Introduction to the Theory of Imprecise Probability

The theory of imprecise probability is a generalization of classical ‘precise’ probability theory that allows modeling imprecision and indecision. This is a practical advantage in situations where a unique precise uncertainty model cannot be justified. This arises, for example, when there is a relatively small amount of data available to learn the uncertainty model or when the model’s structure cannot be defined uniquely. The tools the theory provides make it possible to draw conclusions and make decisions that correctly reflect the limited information or knowledge available for the uncertainty modeling task. This extra expressivity however often implies a higher computational burden. The goal of this chapter is to primarily give you the necessary knowledge to be able to read literature that makes use of the theory of imprecise probability. A secondary goal is to provide the insight needed to use imprecise probabilities in your own research. To achieve the goals, we present the essential concepts and techniques from the theory, as well as give a less in-depth overview of the various specific uncertainty models used. Throughout, examples are used to make things concrete. We build on the assumed basic knowledge of classical probability theory.

Optimal Operation Model of Park Integrated Energy System Considering Uncertainty of Flexible Electrical, Thermal and Gas Load

Flexible Load (FL) of electricity, heat and gas can improve the operation economy, flexibility and reliability of PIES. Aiming at the uncertainty of FL in the actual operation of the park integrated energy system (PIES), an optimal operation model of PIES with uncertainty of FL is proposed. Firstly, the uncertainty models of shiftable electric load and transferable load response are established, respectively. And then an adjustable heat load response model considering the uncertainty of solar radiation intensity is established. On this basis, an optimal operation model of PIES considering the uncertainty of the FL with the goal of maximizing the total revenue is constructed and is solved by the enhanced-interval linear programming method. Simulation indicate that FL can improve the operating economy of PIES and renewable energy consumption.

Evaluating a Taxonomy of Textual Uncertainty for Collaborative Visualisation in the Digital Humanities

The capture, modelling and visualisation of uncertainty has become a hot topic in many areas of science, such as the digital humanities (DH). Fuelled by critical voices among the DH community, DH scholars are becoming more aware of the intrinsic advantages that incorporating the notion of uncertainty into their workflows may bring. Additionally, the increasing availability of ubiquitous, web-based technologies has given rise to many collaborative tools that aim to support DH scholars in performing remote work alongside distant peers from other parts of the world. In this context, this paper describes two user studies seeking to evaluate a taxonomy of textual uncertainty aimed at enabling remote collaborations on digital humanities (DH) research objects in a digital medium. Our study focuses on the task of free annotation of uncertainty in texts in two different scenarios, seeking to establish the requirements of the underlying data and uncertainty models that would be needed to implement a hypothetical collaborative annotation system (CAS) that uses information visualisation and visual analytics techniques to leverage the cognitive effort implied by these tasks. To identify user needs and other requirements, we held two user-driven design experiences with DH experts and lay users, focusing on the annotation of uncertainty in historical recipes and literary texts. The lessons learned from these experiments are gathered in a series of insights and observations on how these different user groups collaborated to adapt an uncertainty taxonomy to solve the proposed exercises. Furthermore, we extract a series of recommendations and future lines of work that we share with the community in an attempt to establish a common agenda of DH research that focuses on collaboration around the idea of uncertainty.

Robust Co-Design: Coupling Morphology and Feedback Design Through Stochastic Programming

This paper proposes a new framework for the computational design of robots that are robust to disturbances. The framework combines trajectory optimization (TO) and feedback control design to produce robots with improved performance under perturbations by co-optimizing a nominal trajectory alongside a feedback policy and the system morphology. Stochastic-programming (SP) methods are used to address these perturbations via uncertainty models in the problem specification, resulting in motions that are easier to stabilize via feedback. Two robotic systems serve to demonstrate the potential of the method: a planar manipulator and a jumping monopod robot. The co-optimized robots achieve higher performance compared to state-of-the-art solutions where the feedback controller is designed separately from the physical system. Specifically, the co-designed controllers show higher tracking accuracy and improved energy efficiency (e.g., 91% decrease in tracking error and approximately 5% decrease in energy consumption for a manipulator) compared to LQR applied to a design optimized for nominal conditions.

