Thank you for this. I've been curious about Monte Carlo techniques ever since I was strongly influenced by Taleb's ideas. He uses Monte Carlo techniques via Mathematica* to produce curves for very complex probability functions. He prefers using Monte Carlo (practice) over using math theory. (He calls it "tinkering" not "Pinkering", a reference to Steve Pinker, whom Taleb criticizes because Taleb argues that Pinker relies excessively on theory, not enough on practice).
My request to experienced Monte Carlo tinkerers on HN: please share "open source + free" tools and resources that you'd recommend to learn Monte Carlo.
*Mathematica is very expensive software, without a free tier.
Separating Monte Carlo methods from math theory is an odd distinction to make. There's a lot of sophisticated theory underlying Monte Carlo methods as well. MC also is more of a loose term referring to a class of techniques, rather than any specific algorithm. In that sense, there aren't really any [specific] tools or software you would use.
A textbook on MC applications to your area of interest is probably the best place to start, there are a ton in practically every field. If theory-heavy presentations aren't your flavor then you can likely find a text or blog series to match.
Does any one know something similar as a primer on Markov Chains? I get the idea of simulating the pattern of behaviors or states with the Markov chain, and how the Monte Carlo is useful for that, but how to actually make a Markov chain and then test it mathematically with the Monte Carlo is something that I don't know how to do.
My request to experienced Monte Carlo tinkerers on HN: please share "open source + free" tools and resources that you'd recommend to learn Monte Carlo.
*Mathematica is very expensive software, without a free tier.