STEP 3: Propagate

Step 1 identified the potentially important uncertainties, and Step 2 expressed the corresponding states of knowledge as well as any relevant state of knowledge dependences probabilistically. The state of knowledge expressions need now to be propagated through the arithmetic and logic instructions of the computer model in order to obtain the subjective probability distributions that follow in a logically consistent manner for the model results. These distributions quantify the combined influence of the uncertainties on the model results and thereby express their state of knowledge. However, they remain unknown since deriving them analytically is out of the question for most practically relevant models. Uncertainty analysis aims at determining estimates of uncertainty measures for the model results through random sampling according to these distributions. The uncertainty measures are either the subjective probability content of a specified value range of the model result or a value range that contains the specified amount of subjective probability. The sampling techniques commonly used, and explained in this chapter, are either simple random sampling (SRS) or Latin Hypercube sampling (LHS). Statistical tolerance limits can be obtained from a relatively small SRS. A sample of size 93 provides already a two-sided (95%, 95%) statistical tolerance limit that contains at least subjective probability 0.95 at a confidence level of at least 95%. Other sampling techniques are required if the subjective probability of a specified value range of the model result is extremely small. Among those techniques are importance sampling and subset sampling. In order to explain the principle, a simple practical procedure is presented for both.