Uncertainty Calculi Research Articles

A Dutch book coherence condition for conditional completely alternating Choquet expectations

Stemming from de Finetti’s coherence for finitely additive (conditional) probabilities, the paradigm of coherence has been extended to other uncertainty calculi. We study the notion of coherence for conditional completely alternating Choquet expectations, providing an avoiding Dutch book like condition.

Raman microimaging as an analytical technique for simultaneous quantification and localization of active principles in pharmaceutical solid dosage forms

AbstractRaman microimaging, as a product of Raman microspectroscopy mapping and multivariate analysis, was used for the localization and quantification of active pharmaceutical ingredients (APIs) in tablets made in laboratory. This was done to develop an analytical strategy to simultaneously recover qualitative and quantitative information of solid dosage forms at a microscopic level by using a nondestructive method. A chemical system, composed of acetaminophen (AMP), caffeine, and one excipient (microcrystalline cellulose), was subjected to chemometric analysis through principal component analysis (PCA) and multivariate curve resolution with alternating least squares (MCR–ALS). This was done by using Raman spectra obtained from microscopic images with pixel sizes of 15 × 15 μm to localize the APIs in the tablets. Partial least squares (PLS) was applied as a calibration method to obtain bulk and single‐pixel concentrations of APIs in the samples. MCR–ALS provided better results than PCA for the localization of APIs. PLS achieved satisfactory root mean standard error values in the external validation set (<4% w/w) in bulk concentration determinations of AMP. This method also achieved concentrations for each pixel of the images, reconstructing images very similar to those obtained by MCR–ALS. Consequently, simultaneous localization and quantification of AMP was possible. Finally, the performance of Raman microimaging was evaluated through estimation of analytical figures of merit (AFOMs) of the technique used to assess the quantification of APIs. This included different calculus of uncertainty in the signal in a technique where the signal/noise ratio is low, and AFOMs for multivariate quantification are not often reported.

Uncertainty study of fiscal orifice meter used in a gas Algerian field

Uncertainty variation of a fiscal orifice measurement system used in an Algerian natural gas exportation station is studied using data from a natural gas production field known as Gas Tin Fouye Tabankort (GTFT) located in the south-east of Algeria. The expected results are uncertainty calculus over a range of temperature and pressure variation and to the customs authorities’ allocation.In fact, each quantity of measured fluid flow has certain uncertainty and then the fiscal measurement station is very important for gas exportation, which means the income. Therefore, the pursuit of flow metering device uncertainty and its influence on the measured quantities in the transmission networks is very important.For that, the uncertainty caused by flowmeter in the measurement station causing economical revenue fluctuations is studied. The work was done to justify why there is a production decrease of hydrocarbons without identifying reasons during summer. The difference between the mass flow rate quantity produced and the transmitted value was important that is why our work is done to clarify exactly from where the problem can come.The measurements setting with two operating conditions (gas temperature and pressure) show that the uncertainty is dominated by seasonal temperatures and pressures variations which induce fluctuation in gas and pipe temperatures and influence the metrological performance of the transmitters. Indeed, the metrological measurement chain performance is affected also by these two operating conditions.The present work is done according to the ONML (National Legal Metrological Office) instructions regarding differences between the measured and the seller values represented by the mass flow rate.In natural gas transmission network, the important problem in the management and control of the network is represented by the unaccounted for gas, a quantity of measuring error which is to be considered in the equation of network balancing. One of the unaccounted for gas sources are the environmental conditions and systematic measurement errors.In this work, the calculation of the combined uncertainty of the mass flow rate measured by an Orifice fiscal gas metering plant is done. From the results founded, the authors confirm that the uncertainty in the measurement system causing by the climatic conditions generates unaccounted for gas.

The evaluation of measurement uncertainties and its epistemological ramifications

The way metrologists conceive of measurement has undergone a major shift in the last two decades. This shift can in great part be traced to a change in the statistical methods used to deal with the expression of measurement results, and, more particularly, with the calculation of measurement uncertainties. Indeed, as we show, the incapacity of the frequentist approach to the calculus of uncertainty to deal with systematic errors has prompted the replacement of the customary frequentist methods by fully Bayesian procedures. The epistemological ramifications of the Bayesian approach merge with a deep empiricist mood tantamount to an “epistemic turn”: measurement results are analysed in terms of degrees of belief, and central concepts such as error and accuracy are called into question. We challenge the perspective entailed by this epistemic turn: we insist on the centrality of the concepts of error and accuracy by underlining the intentional character of measurement that is intimately linked to the process of correction of experimental data. We further circumvent the difficulties posed by the classical analysis of measurement by stressing the social rather than the epistemic dimension of measurement activities.

