Monte Carlo - isn't that quite expensive?

Aren't Monte-Carlo methods relatively expensive when shooting around randomly for parameter studies?

Far from it! For complex problems the usage of Monte-Carlo methods is far more efficient than competing Design-of-Experiments approaches, whose number of necessary samples grows exponentially with the number of parameters to be considered.

The effort for Monte-Carlo methods is not dependent on the number of investigated parameters but only on the desired precision and the complexity of the parameters really affecting the system. Therefore Monte Carlo methods are more natural and finally more efficient.

Contrary to analytical, preconceptioned approaches like Design-of-Experiments the use of Monte-Carlo methods offer the chance to discover things, which have not been thought about in advance. With purely analytical and deterministic approaches one can only verify or falsify the given hypothesis. Therefore these approaches are not really constructive or "creative" in contrast to example based approches like Monte-Carlo methods.

When using purely analytical approaches also the adequate validation and the associated generation of test samples is often forgotten or done insufficiently. The costs then are coming later, and unfortunatly often far more severe.