analysed using the CliniClass system, which captures information about micro-components of clinical decision making and permits a systematic, structured and detailed analysis of how doctors arrive at diagnostic, intervention and management decisions. Video recordings of actors portraying black (both African American and African-Caribbean) and white (both White American and White British) male and female patients (aged 55 years and 75 years) were presented to doctors randomly selected from the Massachusetts Medical Society list and from Surrey/South West London and West Midlands National Health Service lists, stratified by country (US v.UK), gender, and years of clinical experience (less v. very experienced). Findings demonstrated little evidence of bias affecting doctors' decision making processes, with the exception of less attention being paid to the potential outcomes associated with different treatment options for African American compared with White American patients in the US. Instead, findings suggest greater clinical uncertainty in diagnosing depression amongst black compared with white patients, particularly in the UK. This was evident in more potential diagnoses. There was also a tendency for doctors in both countries to focus more on black patients' physical rather than psychological symptoms and to identify endocrine problems, most often diabetes, as a presenting complaint for them. This suggests that doctors in both countries have a less well developed mental model of depression for black compared with white patients. © 2014 The Authors.

Reliability of vegetation community information derived using decorana ordination and fuzzy c-means clustering

Descriptions of vegetation communities are often based on vague semantic terms describing species presence and dominance. For this reason, some researchers advocate the use of fuzzy sets in the statistical classification of plant species data into communities. In this study, spatially referenced vegetation abundance values collected from Greek phrygana were analysed by ordination (DECORANA), and classified on the resulting axes using fuzzy c-means to yield a point data-set representing local memberships in characteristic plant communities. The fuzzy clusters matched vegetation communities noted in the field, which tended to grade into one another, rather than occupying discrete patches. The fuzzy set representation of the community exploited the strengths of detrended correspondence analysis while retaining richer information than a TWINSPAN classification of the same data. Thus, in the absence of phytosociological benchmarks, meaningful and manageable habitat information could be derived from complex, multivariate species data. We also analysed the influence of the reliability of different surveyors' field observations by multiple sampling at a selected sample location. We show that the impact of surveyor error was more severe in the Boolean than the fuzzy classification. © 2007 Springer.

Combining an enterprise resource planning system and informality:a study of efficiency and flexibility complmentarity [sic]

DUE TO COPYRIGHT RESTRICTIONS ONLY AVAILABLE FOR CONSULTATION AT ASTON UNIVERSITY LIBRARY AND INFORMATION SERVICES WITH PRIOR ARRANGEMENT One of the current research trends in Enterprise Resource Planning (ERP) involves examining the critical factors for its successful implementation. However, such research is limited to system implementation, not focusing on the flexibility of ERP to respond to changes in business. Therefore, this study explores a combination system, made up of an ERP and informality, intended to provide organisations with efficient and flexible performance simultaneously. In addition, this research analyses the benefits and challenges of using the system. The research was based on socio-technical system (STS) theory which contains two dimensions: 1) a technical dimension which evaluates the performance of the system; and 2) a social dimension which examines the impact of the system on an organisation. A mixed method approach has been followed in this research. The qualitative part aims to understand the constraints of using a single ERP system, and to define a new system corresponding to these problems. To achieve this goal, four Chinese companies operating in different industries were studied, all of which faced challenges in using an ERP system due to complexity and uncertainty in their business environments. The quantitative part contains a discrete-event simulation study that is intended to examine the impact of operational performance when a company implements the hybrid system in a real-life situation. Moreover, this research conducts a further qualitative case study, the better to understand the influence of the system in an organisation. The empirical aspect of the study reveals that an ERP with pre-determined business activities cannot react promptly to unanticipated changes in a business. Incorporating informality into an ERP can react to different situations by using different procedures that are based on the practical knowledge of frontline employees. Furthermore, the simulation study shows that the combination system can achieve a balance between efficiency and flexibility. Unlike existing research, which emphasises a continuous improvement in the IT functions of an enterprise system, this research contributes to providing a definition of a new system in theory, which has mixed performance and contains both the formal practices embedded in an ERP and informal activities based on human knowledge. It supports both cost-efficiency in executing business transactions and flexibility in coping with business uncertainty.This research also indicates risks of using the system, such as using an ERP with limited functions; a high cost for performing informally; and a low system acceptance, owing to a shift in organisational culture. With respect to practical contribution, this research suggests that companies can choose the most suitable enterprise system approach in accordance with their operational strategies. The combination system can be implemented in a company that needs to operate a medium amount of volume and variety. By contrast, the traditional ERP system is better suited in a company that operates a high-level volume market, while an informal system is more suitable for a firm with a requirement for a high level of variety.

