what if what???

[Here is a section of the Wikipedia page on Monte Carlo methods which makes little sense to me. What if it was not part of this page?!]

Monte Carlo simulation versus “what if” scenarios

There are ways of using probabilities that are definitely not Monte Carlo simulations – for example, deterministic modeling using single-point estimates. Each uncertain variable within a model is assigned a “best guess” estimate. Scenarios (such as best, worst, or most likely case) for each input variable are chosen and the results recorded.^[55]

By contrast, Monte Carlo simulations sample from a probability distribution for each variable to produce hundreds or thousands of possible outcomes. The results are analyzed to get probabilities of different outcomes occurring.^[56] For example, a comparison of a spreadsheet cost construction model run using traditional “what if” scenarios, and then running the comparison again with Monte Carlo simulation and triangular probability distributions shows that the Monte Carlo analysis has a narrower range than the “what if” analysis. This is because the “what if” analysis gives equal weight to all scenarios (see quantifying uncertainty in corporate finance), while the Monte Carlo method hardly samples in the very low probability regions. The samples in such regions are called “rare events”.

xkcd [interview & book]

Of interest for xkcd fans: What If?: Serious Scientific Answers to Absurd Hypothetical Questions is out! Actually, it is currently the #1 bestseller on amazon! (A physics book makes it to the top of the bestseller list, a few weeks after a theoretical economics book got there. Nice! Actually, a statistics book also made it to the top: Nate Silver’s The SIgnal and the Noise….) I did not read the book, but it is made of some of the questions answered by Randall Munroe (the father of xkcd) on his what if blog. In connection with this publication, Randall Munroe is interviewed on FiveThirtyEight (Nate Silver’s website), as kindly pointed out to me by Bill Jefferys. The main message is trying to give people a feeling about numbers, a rough sense of numeracy. Which was also the purpose of the guesstimation books.