Causal compositional models in valuation-based systems with examples in specific theories

We show that Pearl's causal networks can be described using causal compositional models (CCMs) in the valuation-based systems (VBS) framework. One major advantage of using the VBS framework is that as VBS is a generalization of several uncertainty theories (e.g., probability theory, a version of possibility theory where combination is the product t -norm, Spohn's epistemic belief theory, and Dempster–Shafer belief function theory), CCMs, initially described in probability theory, are now described in all uncertainty calculi that fit in the VBS framework. We describe conditioning and interventions in CCMs. Another advantage of using CCMs in the VBS framework is that both conditioning and intervention can be easily described in an elegant and unifying algebraic way for the same CCM without having to do any graphical manipulations of the causal network. We describe how conditioning and intervention can be computed for a simple example with a hidden (unobservable) variable. Also, we illustrate the algebraic results using numerical examples in some of the specific uncertainty calculi mentioned above. • We show that Pearl's causal networks can be described using causal compositional models in the valuation-based systems. • We introduce a novel notion of dominance that is necessary to describe the composition of valuations. • We present an algebraic example of hidden variables elimination in the VBS framework. • We provide numerical examples in probability, possibility, and Spohn's theories.

Uncertainty quantification based on pillars of experiment, theory, and computation. Part II: Theory and computation

This paper deals with theoretical and computational aspects of different uncertainty calculi, introduced in Part I, specifically when the data is bounded by any of the following five figures: triangle; rectangle; parallelogram; ellipse or super ellipse. We consider elastic structures subjected to uncertainty, and evaluate the least favorable, maximum response and the most favorable, minimum response. Comparison is conducted between the treated uncertainty calculi with preference given to the one which predicts the least estimate for the favorable response. In considered elastic structures the solution or displacements is available analytically; in cases when analytical solution is absent purely numerical solution ought to be implemented. Such a case is now under development and will be published elsewhere.

A Sociology of Management in Management Education

Treating the sociology of management in management education means first specifying then generalising the notion of management such that students begin to contextualize the complexity and contingency of management and understand the means of communication necessary to meet its expectations. The chapter looks at Erich Gutenberg's ingenious foundation of German Betriebswirtschaftslehre, which calls for economic efficiency and technological efficacy to rule an organisation turned into a Betrieb by bracketing (i.e., suspending) its nevertheless acknowledged complexity. If with respect to other organisations we drop reference to efficiency and efficacy, we come up with a generalised notion of management, understanding it as getting action by blocking action (Harrison C. White). We introduce an understanding of communication to explain the one in terms of the other, and conclude by drawing some consequences for management education, which revealingly begins and ends with students gaining a critical knowledge of themselves moving reflexively within different domains of communication and coming up with ideas about agencies legitimising action, games framing strategies, references owing to systems differentiation and a calculus of uncertainty gained by observing networks.

Compositional models in valuation-based systems

Compositional models were initially described for discrete probability theory, and later extended for possibility theory and for belief functions in Dempster–Shafer (D–S) theory of evidence. Valuation-based system (VBS) is an unifying theoretical framework generalizing some of the well known and frequently used uncertainty calculi. This generalization enables us to not only highlight the most important theoretical properties necessary for efficient inference (analogous to Bayesian inference in the framework of Bayesian network), but also to design efficient computational procedures. Some of the specific calculi covered by VBS are probability theory, a version of possibility theory where combination is the product t-norm, Spohn’s epistemic belief theory, and D–S belief function theory. In this paper, we describe compositional models in the general framework of VBS using the semantics of no-double counting, which is central to the VBS framework. Also, we show that conditioning can be expressed using the composition operator. We define a special case of compositional models called decomposable models, again in the VBS framework, and demonstrate that for the class of decomposable compositional models, conditioning can be done using local computation. As all results are obtained for the VBS framework, they hold in all calculi that fit in the VBS framework. For the D–S theory of belief functions, the compositional model defined here differs from the one studied by Jiroušek, Vejnarová, and Daniel. The latter model can also be described in the VBS framework, but with a combination operator that is different from Dempster’s rule of combination. For the version of possibility theory in which combination is the product t-norm, the compositional model defined here reduces to the one studied by Vejnarová.

