Uncertainty interpreting

Increased trust in pattern recognition The active user involvement in the data mining process can lead to a deeper understanding of the data and increases the trust in the resulting patterns. In contrast, "black box" systems often lead to a higher uncertainty, because the user usually does not know, in detail, what happened during the data analysis process. This may lead to a more difficult data interpretation and/or model prediction. 

How to extract from E(qj,t) knowledge about momenta is treated below in Sec. III. A, where the structure of quantum mechanics, the use of operators and wavefunctions to make predictions and interpretations about experimental measurements, and the origin of uncertainty relations such as the well known Heisenberg uncertainty condition dealing with measurements of coordinates and momenta are also treated. 

Accuracy and Interpretation of Measured pH Values. The acidity function which is the experimental basis for the assignment of pH, is reproducible within about 0.003 pH unit from 10 to 40°C. If the ionic strength is known, the assignment of numerical values to the activity coefficient of chloride ion does not add to the uncertainty. However, errors in the standard potential of the cell, in the composition of the buffer materials, and ia the preparatioa of the solutioas may raise the uacertaiaty to 0.005 pH unit. 

Third, any analysis must recognize that the measurements have significant uncertainty, random and systematic. These affect any conclusions drawn and models developed. Multiple interpretations of the same set of measurements, describing them equally well, can lead to markedly different conclusions and, more significantly, extrapolations. 

This is a formidable analysis problem. The number and impact of uncertainties makes normal pant-performance analysis difficult. Despite their limitations, however, the measurements must be used to understand the internal process. The measurements have hmited quahty, and they are sparse, suboptimal, and biased. The statistical distributions are unknown. Treatment methods may add bias to the conclusions. The result is the potential for many interpretations to describe the measurements equaUv well. 

Motivation Unit tests require a substantial investment in time and resources to complete successfully. This is the case whether the test is a straightforward analysis of pump performance or a complex analysis of an integrated reactor and separation train. The uncertainties in the measurements, the likelihood that different underlying problems lead to the same symptoms, and the multiple interpretations of unit performance are barriers against accurate understanding of the unit operation. The goal of any unit test should be to maximize the success (i.e., to describe accurately unit performance) while minimizing the resources necessary to arrive at the description and the subsequent recommendations. The number of measurements and the number of trials should be selected so that they are minimized. 

Measurement Error Uncertainty in the interpretation of unit performance results from statistical errors in the measurements, low levels of process understanding, and differences in unit and modeled performance (Frey, H.C., and E. Rubin, Evaluate Uncertainties in Advanced Process Technologies, Chemical Engineering Progress, May 1992, 63-70). It is difficult to determine which measurements will provide the most insight into unit performance. A necessary first step is the understanding of the measurement errors hkely to be encountered. 

An example adapted from Verneuil, et al. (Verneuil, V.S., P. Yan, and F. Madron, Banish Bad Plant Data, Chemical Engineeiing Progress, October 1992, 45-51) shows the impact of flow measurement error on misinterpretation of the unit operation. The success in interpreting and ultimately improving unit performance depends upon the uncertainty in the measurements. In Fig. 30-14, the materi balance constraint would indicate that S3 = —7, which is unrealistic. However, accounting for the uncertainties in both Si and S9 shows that the value for S3 is —7 28. Without considering uncertainties in the measurements, analysts might conclude that the flows or model contain bias (systematic) error. 

Analysts should review the technical basis for uncertainties in the measurements. They should develop judgments for the uncertainties based on the plant experience and statistical interpretation of plant measurements. The most difficult aspect of establishing the measurement errors is estabhshing that the measurements are representative of what they purport to oe. Internal reactor CSTR conditions are rarely the same as the effluent flow. Thermocouples in catalyst beds may be representative of near-waU instead of bulk conditions. Heat leakage around thermowells results in lower than actual temperature measurements. 

The goal of measurement selection is to identify a set of measurements that, when interpreted, will lead to unique values for the model parameters, insensitive to uncertainties in the measurements. This is an iterative process where ... 

QRA is fundamentally different from many other chemical engineering activities (e.g., chemistry, heat transfer, reaction kinetics) whose basic property data are theoretically deterministic. For example, the physical properties of a substance for a specific application can often be established experimentally. But some of the basic property data used to calculate risk estimates are probabilistic variables with no fixed values. Some of the key elements of risk, such as the statistically expected frequency of an accident and the statistically expected consequences of exposure to a toxic gas, must be determined using these probabilistic variables. QRA is an approach for estimating the risk of chemical operations using the probabilistic information. And it is a fundamentally different approach from those used in many other engineering activities because interpreting the results of a QRA requires an increased sensitivity to uncertainties that arise primarily from the probabilistic character of the data. 

