So I never really understood what’s so ingenious about Monte Carlo simulation, or why it needs a name attached to it.
Monte Carlo simulation in essence is just the dumb man’s way of finding out the answer, literally by doing things many many times and see what the result is. But isn’t that just the definition of a simulation?
When I first heard this method I thought it was some neat trick. Turns out it’s something any kid could’ve come up with. I feel deceived.
Sensei: what will happen if we play this complicated game?
Monte Carlo: let’s start playing and find out
Monte carlo algorithms use probabilistic methods to find the approximately right answer in a set amount of time.
Las Vegas methods find the right answer to a certain precision in an uncertain amount of time.
I think it’s best to appreciate statistical MC methods as compared to what was available before, namely using theoretical approaches to find approximate integrals (remember and average or percentile is just an integral.) It’s a huge improvement over that.
The Monte Carlo Method was invented by John von Neumann and Stanislaw Ulam during World War II to improve decision making under uncertain conditions. It was named after a well-known casino town, called Monaco , since the element of chance is core to the modeling approach, similar to a game of roulette
For integrals, you have various finite difference methods, runge-kutta, spectral methods, etc.
For more general simulation, it can always have it be deterministic. The major hurricane forecast models all have deterministic versions that are presumably more computationally expensive that the MC probabilistic ones.
I mean, a lot of non-actudonks would just say you can’t model uncertainty.
And they would use the same spreadsheet and make a best guess.
And then yeah, there’s old geniuses like magilliaG who would pull out 8 dimensional PDEs to solve your problem.