The uncertain reasoner: Bayes, logic, and rationality

AbstractHuman cognition requires coping with a complex and uncertain world. This suggests that dealing with uncertainty may be the central challenge for human reasoning. InBayesian Rationalitywe argue that probability theory, the calculus of uncertainty, is the right framework in which to understand everyday reasoning. We also argue that probability theory explains behavior, even on experimental tasks that have been designed to probe people's logical reasoning abilities. Most commentators agree on the centrality of uncertainty; some suggest that there is a residual role for logic in understanding reasoning; and others put forward alternative formalisms for uncertain reasoning, or raise specific technical, methodological, or empirical challenges. In responding to these points, we aim to clarify the scope and limits of probability and logic in cognitive science; explore the meaning of the “rational” explanation of cognition; and re-evaluate the empirical case for Bayesian rationality.

Formal Models for Real People

( 1 ) Experiments with reasoning tasks, such as the famous Wason selection task (Wason 1968), show that logical form is not a determinant of reasoning (2) Logic cannot deal with vagueness and prototypicality (3) Logic cannot deal with uncertainty and must be replaced by probability theory, which is after all the calculus of uncertainty (4) What we know about the neocortex suggests that the computations executed by the brain are very different from logical computations (5) The computational complexity of logic is too high for logic to be a realistic model of cognition

Validated Uncertainty Evaluation for Self-Validating Sensor

This paper evaluates the validated uncertainty in SEVA sensor by integrating fault detection, identification and reconstruction (FDIR) and reliability engineering. The impact of each fault mode on measurement quality is evaluated quantitatively by using a priori sensor reliability information to investigate the impact of incomplete fault coverage, FDIR and manual maintenance intervention. Bayesian probabilistic approach and uncertainty calculus are employed to model the impact of sensor validation on parameter uncertainty and to fuse the individual modes into a complete sensor model. A simulation of SEVA pressure sensor example illustrates the concept and conclusions.

Two coupling media method for ultrasonic velocity measurement in biological tissues

Measuring the ultrasonic velocity in soft materials, especially in biological tissues, is never easy. One of the main problems is that the thickness of the sample in test is badly defined. From time-of-flight measurement method uncertainties in the thickness induce important uncertainties in experimental results. This causes that the ultrasonic velocity is often a poor criteria whereas it could be a good one. This paper brings a new method to measure the ultrasonic velocity in soft materials without knowing the sample thickness The main idea of this method is to use two different coupling media for making two relative time-of-flight measurements. The comparison of these two measurements gives the ultrasonic velocity in the sample in test. Furthermore, this comparison can give the local sample thickness of the sample. The uncertainty calculi show up that the effect on the thickness uncertainties is drastically reduced by using this new ultrasound method. This method is validated on reference samples, in silicon. Before concluding, some experimental results obtained with mouse skin samples are presented.

A New Uncertainty Calculus For Rule-Based Expert Systems

The solution of non-deterministic expert systems consists of two components –the solution reached and a calculated measure of belief in each solution. This measure of belief is often the most critical factor in analyzing the solution. Unfortunately, as this paper reviews, the issue of how best to implement uncertainty calculi in expert systems has never been settled. Some popular rulebased approaches have in fact been shown to produce results no better than random guessing. To improve the accuracy of rule-based systems, we propose a new calculus we call gamma factors. This calculus combines ideas from two popular certainty factor calculi the product method, and the probability sum method. It includes a tuning mechanism which the expert can use in a rule pre-processing step to compensate for dependent parallel evidence combination.

Choquet weak convergence of capacity functionals of random sets

The results in this paper are about the convergence of capacity functionals of random sets. The motivation stems from asymptotic aspects in inference and decision-making with coarse data in biostatistics, set-valued observations, as well as connections between random sets with several emerging uncertainty calculi in intelligent systems such as fuzziness, belief functions and possibility theory. Specifically, we study the counter-part of Billingsley’s Portmanteau Theorem for weak convergence of probability measures, namely, convergence of capacity functionals of random sets in terms of Choquet integrals.

