Level of confidence

Resource estimates are divided into separate categories reflecting different levels of confidence in the quantities reported, and further separated into categories based on the cost of production. A listing of uranium resources by country is given in Table 3. 

Often the goal of a data analysis problem requites more than simple classification of samples into known categories. It is very often desirable to have a means to detect oudiers and to derive an estimate of the level of confidence in a classification result. These ate things that go beyond sttictiy nonparametric pattern recognition procedures. Also of interest is the abiUty to empirically model each category so that it is possible to make quantitative correlations and predictions with external continuous properties. As a result, a modeling and classification method called SIMCA has been developed to provide these capabihties (29—31). 

Extended Plant-Performance Triangle The historical representation of plant-performance analysis in Fig. 30-1 misses one of the principal a ects identification. Identification establishes troubleshooting hypotheses and measurements that will support the level of confidence required in the resultant model (i.e., which measurements will be most beneficial). Unfortunately, the relative impact of the measurements on the desired end use of the analysis is frequently overlooked. The most important technical step in the analysis procedures is to identify which measurements should be made. This is one of the roles of the plant-performance engineer. Figure 30-3 includes identification in the plant-performance triangle. 

With one global scheme, disparities between the various schemes employed at a national level should be eliminated. This will give a vehicle manufacturer in one country procuring product from another country the same level of confidence as would be obtained had the product been procured from the home country. This will be achieved by ... 

These assessments do not need to be carried out on the subcontractor s premises. Much of the data needed can be accumulated from a subcontractor questionnaire and searches through directories and registers of companies, and you can choose to rely on assessments carried out by accredited third parties to provide the necessary level of confidence. (The Directories of Companies of Assessed Capability that are maintained by the Accreditation Agencies can be a good place to start.) The assessments may yield subcontractors over a wide range and you may find it beneficial to classify subcontractors as follows ... 

Within your procedures you need to provide a means of identifying which items have been subject to inspection at the subcontractor s premises and the receipt inspection action to be taken depending on the level of that inspection. In one case, the product may have been accepted by your representative on the subcontractor s premises. In another case, a product from the same batch may have been accepted by your representative but not the one that has been delivered. Alternatively your representative may have only performed a quality audit to gain a level of confidence. You need to specify the inspection to be carried out in all such cases. The standard emphasizes that consideration should also be given to the recorded evidence provided. Even if someone has performed inspection at the subcontractor s premises, if there is no evidence of conformance the inspections are of little value. The fact that an inspection was carried out is insufficient. There has to be a statement of what was checked and what results were obtained and a decision as to whether conformance has been achieved. Without such evidence you may need to repeat some of the inspections carried out on the subcontractor s premises. 

Plant-specific data are frequently unavailable or are low in their level of confidence. Further, this source of data cannot provide information on equipment not in use at the plant, nor can it do more than suggest how plant equipment might behave under different circumstances. Since data collection is very difficult, using shared or generic data is one way of resolving these problems without the expense of extensive data collection systems. 

When using failure rate data for a CPQRA, the ideal situation is to have valid historical data from the identical equipment in the same application. In most cases, plant-specific data are unavailable or may carry a level of confidence that is too low to allow those data to be used without corroborating data. Risk analysts often overcome these problems by using generic failure rate data as surrogates for or supplements to plant-specific data. Because of the uncertainties inherent in risk analysis methodology, generic failure rate data are frequently adequate to identify the major risk contributors in a process or plant. 

It should be noted that data were not rejected through consideration of upper or lower bounds. These limits for the input data included a variety of assumed and calculated limits using various levels of confidence. 

There are several limitations to tliis approach that must be acknowledged. As mentioned earlier, tlie level of concern does not increase linearly as the reference dose is approached or exceeded because the RfDs do not luive equal accuracy or precision and are not based on the same severity of effects. Moreover, luizm-d quotients are combined for substances with RfDs based on critical effects of vaiy ing toxicological significance. Also, it will often be the case that RfDs of varying levels of confidence Uiat include different uncertainty adjustments and modifying factors will be combined (c.g., extrapolation from animals to hmnans, from LOAELs to NOAELs, or from one exposure duration to anoUier). 

