Predictive models error analysis

The quantity J is identical to J of Eq. (52) in 3DVAR, except that the analysis field at r = 0 is denoted by Xo. Because all observations during r = 0 to t are used, the constraint is expressed as the integral form of J2 of Eq. (53) with respect to time. The observational error co-variance matrix O depends on time t. The quantity J3 can be interpreted in the same way as J, exeept that the prediction model errors are involved instead of the observational errors. The quantity P in Eq. (58) denotes a covariance matrix that deseribes predietion error statistics. 

In addition, the chapter will provide an overview of htunan reliability quantification techniques, and the relationship between these techniques and qualitative modeling. The chapter will also describe how human reliability is integrated into chemical process quantitative risk assessment (CPQRA). Both qualitative and quantitative techniques will be integrated within a framework called SPEAR (System for Predictive Error Analysis and Reduction). 

First-order error analysis is a method for propagating uncertainty in the random parameters of a model into the model predictions using a fixed-form equation. This method is not a simulation like Monte Carlo but uses statistical theory to develop an equation that can easily be solved on a calculator. The method works well for linear models, but the accuracy of the method decreases as the model becomes more nonlinear. As a general rule, linear models that can be written down on a piece of paper work well with Ist-order error analysis. Complicated models that consist of a large number of pieced equations (like large exposure models) cannot be evaluated using Ist-order analysis. To use the technique, each partial differential equation of each random parameter with respect to the model must be solvable. 

Error Analysis and Quantification of Uncertainty. The error associated with paleolimnological inferences must be understood. Two sources of error worthy of special attention are the predictive models (transfer functions) developed to infer chemistry and inferences generated by using those equations with fossil samples in sediment strata. Much of the following discussion is based on the pioneering work reviewed by Sachs et al. (35) and by Birks et al. (17, 22), among others. We emphasize error analysis here because it is not covered in detail in most of the general review articles cited earlier. 

Various issues in the development of a flow model and its numerical simulation have been already discussed in the previous section. It will be useful to make a few comments on the validation of the simulated results and their use in reactor engineering. More details are discussed in Part III and Part IV. Even before validation, it is necessary to carry out a systematic error analysis of the generated computer simulations. The influence of numerical issues on the predicted results and errors in integral balances must be checked to ensure that they are within the acceptable tolerances. The simulated results must be examined and analyzed using the available post-processing tools. The results must be checked to verify whether the model has captured the major qualitative features of the flow such as shear layers and trailing vortices. 

O Neill, R.V. 1979. Natural variability as a source of error in model predictions. In Systems Analysis of Ecosystems, G.W. Innis and R.V. O Neill, Eds. International Cooperative Publishing, Burtonsville, MD. pp. 23-32. 

The core of model population analysis is statistical analysis of an interesting output, e.g. prediction errors or regression coefficients, of all these sub-models. Indeed, it is difficult to give a clear answer on what output should be analyzed and how the analysis should be done. Different designs for the analysis will lead to different algorithms. As proof-of-principle, it was shown in our previous work that the analysis of the distribution of prediction errors is effective in outlier detection [13],... 

The technique for human error-rate prediction (THERP) [ Swain and Guttmann, 1980] is a widely applied human reliability method (Meister, 1984] used to predict human error rates (i.e., probabilities) and the consequences of human errors. The method relies on conducting a task analysis. Estimates of the likelihood of human errors and the likelihood that errors will be undetected are assigned to tasks from available human performance databases and expert judgments. The consequences of uncorrected errors are estimated from models of the system. An event tree is used to track and assign conditional probabilities of error throughout a sequence of activities. 

Table 5.2 Error analysis for various model predictions...

When building any sort of predictive model, it is important to carry out the type of analysis outlined earlier in order to account for experimental error. Any predictive models that perform better than the theoretical limit should be viewed with extrone skepticism. 

One of the biggest problems in using PCA spectral decomposition for discriminant analysis is identifying the correct number of factors to use for the models. In the case of quantitative analysis methods, there is always a set of secondary benchmarks to compare the quality of the model the primary calibration data. By performing a prediction residual error sum of squares (PRESS) analysis, it is very easy to determine the number of factors by calculating the prediction error of the constituent values at every factor. The smaller the error, the better the model. 

CREAM Cognitive reliability and error analysis method. In CREAM, the operator model is more significant and less simplistic than that of first generation approaches. It can be used both for performance prediction as well as accident analysis. CREAM is used for evaluation of the probability of a human error for completion of a specific task. There is good application of fuzzy logic in this method. It was again started for nuclear application but has wider applications, too. 

An experimental approach for the prediction of thrust force produced by a step drill using linear regression analysis and RBFN has been proposed. In the confirmation tests, RBFN (errors within 0.3 per cent) has been shown to be a better predictive model than multi-variable linear regression analysis (errors within 28 per cent) (Tsao, 2008). 

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