The work required to evaluate risk results will be a function of the objectives of the study. For relative risk studies, this evaluation is usually not very time-consuming. For absolute risk studies, in which many uncertainty and sensitivity cases may have been produced, the risk evaluation step may account for to 35% of the total effort of a large-scale QRA. Chapter 4 discusses the problems associated with interpreting risk results. 

When managers are faced with the necessity of using QRA results on an absolute basis, they must respect the potentially large uncertainties associated with the numbers and use prudent and conservative interpretations of these results for their decisions. Absolute risk estimates in... 

Although extremelv useful, tracer experiments require considerable capital expenditures and personnel. In addition to the difficulties and uncertainty in making estimates of various parameters, especially cr, one of the fficulties in interpreting tracer studies is relating the atmospheric conditions under which the study was conducted to the entire spectrum of atmospheric conditions. For example, trying to interpret a series of tracer... 

Assists in planning disposal systems for community waste. The model accepts appropriate inputs describing the community s situation and constraints, performs cost analyses for various scenarios to account for uncertainties in the input, and provides the system with heuristic indicators which describe the results. Interprets the results and provides advice on planning scenarios to be used as guidelines for making a study of appropriate alternative scenarios. 

As Tribus, 1969, says, all probabilities are conditional. In the example of the dree, the probabilities are conditioned on the assumption that the dice are perfect and the method of throwing has no effect on the outcome. Some writers (e.g., deMorgan, 1847) say, probability refers to the belief by a mind having uncertain knowledge. This is the interpretation of probability in the Zion-Indian Point (ZIP) and some other PSAs. IVobabiiity in this sense attempts to include all information e.g., QA that could affect the performance of a piece of equipment. Such information may be conveyed as a distribution whose height is proportional to confidence in the belief and who.se width reflects uncertainty (refer to Section 2.6). 

Virolainen, R 1984, On Common Cause Failures Statistical Dependence and Calculation of Uncertainty Disagreement in Interpretations of Data, Nuc. Eng. and E 77 pp 103-108. 

The interpretation of these remarkable properties has excited considerable interest whilst there is still some uncertainty as to detail, it is now generally agreed that in dilute solution the alkali metals ionize to give a cation M+ and a quasi-free electron which is distributed over a cavity in the solvent of radius 300-340 pm formed by displacement of 2-3 NH3 molecules. This species has a broad absorption band extending into the infrared with a maximum at 1500nm and it is the short wavelength tail of this band which gives rise to the deep-blue colour of the solutions. The cavity model also interprets the fact that dissolution occurs with considerable expansion of volume so that the solutions have densities that are appreciably lower than that of liquid ammonia itself. The variation of properties with concentration can best be explained in terms of three equilibria between five solute species M, M2, M+, M and e ... 

VSEPR model, the dihalides of Be and Mg and the heavier halides of Ca and Sr are essentially linear. However, the other dihalides are appreciably bent, e.g. Cap2 145°, Srp2 -- 120°, Bap2 108° SrCl2 - 130°, BaCh - 115° BaBri -115° Bah 105°. The uncertainties on these bond angles are often quite large ( 10°) and the molecules are rather flexible, but there seems little doubt that the equilibrium geometry is substantially non-linear. This has been interpreted in terms of sd (rather than sp) hybridization or by a suitable id hoc modification of the VSEPR theory. ... 

The interpretation of the square of the wave function as a probability distribution, the Heisenberg uncertainty principle and the possibility of tunnelling. 

We shall see, in Section 5, that these expectations are broadly fulfilled by the history—though they are overlaid not only with the usual uncertainties about interpreting historical data, but also with a number of interesting complications which differentiate this case from other cases (taken almost exclusively from physics) that have been analysed in this regard. 

It is apparent, from the above short survey, that kinetic studies have been restricted to the decomposition of a relatively few coordination compounds and some are largely qualitative or semi-quantitative in character. Estimations of thermal stabilities, or sometimes the relative stabilities within sequences of related salts, are often made for consideration within a wider context of the structures and/or properties of coordination compounds. However, it cannot be expected that the uncritical acceptance of such parameters as the decomposition temperature, the activation energy, and/or the reaction enthalpy will necessarily give information of fundamental significance. There is always uncertainty in the reliability of kinetic information obtained from non-isothermal measurements. Concepts derived from studies of homogeneous reactions of coordination compounds have often been transferred, sometimes without examination of possible implications, to the interpretation of heterogeneous behaviour. Important characteristic features of heterogeneous rate processes, such as the influence of defects and other types of imperfection, have not been accorded sufficient attention. 

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