Goals and use

The goal of Monte Carlo analysis is to trace out the structure of the distributions of model output that results from specified uncertainty distributions of model inputs and model parameters. In its simplest form this distribution is mapped by calculating the deterministic results (realizations) for a large number of random draws from the individual distribution functions of input data and parameters of the model. To reduce the required number of model runs needed to get sufficient information about the distribution in the outcome (mainly to save computation time), advanced sampling methods have been designed such as Latin Hyper Cube sampling. The latter makes use of stratification in the sampling of individual parameters; like in random Monte Carlo sampling, pre-existing information about correlations between input variables can be incorporated. Monte Carlo analysis requires the analyst to specify probability distributions of all inputs and parameters, and the correlations between them. Both probability distributions and correlations are usually poorly known.

A number of software packages are available to do Monte Carlo analysis. Widely used are the commercial packages @Risk ( and Crystal Ball ( Both are packages that are designed as fully integrated MS-Excel add-in programs with its own toolbar and menus. These packages can be used with minimal knowledge on the sampling and calculations techniques itself, which makes Monte Carlo Assessment easy (but tricky because it allows incompetent use). Another commercial package is Analytica (, which is a quantitative modelling environment with built-in Monte Carlo algorithms.

If your model is not built in Excel you can use the SimLab package, which is freely available from the JRC ( SimLab can also be interfaced with Excel, but this requires some programming skills. For the UNIX and MS-Dos environments you can use the UNSCAM (Janssen et al., 1994) software tool. RIVM is presently developing a new tool for Monte Carlo analysis, USATOOL, which will run under Windows.

Additionally most Monte Carlo analysis software offers the possibility to determine the relative contribution of uncertainty in each parameter to the uncertainty in a model output, e.g. by sensitivity charts, and can be used for a sophisticated analysis of trends in the presence of uncertainty.