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Comment by blauditore | Hacker News Reader

The term "monte carlo methods" in statistics/probability bothers me, since it literally just means trying out, or simulating. I can't help but think someone started using it to just sound smart. Such shenanigans seem make science harder to grasp especially for newcomers, so I think it would be better to keep naming simple and obvious where possible. There are enough topics that are too abstract, so it can't be done there.

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> just means trying out

this statement trivializes a very hard problem.

> literally just means trying out, or simulating

Simulating is an incredibly hard problem and MC methods and theory is an incredibly rich area of study. Some tools I use for my work in probabilistic machine learning models are MCMC techniques like HMC (Hamiltonian Monte Carlo), variance reduction techniques (Rao Blackwellization). If you would like to learn more, here is a great course: https://statweb.stanford.edu/~owen/mc/ -- you can take a look at the syllabus. Also, Casella Berger is a standard MC method book.

I don't think there's universal agreement about terminology, but to many of us who work in the area, Monte Carlo (MC) means specifically using random sampling to estimate a deterministic quantity. For example, MC methods can be used to compute the ground state energy of atoms and molecules. This in principle can also be done by solving the many-body Schroedinger equation, but direct numerical solution is simply not feasiable except for systems with very few degrees of freedom. In contrast, the term "simulation" often (but not always) means to simulate to take a look.

As is usual with these things, the boundary is not sharp. One selling point of sampling is that with greater expense you also get more information about the "energy landscape," can do uncertainty quantification, etc.

My understanding is Monte Carlo method refers to sampling using a random component, evoking the casinos of the real Monte Carlo

Those “someones” who started using it were Stan Ulam and John von Neumann: https://en.wikipedia.org/wiki/Monte_Carlo_method#History

It’s a beautiful piece of math history.

The alternative would be calling it something like stochastic methods, which would probably be even more confusing. Monte Carlo is a convenient term to make it clear the stochastic part is in the method itself, and not in the measurements or the modeled system.

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