Comment: Expert Elicitation for Reliable System Design

1. It addresses the importance of expert elicitation in systems design and the statistical and practical chal lenges faced when trying to use expert judgements in a way that is consistent with established ap proaches based on statistical reliability testing. 2. It rightly focuses our attention on the need for a holistic approach to reliability evaluation that goes beyond analysis of single projects to also include in formation from softer sources such as design and operational use. 3. It recognizes the emerging importance of Bayesian methods in providing the uncertainty calculus to combine evidence from experts with statistical re liability data in such a way that system reliability assessments and forecasts can grow and evolve as a system changes throughout its life.

Factors contributing to the uncertainty in circumaural earphone calibration for audiometric testing

This paper describes important factors that need to be considered when determining the uncertainty in the calibration of the HDA200 circumaural earphones which are used in audiometric and psychoacoustic tests. This paper describes the instruments that were used, the procedures and the results of the measurements. Each of these measurements generated an uncertainty component and the final calculus of the total uncertainty was computed using standard procedures. This paper highlights the necessity for researches on the contribution that the artificial ears have on the uncertainty and establishes a calibration method.

Categorial expert systems

Abstract: Expert systems can be used to determine some objects or consequences from uncertain knowledge by hierarchical categorization. Categorical representation is psychologically motivated and also offers an explanation of how to deal with uncertain knowledge based on counting during approximate reasoning. It is an alternative to other well‐known uncertainty calculi. A knowledge base which is used during approximate reasoning is represented by a taxonomical arrangement of verbal categories. Priming eases the formation of the final hypothesis, as more exact possible hypotheses are formed. The approximate reasoning is demonstrated on an expert system ‘Jurassic’ from the field of paleontology for the determination of a dinosaur species. It helps the paleontologist to determine creatures from uncertain knowledge. The system is composed of 423 rules arranged in a directed acyclic graph with a depth of 5. This knowledge is represented by a taxonomical arrangement of verbal categories represented by associative memories.

Managing uncertainty in diagnosis of acute coronaric ischemia

The paper presents the reasoning mechanism of COR, a knowledge-based system (KBS) able to provide support for the diagnosis of coronaric ischemia by integrating the interpretation of chest pain, 12-lead ECG, and bio-marker concentrations. Chest pain features are collected interactively through a questionnaire. The ECG signal is acquired in SCP format. Any set of bio-markers can be considered. Data input is incremental and possibly incomplete. Reasoning is based on revised uncertainty calculus, which allows a formal treatment of verbally expressed uncertainty concerning both input data and diagnostic rules. Each diagnosis is supplemented by a linguistic label, expressing the plausibility of the disease identified, given the symptoms observed.

A comparison of three uncertainty calculi for building sonar-based occupancy grids

In this paper, we describe and compare three different uncertainty calculi techniques to build occupancy grids of an unknown environment using sensory information provided by a ring of ultrasonic range-finders. These techniques are based on Bayesian theory, Dempster–Shafer theory of evidence, and fuzzy set theory. Several sensor models are presented to handle uncertainty according to the selected building procedure. Experimental examples of occupancy grids, built from real data recorded by two different mobile robots in office-like environment, are presented to perform a comparison among the proposed calculi techniques. Probabilistic and evidence theoretic methods are more accurate in structured environments, while in cases of multiple reflections only the possibilistic approach provides correct results.

Homogeneity and stability of reference materials

Homogeneity and stability are two crucial characteristics of any certified reference material (CRM). Utmost care must be taken during preparation to create materials as homogeneous and stable as possible. Degradation can generally be minimised by reducing the water activity of the material to a level between 0.15 and 0.35. However, careful preparation by itself is not enough. Positive demonstration of homogeneity and stability is required from the perspective of implementing uncertainty calculus according to the Guide to the Expression of Uncertainty in Measurement (GUM). In many cases, homogeneity and stability studies fail to give sufficient quantitative information on homogeneity and stability, mainly because of a lack of measurement repeatability and insufficient number of replicates. In this work, some solutions to these problems and their implications are presented.