Uncertainty stochastic

Aleatory uncertainty The kind of uncertainty resulting from randomness or unpredictability due to stochasticity. Aleatory uncertainty is also known as variability, stochastic uncertainty. Type I or Type A uncertainty, irreducible uncertainty, conflict, and objective uncertainty. 

There are a number of sources of uncertainty surrounding the results of economic assessments. One source relates to sampling error (stochastic uncertainty). The point estimates are the result of a single sample from a population. If we ran the experiment many times, we would expect the point estimates to vary. One approach to addressing this uncertainty is to construct confidence intervals both for the separate estimates of costs and effects as well as for the resulting cost-effectiveness ratio. A substantial literature has developed related to construction of confidence intervals for cost-effectiveness ratios. 

In addition to addressing stochastic uncertainty, one may want to address uncertainty related to parameters measured without variation (e.g., unit cost estimates, discount rates, etc.), whether or not the results are generalizable to settings other than those studied in the trial, and, for chronic therapies, whether the cost-effectiveness ratio observed within the trial is likely to be representative of the ratio that would have been observed if the trial had been conducted for a longer period. These sources of uncertainty are often addressed using sensitivity analysis. 

From a mathematical perspective (see Equation 4.1), CA simply represents the weighted harmonic mean of the individual ECx values, with the weights just being the fractions / , of the components in the mixture. This has important consequences for the statistical uncertainty of the CA-predicted joint toxicity. As the statistical uncertainty of the CA-predicted ECx is a result of averaging the uncertainties of the single substance ECx values, the stochastic uncertainty of the CA prediction is always smaller than the highest uncertainty found in all individual ECx values. Perhaps contrary to intuition, the consideration of mixtures actually reduces the overall stochastic uncertainty, which is a result of the increased number of input data. 

Reagan MT, Naim HN, Debusschere BJ, Le Maitre OP, Knio OM, Ghanem RG (2004) Spectral stochastic uncertainty quantification in chemical systems. Combust Theory Model 8(3) 607-632... 

As mentioned, the uncertainty in Wf ) could come from stochastic uncertainty, model uncertainty or data and parameter uncertainty. In our model, stochastic uncertainly is related to the random behavior of z(t). Model uncertainty will more or less always be present, as g() only is a simplification of the leaUly. Data and parameter uncertainty is in this context related to both the parameters in g() as well as the parameters in the probability distribution of z(t). 

The stochastic behavior of AX(t) is as described in the introduction, basically due to two conditions. First of all there will be a large stochastic uncertainty in what the value of z(t) will be in the future. We consider Z(t) as a stochastic variable, and thus we have a stochastic process. As an example we consider a simple linear first order model. 

Simple Monte Carlo simulations was performed to illustrate the stochastic uncertainty in z(t). Only one variable, the temperature, was investigated. The temperatures were drawn fi"om a PERT distribution, with (minimum mean maximum) values assumed known hence the aleatory uncertainty was investigated. One may also expect that the mean value is not known, or that uncertainty in earlier measured data would affect the expected values, but this was not investigated at this time. Simulations were performed for temperatures between 20 and 120°C as this could be reahstic temperatures for a real process. Four temperature ranges were investigated, ah with a temperature range of 30°C (20 35 50), (50 65 80), (70 85 100), (60 69 90 and (90 105 120)°C. 

High variation in populations (high stochastic uncertainty). 

Petryna, Y.S., Kratzig, W.B. 2002. On sensitivity of structural damage measures to stochastic uncertainties. In H.A. Mang, EG. Rammerstorfer, J. Eberhardsteiner (eds.), CD-Proc. 5th World Congr. of Comp. Mech., Vienna. 

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