Expressing uncertainty

The most informative method of expressing uncertainty in HCIIP or ultimate recovery (UR) is by use of the expectation curve, as introduced in Section 6.2. The high (H) medium (M) and low (L) values can be read from the expectation curve. A mathematical representation of the uncertainty n a parameter (e.g. STOMP) can be defined as... 

Considering the different uses of RMs in the estimation of uncertainty would mean that more routine results overlap the certified value, but it would also make the certified values given by some agencies less usefiil for the broad user community. So there needs to be a better way of expressing uncertainty, possibly by showing the existing uncertainty and a wider total uncertainty. 

Specify the number of inner and outer loop simulations for the 2nd-order Monte Carlo analysis. In the 1st outer loop simulation, values for the parameters with uncertainty (either constants or random variables) are randomly selected from the outer loop distributions. These values are then used to specify the inner loop constants and random variable distributions. The analysis then proceeds for the number of simulations specified by the analyst for the inner loop. This is analogous to a Ist-order Monte Carlo analysis. The analysis then proceeds to the 2nd outer loop simulation and the process is repeated. When the number of outer loop simulations reaches the value specified by the analyst, the analysis is complete. The result is a distribution of distributions, a meta-distribution that expresses uncertainty both from uncertainty and from variability (Figure 7.1). 

In contrast, both expressed uncertainty in predicting packing efficiency. Harrison presented two case studies In one, adding water to two water-insoluble organics had no effect on HETP in another, a key... 

The concept of measurement uncertainty has been recognized by chemists for many years, and general rules for evaluating and expressing uncertainty in analytical measurement have been formulated in the international guide [5] based on practical experience. The uncertainty estimation, according to the guide, consists of four steps ... 

Bayesian methods have often proved useful for design of experiments, especially in situations in which the optimal design depends on unknown quantities. Certainly, to identify a design for optimal estimation of /3, the correct subset of active effects must be identified. Bayesian approaches that express uncertainty about the correct subset enable construction of optimality criteria that account for this uncertainty. Such approaches typically find a design that optimizes a criterion which is averaged over many possible subsets. DuMouchel and Jones (1994) exploited this idea with a formulation in which some effects have uncertainty associated with whether they are active. Meyer et al. (1996) extended the prior distributions of Box and Meyer (1993) and constructed a model discrimination design criterion. The criterion is based on a Kullback-Leibler measure of dissimilarity between... 

As shown above, EU bureaucrats and policy-makers find these kinds of statements difficult to interpret, and committee members agree that it is extremely difficult to express uncertainty in a way that is both accurate and intelligible to laymen. In our view, it is usually difficult to discern any explicit recommendations for policy-making in SCHER s reports, although implicitly it might matter whether indications of risks are described in terms of, for example, possible risk or uncertain risk . Nevertheless, the Commission finds SCHER s opinions useful, as they are seen as legitimating Commission policy, even when the opinions explicitly state that no firm conclusions can be reached. The very existence of SCHER and the other scientific committees gives scientific credibility to Commission policy, whether or not the experts offer instrumental advice. This is a symbolic function (Amara et al. 2004 Beyer 1997) of expert committees that should not be underestimated. 

If an interviewee expressed uncertainty as to the validity of his/ her response, the data were omitted from the research findings. Information provided by the interviewees that was outside the scope of the study was excluded, for example ... 

The use of an asterisk ( ) at the oxygen atom expresses uncertainty as to whether this species is actually a radical-anion (addition of one electron) or a dianion addition of two electrons). See p. 199. 

The second classical theory of uncertainty—probability theory— expresses uncertainty in terms of a classical measure on subsets of a given universal set of alternatives. The measure is a function that, according to the situation, assigns a number in the unit interval [0,1] to each subset of the universal set. This number, called the probability of the subset,... 

Developing alternative techniques for expressing uncertainty in risk characterization... 

How does the criterion [insert placement criterion] express uncertainty in placement discussions and/or decisions ... 

Studies of informatics and clinical decision making concentrate on the benefits of using computerized decision support systems in clinical practice and in research to measure outcomes, efficiency, and effectiveness of care. Decision analysis in clinical research employs probability analysis to express uncertainty and utility theory to express patient preferences for health outcomes. 

I Apply rules for significant figures to express uncertainty in measured and calculated values. 

The GUM establishes general rules for expressing uncertainty in measurement that can be followed at various levels of accuracy and in many fields from the shop floor to fundamental research as reflected in the scope of the GUM. The quantity used to express uncertainty should be directly derivable from the components that contribute to it. In addition, it should be transferable, so the uncertainty evaluated for one result as a component could be applicable in evaluating the uncertainty of another measurement in which the first result was used. 

Expected duration, E[ f/], given as a function of the performance of implemented controls, can be applied in subsequent modelling of the losses from a loss event directly e.g. as a scaling factor of the loss severity of a loss event. In some cases however, we may be more interested in the probability distribution of duration, P(f/ < u), expressing uncertainty regarding the time... 

Still, a general guideline does not make the task simple. Each case is different and it is impossible to describe a detailed, universally appUcable method. Rather, a general framework is established where the details are left to the analysts and the experts involved. Thus it is crucial that they have the necessary competence within their fields. A bad judgment may have significant catastrophic consequences in terms of safely, environment or economy. The analyst must for instance know how to convert information to reliability and know how to express uncertainty. The system expert must be able to see the difference of the novel technology and similar qualified technology, identify possible failure modes and predict functionality. 

Kacker, R., Sommer, K.-D., and Kessel, R. (2007) Evolution of modern approaches to express uncertainty in measurement. Metrologia, 44, 513-529. 

To make measurement results comparable and interpretable, each result needs to be associated with a statement of uncertainty of the measurement result. Although this is commonplace, ways of how to express uncertainties (erroneously called errors ) are diverse, unclear, and often without proper statements on how the uncertainty budget was derived (see also [1]). It should be noted that through the definitions it is clear that whereas measurement uncertainty defines a range in which the true value should lie with a given confidence, measurement error is a difference between two values. 

Though the equivalent EN structures look the same for the two logic gates in Figure 1, the Conditional Belief Mass Tables (CBMTs) are different. The CBMTs for AND and OR logic gates are defined and shown respectively in Tables 1 and 2 in which AT means normal, F means failure and A, F means that the system is exclusively in one of the two conditions without distinguishing exactly which. This allows us to express uncertainties on the states of events in FTs. 

Leaf nodes in ENs represent basic events. The belief masses must be assigned in order to make the EN inference process work. Expert knowledge is used to define the probability of occurrence. Generally, there are two ways of expressing uncertainties to get the belief masses. 

Kaplan (1997) proposes the so-called probability of frequency approach to risk assessment, based on a risk concept in line with risk definition C6 (R = P C), where subjective probabilities are used to express uncertainty about true frequen-tist probabilities. The assessment thus focuses on quantifying uncertainty about an underlying true risk, which is estimated. Kaplan s view is strongly tied to realism, as the risk description focuses on a true risk as determined by experts. Closely related perspectives are those where uncertainty is quantified around a true risk, such as in the traditional Bayesian perspective where uncertainty is quantified in relation to model parameters (Aven Heide 2009). Such uncertainty quantification can also be done using non-probabilistic representations of epistemic uncertainty (Helton Johnson 2011). These methods typicdly consider a risk problem in a highly mathematized form. 

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