Probabilistic topographic information visualisation

The focus of this thesis is the extension of topographic visualisation mappings to allow for the incorporation of uncertainty. Few visualisation algorithms in the literature are capable of mapping uncertain data with fewer able to represent observation uncertainties in visualisations. As such, modifications are made to NeuroScale, Locally Linear Embedding, Isomap and Laplacian Eigenmaps to incorporate uncertainty in the observation and visualisation spaces. The proposed mappings are then called Normally-distributed NeuroScale (N-NS), T-distributed NeuroScale (T-NS), Probabilistic LLE (PLLE), Probabilistic Isomap (PIso) and Probabilistic Weighted Neighbourhood Mapping (PWNM). These algorithms generate a probabilistic visualisation space with each latent visualised point transformed to a multivariate Gaussian or T-distribution, using a feed-forward RBF network. Two types of uncertainty are then characterised dependent on the data and mapping procedure. Data dependent uncertainty is the inherent observation uncertainty. Whereas, mapping uncertainty is defined by the Fisher Information of a visualised distribution. This indicates how well the data has been interpolated, offering a level of ‘surprise’ for each observation. These new probabilistic mappings are tested on three datasets of vectorial observations and three datasets of real world time series observations for anomaly detection. In order to visualise the time series data, a method for analysing observed signals and noise distributions, Residual Modelling, is introduced. The performance of the new algorithms on the tested datasets is compared qualitatively with the latent space generated by the Gaussian Process Latent Variable Model (GPLVM). A quantitative comparison using existing evaluation measures from the literature allows performance of each mapping function to be compared. Finally, the mapping uncertainty measure is combined with NeuroScale to build a deep learning classifier, the Cascading RBF. This new structure is tested on the MNist dataset achieving world record performance whilst avoiding the flaws seen in other Deep Learning Machines.

Ultra-long range distributed fibre sensing using virtually transparent propagation

Distributed fibre sensors provide unique capabilities for monitoring large infrastructures with high resolution. Practically, all these sensors are based on some kind of backscattering interaction. A pulsed activating signal is launched on one side of the sensing fibre and the backscattered signal is read as a function of the time of flight of the pulse along the fibre. A key limitation in the measurement range of all these sensors is introduced by fibre attenuation. As the pulse travels along the fibre, the losses in the fibre cause a drop of signal contrast and consequently a growth in the measurement uncertainty. In typical single-mode fibres, attenuation imposes a range limit of less than 30km, for resolutions in the order of 1-2 meters. An interesting improvement in this performance can be considered by using distributed amplification along the fibre [1]. Distributed amplification allows having a more homogeneous signal power along the sensing fibre, which also enables reducing the signal power at the input and therefore avoiding nonlinearities. However, in long structures (≥ 50 km), plain distributed amplification does not perfectly compensate the losses and significant power variations along the fibre are to be expected, leading to inevitable limitations in the measurements. From this perspective, it is simple to understand intuitively that the best possible solution for distributed sensors would be offered by a virtually transparent fibre, i.e. a fibre exhibiting effectively zero attenuation in the spectral region of the pulse. In addition, it can be shown that lossless transmission is the working point that allows the minimization of the amplified spontaneous emission (ASE) noise build-up. © 2011 IEEE.