Bi-level optimization approach for robust mean-variance problems

Portfolio Optimization is based on the efficient allocation of several assets, which can get heavily affected by the uncertainty in input parameters. So we must look for such solutions which can give us steady results in uncertain conditions too. Recently, the uncertainty based optimization problems are being dealt with robust optimization approach. With this development, the interest of researchers has been shifted toward the robust portfolio optimization. In this paper, we study the robust counterparts of the uncertain mean-variance problems under box and ellipsoidal uncertainties. We convert those uncertain problems into bi-level optimization models and then derive their robust counterparts. We also solve a problem using this methodology and compared the optimal results of box and ellipsoidal uncertainty models with the nominal model.

Delimitation and classification of coastal wetlands: Implications for the environmental management of the Colombian Continental Caribbean

This article describes the cartographic layer construction process of Colombian Caribbean coastal wetlands at a scale of 1:100,000 and the results obtained in terms of their quantification and typing. Two cartographic layers were constructed and subsequently joined, one of the permanent water bodies and another of temporary water bodies and associated coverages. The layers were generated by multitemporal analysis of 45 Landsat 8-OLI satellite images, based on the NDVI index, uncertainty models by superposition of cartographic attributes, and a flood frequency consultation model on ALOS PALSAR 1 images. As a result, 576,279 ha of coastal wetlands were delimited (1.9 % of total wetlands in Colombia), of which 20.4 % are within protected areas. The cartographic legend makes it possible to typify wetlands based on the coverage and temporality of water bodies; discriminates permanent wetlands (42.7 %) with five categories and temporary wetlands (57.3 %) with 15 categories, mostly distributed in seven large complexes. This study is the first description of the colombian Caribbean coastal wetlands based on a cartographic construction, is methodologically replicable, and will support decision-making in the planning of colombian Caribbean coastal areas, especially for risk management and ecosystem-based adaptation to climate change.

Can machine learning be used to forecast the future uncertainty of military teams?

Uncertainty is a fundamental property of neural computation that becomes amplified when sensory information does not match a person’s expectations of the world. Uncertainty and hesitation are often early indicators of potential disruption, and the ability to rapidly measure uncertainty would have implications for future educational and training efforts by targeting reflective discussions about past actions, supporting in-progress corrections, and generating forecasts about future disruptions. An approach is described combining neurodynamics and machine learning to provide quantitative measures of uncertainty. Models of neurodynamic information derived from electroencephalogram (EEG) brainwaves have provided detailed neurodynamic histories of US Navy submarine navigation team members. Persistent periods (25–30 s) of neurodynamic information were seen as discrete peaks when establishing the submarine’s position and were identified as periods of uncertainty by an artificial intelligence (AI) system previously trained to recognize the frequency, magnitude, and duration of different patterns of uncertainty in healthcare and student teams. Transition matrices of neural network states closely predicted the future uncertainty of the navigation team during the three minutes prior to a grounding event. These studies suggest that the dynamics of uncertainty may have common characteristics across teams and tasks and that forecasts of their short-term evolution can be estimated.

Using the Variable Geometry in a Planar Inductor for an Optimised Performance

In this paper, the performance, modelling and application of a planar electromagnetic sensor are discussed. Due to the small size profiles and their non-contact nature, planar sensors are widely used due to their simple and basic design. The paper discusses the experimentation and the finite element modelling (FEM) performed for developing the design of planar coils. In addition, the paper investigates the performance of various topologies of planar sensors when they are used in inductive sensing. This technique has been applied to develop a new displacement sensor. The ANSYS Maxwell FEM package has been used to analyse the models while varying the topologies of the coils. For this purpose, different models in FEM were constructed and then tested with topologies such as circular, square and hexagon coil configurations. The described methodology is considered an effective way for the development of sensors based on planar coils with better performance. Moreover, it also confirms a good correlation between the experimental data and the FEM models. Once the best topology is chosen based on performance, an optimisation exercise was then carried out using uncertainty models. That is, the influence of variables such as number of turns and the spacing between the coils on the output inductance has been investigated. This means that the combined effects of these two variables on the output inductance was studied to obtain the optimum values for the number of turns and the spacing between the coils that provided the highest level of inductance from the coils. Integrated sensor systems are a pre-requisite for developing the concept of smart cities in practice due to the fact that the individual sensors can hardly meet the demands of smart cities for complex information. This paper provides an overview of the theoretical concept of smart cities and the integrated sensor systems.