Upon formulating these relationships, phenols with branched alkyl substituents were not included in the data of a-cyclodextrin systems, though they were included in (3-cyclodextrin systems. In all the above equations, the n term was statistically significant at the 99.5 % level of confidence, indicating that the hydrophobic interaction plays a decisive role in the complexation of cyclodextrin with phenols. The Ibrnch term was statistically significant at the 99.5% level of confidence for (3-cyclo-dextrin complexes with m- and p-substituted phenols. The stability of the complexes increases with an increasing number of branches in substituents. This was ascribed to the attractive van der Waals interaction due to the close fitness of the branched substituents to the (3-cyclodextrin cavity. The steric effect of substituents was also observed for a-cyclodextrin complexes with p-substituted phenols (Eq. 22). In this case, the B parameter was used in place of Ibmch, since no phenol with a branched... 

In fact, a measure of the degree of confidence can be gained from the t calculation. Shown in Appendix A are columns for greater degrees of confidence. The value for df = 4 for a 98% confidence level is 3.747 and it can be seen that the experimentally calculated value is also greater than this value. Therefore, the level of confidence that these samples came from different populations is raised to 98%. However, the level of confidence in believing that these two samples came from separate populations does not extend to 99% (t = 4.604). Therefore, at the 98% confidence level this analysis indicates that the potency of human calcitonin is effectively increased by enrichment of G -protein in the cell. 

As can be seen from the analysis in Table 11.3, the paired t-test indicates that the effect of AC512 on the constitutive activity is significant at the 99% level of confidence (p<0.01 and AC512 is an inverse agonist and does decrease the constitutive receptor activity of calcitonin receptors). 

This value is identified in F tables for the corresponding dfc and dfs. For example, for the data in Figure 11.13, F = 7.26 for df=6, 10. To be significant at the 95% level of confidence (5% chance that this F actually is not significant), the value of F for df = 6, 10 needs to be > 4.06. In this case, since F is greater than this value there is statistical validation for usage of the most complex model. The data should then be fit to a four-parameter logistic function to yield a dose-response curve. 

The function of the analyst is to obtain a result as near to the true value as possible by the correct application of the analytical procedure employed. The level of confidence that the analyst may enjoy in his results will be very small unless he has knowledge of the accuracy and precision of the method used as well as being aware of the sources of error which may be introduced. Quantitative analysis is not simply a case of taking a sample, carrying out a single determination and then claiming that the value obtained is irrefutable. It also requires a sound knowledge of the chemistry involved, of the possibilities of interferences from other ions, elements and compounds as well as of the statistical distribution of values. The purpose of this chapter is to explain some of the terms employed and to outline the statistical procedures which may be applied to the analytical results. 

Student s f-test. This is a test1 used for small samples its purpose is to compare the mean from a sample with some standard value and to express some level of confidence in the significance of the comparison. It is also used to test the difference between the means of two sets of data x, and x2. 

Sometimes it is just not feasible to assemble any validation samples. In such cases there are still other tests, such as cross-validation, which can help us do a certain amount of validation of a calibration. However, these tests do not provide the level of information nor the level of confidence that we should have before placing a calibration into service. More about this later. 

Ocean-Atmosphere Interactions. To determine how the ocean responds to a C02-induced climate forcing, it will be necessary to develop a combined ocean and atmospheric general circulation model. It will take 10-20 years to develop a model with appropriate chemistry and biology to the level of confidence necessary to make valid projections. In the interim, two approaches can be pursued in parallel with this model development. 

On the other hand, users must be involved in the whole process of EDSS design and development to ensure the usability of the final system. The degree to which users become involved in EDSS development will determine their level of confidence in the final system. In the worst case, the system might remain unused. 

In all analyses, there is uncertainty about the accuracy of the results that may be dealt with via sensitivity analyses [1, 2]. In these analyses, one essentially asks the question What if These allow one to vary key values over clinically feasible ranges to determine whether the decision remains the same, that is, if the strategy initially found to be cost-effective remains the dominant strategy. By performing sensitivity analyses, one can increase the level of confidence in the conclusions. Sensitivity analyses also allow one to determine threshold values for these key parameters at which the decision would change. For example, in the previous example of a Bayesian evaluation embedded in a decision-analytic model of pancreatic cancer, a sensitivity analysis (Fig. 24.6) was conducted to evaluate the relationship... 

Confirmation of identity of nitrosamines via an independent detection system is desirable since a higher level of confidence is achieved if a different physical property or structural characteristic is measured. Mass spectrometry (MS) has been used... 

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