Stochastic endpoints

The risk index for any hazardous substance in Equation 1.1 or 1.2 (see Section 1.5.1) is calculated based on assumed exposure scenarios for hypothetical inadvertent intruders at near-surface waste disposal sites and a specified negligible risk or dose in the case of exempt waste or acceptable (barely tolerable) risk or dose in the case of low-hazard waste. Calculation of the risk index also requires consideration of the appropriate measure of risk (health-effect endpoint), especially for carcinogens, and the appropriate approaches to estimating the probability of a stochastic response per unit dose for carcinogens and the thresholds for deterministic responses for noncarcinogens. Given a calculated risk index for each hazardous substance in a particular waste, the waste then would be classified using Equation 1.3. 

Measures of stochastic responses. The primary measure of stochastic responses used in radiation protection and radiation risk assessment by ICRP and NCRP has been fatalities (i.e., fatal cancers and severe hereditary effects). Fatalities have been emphasized essentially because this was the only health-effect endpoint for which data generally were available, both for study populations... 

This option does not appear to be advantageous for either radionuclides or chemicals that cause stochastic responses. In radiation protection, total detriment is used mainly to develop the tissue weighting factors in the effective dose (see Section 3.2.2.3.3), but ICRP and NCRP have continued to emphasize fatal responses as the primary health effect of concern in radiation protection and radiation risk assessments. Since total detriment is based on an assumption that fatalities are the primary health effect of concern, the same difficulties described in the previous section would occur if this measure of response were used for chemicals that induce stochastic responses. Other disadvantages of using total detriment include that detriment is not a health-effect endpoint experienced by an exposed individual and the approach to weighting nonfatal responses in relation to fatalities is somewhat arbitrary. Furthermore, total detriment is not as simple and straightforward to understand as either incidence or fatalities. 

More recently, studies have applied the probability of extinction as an endpoint to extrapolate short-term effects on long-term population consequences. Based on population viability analysis (Boyce 1992 Groom and Pascual 1997), population size is projected into the future using demographic rates and models that incorporate stochastic effects (Snell and Serra 2000). In practice, it would be difficult to determine extinction rates experimentally due to the need to conduct experiments over multiple generations. Thus, the probability of extinction is typically modeled using the instantaneous rate of increase (Snell and Serra 2000). 

Figures 5(a) and 5(b) show the simulated breakthrough curves of both total protein and HSV-1 respectively. It should be noticed that the dimensionless time scales in these two figures differ by four orders of magnitude. The breakpoint of HSV-1 is the operating endpoint at which the effluent from the adsorption column can no longer meet the desired sterilization criterion. Since the HSV-1 has a much higher affinity to the bead surface, the breakpoint of HSV-1 appears much later than that of the total protein. To optimize the protein recovery, one should improve the design of the bead surface (better selectivity, higher loading capacity), size, and operating parameters of the filter to further delay the breakpoint of the virus elution. A stochastic approach to model the removal process may be more appropriate in low concentrations of viruses.

The perspective exploited by transition path sampling, namely, a statistical description of pathways with endpoints located in certain phase-space regions, was hrst introduced by Pratt [27], who described stochastic pathways as chains of states, linked by appropriate transition probabilities. Others have explored similar ideas and have constructed ensembles of pathways using ad hoc probability functionals [28-35]. Pathways found by these methods are reactive, but they are not consistent with the true dynamics of the system, so that their utility for studying transition dynamics is limited. Trajectories in the transition path ensemble from Eq. (1.2), on the other hand, are true dynamical trajectories, free of any bias by unphysical forces or constraints. Indeed, transition path sampling selects reactive trajectories from the set of all trajectories produced by the system s intrinsic dynamics, rather than generating them according to an artificial bias. This important feature of the method allows the calculation of dynamical properties such as rate constants. 

The MCDA approach mainly relies on the estimate of the overall BR score in BR assessment, which does not accoimt for the uncertainties associated with sampling variation in the data for the benefit and risk endpoints. In addition, MCDA requires an explicit supply of weights for each criterion. Such weights are not easy to derive and are likely to differ among different decision makers. Stochastic multicriteria acceptability analysis (SMAA) was extended for BRA to deal with these limitations in MCDA (Tervonen et al. 2011). 

The literature indicates numerous, often widely different values for assigning probabilities to scenarios such as those of Figs. 10.2, 10.3 and 10.4. This reflects uncertainties due to lack of knowledge (epistemic) and stochastic (aleatory) effects. If properly treated these uncertainties should be represented by probability distributions. Table 10.15 gives an overview of conditional probabilities for the consequences of a puff release of a pressurized flammable gas from various sources. Not only are the differences in probabilities evident but also the differences as to the endpoints. 

The paper presents a developed version of an algorithm for safe ship trajectory plarming using stochastic global optimization method, what has allowed to include the COLREGs, a greater number of static obstacles and moving objects, dynamic properties of the vessel, the determination of a safe trajectory to the specified endpoint and consistent solutions from the perspective of all the vessels involved in the coUision situation. 

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