Cause-effect model

Bayesian statistics are applicable to analyzing uncertainty in all phases of a risk assessment. Bayesian or probabilistic induction provides a quantitative way to estimate the plausibility of a proposed causality model (Howson and Urbach 1989), including the causal (conceptual) models central to chemical risk assessment (Newman and Evans 2002). Bayesian inductive methods quantify the plausibility of a conceptual model based on existing data and can accommodate a process of data augmentation (or pooling) until sufficient belief (or disbelief) has been accumulated about the proposed cause-effect model. Once a plausible conceptual model is defined, Bayesian methods can quantify uncertainties in parameter estimation or model predictions (predictive inferences). Relevant methods can be found in numerous textbooks, e.g., Carlin and Louis (2000) and Gelman et al. (1997). 

EXAMPLES RELEVANT TO UNCERTAINTY IN RISK ASSESSMENT QUANTIFYING PLAUSIBILITY OF A CAUSE-EFFECT MODEL... 

Faidt tree models These logical cause-effect models trace the failures of the safety system functions considered in the event-trees back to basic events hke, for instance, the failures of system components. As result, they provide values for the unavailabiUties of the individual functions. 

The time-dependent evolution of the system and process dynamics in interaction with the stochastic failure behaviour of safety systems and hiunan actions is reduced to static cause-effect models which operate with fixed probabilistic assessments for the stochastic behaviour. The order of events is predetermined by the expert and may possibly represent the chronological order of some reference sequences, but the question is, whether it is apphcable to all sequences. What is the consequence, if specific process conditions induce another order of different events ... 

Fault-tree models are used to determine the unavail-ahflities of the safety system functions to be considered in the event-trees. They are logical cause-effect models which trace the failure of a system function like, for instance, a technical safety system back to basic events like the failures of technical components. Finally, the fault-tree model provides a value for the unavailability of a system function which is derived from the unavailahilities of the components. 

BBNs are also sometimes called causal probabilistic networks, probabilistic cause-effect models or probabilistic influence diagrams. 

The main advantage of a hybrid system is the possibility of describing some well-assessed phenomena by means of a fundamental approach. Other phenomena, that could be very difficult to interpret, are, instead, described by straightforward cause-effect models, as represented, for instance, by ANN. 

Clearly, more parameters allow more freedom in representing common cause effects in svstem.s of complex redundancy. NUREG-1150 describes the Multiple Greek Letter Model (MGL), Parameter (BP) model and the Binomial Failure Rate (BFR) model. 

Cause-consequence analysis serx es to characterize tlie physical effects resulting from a specific incident and the impact of these physical effects on people, the environment, and property. Some consequence models or equations used to estimate tlie potential for damage or injury are as follows Source Models, Dispersion Models, Fire Explosion Models, and Effect Models. Likelihood estimation (frequency estimation), cliaractcrizcs the probability of occurrence for each potential incident considered in tlie analysis. The major tools used for likelihood estimation are as follows Historical Data, Failure sequence modeling techniques, and Expert Judgment. 

In this approach, connectivity indices were used as the principle descriptor of the topology of the repeat unit of a polymer. The connectivity indices of various polymers were first correlated directly with the experimental data for six different physical properties. The six properties were Van der Waals volume (Vw), molar volume (V), heat capacity (Cp), solubility parameter (5), glass transition temperature Tfj, and cohesive energies ( coh) for the 45 different polymers. Available data were used to establish the dependence of these properties on the topological indices. All the experimental data for these properties were trained simultaneously in the proposed neural network model in order to develop an overall cause-effect relationship for all six properties. 

Because physicochemical cause-and-effect models are the basis of all measurements, statistics are used to optimize, validate, and calibrate the analytical method, and then interpolate the obtained measurements the models tend to be very simple (i.e., linear) in the concentration interval used. 

In summary, models can be classified in general into deterministic, which describe the system as cause/effect relationships and stochastic, which incorporate the concept of risk, probability or other measures of uncertainty. Deterministic and stochastic models may be developed from observation, semi-empirical approaches, and theoretical approaches. In developing a model, scientists attempt to reach an optimal compromise among the above approaches, given the level of detail justified by both the data availability and the study objectives. Deterministic model formulations can be further classified into simulation models which employ a well accepted empirical equation, that is forced via calibration coefficients, to describe a system and analytic models in which the derived equation describes the physics/chemistry of a system. 

USEtox calculates characterization factors for human toxicity and freshwater ecotoxicity. Assessing the toxicological effects of a chemical emitted into the environment implies a cause-effect chain that links emissions to impacts through three steps environmental fate, exposure, and effects. Linking these steps, a systematic framework for toxic impacts modeling based on matrix algebra was developed to some extent within the OMNIITOX project [10]. USEtox covers two spatial scales, the continental and the global scales. 

In example 2 a simpler approach is used to correctly handle backward cycles (co-products). The difference to the forward cycle is that the co-product quant B created by a quant A cannot be used as predecessor of A, because cycles in the quant network are not allowed (violates the cause effect principle). A model can avoid this cycles using aggregation in such a way that cycles are within these quants A and B (see Figure 4.15). 

Cause-effect-relations of these dynamics in the value chain may still be obvious, when operating a simple value chain comprising few products, locations and production steps. Considering the global multi-stage, multilocation value chain network, price changes in raw materials cannot directly be related to intermediate or even sales products and their prices. This problem requires specific planning models and methods. 

Central to any risk assessment is a model of causality. At the onset, a conceptual model is needed that identifies a plausible cause-effect relationship linking stressor exposure to some effect. Most ecological risk assessments rely heavily on weight-of-evidence or expert opinion methods to foster plausibility of the causal model. Unfortunately, such methods are prone to considerable error (Lane et al. 1987 Hutchinson and Lane 1989 Lane 1989), and attempts to quantify that error are rare. Although seldom used in risk assessment, Bayesian methods can explicitly quantify the plausibility of a causal model. 

Not surprisingly, the use of acidified water increased the level of fluoride release from the glass, and this effectively models what happens in a setting cement. The acid-base reaction between the glass and the water-soluble polymeric acid liberates fluoride from the glass, causing it to move to the matrix, from where it is gradually leached as the cement releases fluoride [227,228]. 

Both sets of calculations found that ring closure of 8 preferentially occurs by the same mode of coupled methylene rotations as ring opening of 7. Crudely put, the dynamical behavior of 8 can be predicted by, what would be called in classical mechanics, conservation of angular momentum. Chapter 21 in this volume provides examples of other reactions in which dynamical effects cause statistical models, such as TST, to fail to make correct predictions. 

We do not imply here that scientists know all cause-effect relations for human biomonitoring in fact, the mental-model technique probably becomes more useful as it makes expert uncertainties and disagreements more explicit. However, experts mental models of the causal links are likely to be more comprehensive than those of nonscientists and thus provide a useful guide for topics on which to probe lay mental models about biomonitoring and biomarkers. 

In addition it is now time to think about the two assumption models, or types of analysis of variance. ANOVA type 1 assumes that all levels of the factors are included in the analysis and are fixed (fixed effect model). Then the analysis is essentially interested in comparing mean values, i.e. to test the significance of an effect. ANOVA type 2 assumes that the included levels of the factors are selected at random from the distribution of levels (random effect model). Here the final aim is to estimate the variance components, i.e. the variance fractions with respect to total variance caused by the samples taken or the measurements made. In that case one is well advised to ensure balanced designs, i.e. equally occupied cells in the above scheme, because only then is the estimation process straightforward. 

Quantitative cause-effect relationships Simple pop models (exponential models)... 

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