Allowable uncertainty

Any analytical method inherently carries with it limitations in terms of speed, allowable uncertainty (as MDL), and specificity. These characteristics of a method (or analytical technique) determine where and how the method can be used. Table 71-1 shows a method to relate purpose of analytical method to the speed of analysis and error types permitted. 

Table 71-1 Characteristics and allowable uncertainty for different analytical methods...

A widely used example is not to take into account the uncertainty when deciding upon compliance. But in this case it necessary to specify a maximum allowed uncertainty. Otherwise the risk of making a wrong decision is unknown. 

If the maximum allowed uncertainty is U and the variance of the population is s2, which includes the variances of all steps of the analytical process from sampling to analysis, the sample size n is given very simply and pragmatically by ... 

Ihe treatment of uncertainty varies considerably from one model to another. Simpler models allow uncertainty in the input data to be treated through the use of alternative estimates of uncertain variables. For example, in the next section of this paper, uncertainty about the length of utility coal plant lifetimes is addressed by comparing results of two assumptions about the lifetime — 60 years and 40 years. In that way, ranges of emission estimates are obtained that, it is hoped, provide reasonable upper and lower bounds on emissions. More sophisticated models allow users to specify percentage ranges of uncertainty for input data the model then incorporates these uncertainty estimates into upper and lower bounds on estimated emissions. The Electric Power Research Institute has sponsored a number of such models (IQ.). 

Probabilistic analysis Calculations and expression of health risks using multiple-risk descriptors to provide the likelihood of various risk levels. Probabilistic risk results approximate a full range of possible ontcomes and the likelihood of each, which is often presented as a freqnency distribntion graph, thns allowing uncertainty or variability to be expressed quantitatively (USEPA, 1999). 

An appealing property of Boolean networks is that they are inherently simple but emphasize generic network behavior. Nevertheless, the coarse abstraction to two possible activity values of genes and the synchronous state update are strong assumptions that may not always be justified. Various extensions of Boolean networks have been proposed to cope with these limitations. The formalism of generalized logical networks [Thomas and d Ari 1990] allows variables to have more than two values and transitions between states to occur asynchronously, whereas probabilistic Boolean networks allow uncertainty in the data and permit interactions between genes to be quantified [Shmulevich et al. 2002]. 

The volume analyzed for each individual sample is a tightly controlled variable. Although the four-liter marlnelli beakers (a water containing volume having a center cavity which will house the photon detector) used in the analysis are currently filled to a specified height (14.1 cm), the allowed variation does not (by protocol) exceed 0.2 cm. For chemically pure water specimens, this translates to a maximum allowable difference of 1.4 percent by volume. This maximum allowable uncertainty has been used for the final estimation of the relative systematic uncertainty in the volume term of the activity or LLD equation. 

In the past 20 to 30 years the use of probabilistic concepts has allowed uncertainties in the size, location and rate of recurrence of earthquakes and in the variation of ground motion characteristics with earthquake size and location to be explicitly considered in the evaluation of seismic hazards. Probabilistic seismic hazard analysis (PSHA) provides aframe-work in which these uncertainties can be identified, quantified, and combined in a rational mannerto provide amore complete picture of seismic hazard. The proper performance of a PSHA requires careful attention to the problems of source characterization and ground motion parameter prediction and to the mechanics of the probability computations. 

A major difference between ODE s and SDE s is the inclusion of a stochastic term in the latter, which allows uncertainty to be accomodated, and which, if the constitutive equations of interest are reformulated as additional state equations, allows estimates of the corresponding state variables to be computed from the experimental data. The specific approach used for this purpose involves parameter estimation and subsequent state estimation by means of methods based on the extended Kalman filter (EKF). 

This result shows that the deviations have been of the order of the allowed uncertainties of the forces. 

---