1

How's Monte Carlo different from random sampling with replacement?

Because Wikipedia page for Monte Carlo says:

Monte Carlo methods vary, but tend to follow a particular pattern:

  1. Define a domain of possible inputs
  2. Generate inputs randomly from a probability distribution over the domain
  3. Perform a deterministic computation on the inputs
  4. Aggregate the results

Isn't 2 about doing exactly the same thing as sampling with replacement?

Or is it Monte Carlo, because one does 3. and 4. in addition?

mavavilj
  • 3,167
  • 4
  • 20
  • 44
  • 2
    I think "Monte Carlo methods" is a general term "randomized algorithms". It includes a lot of algorithms. – Haitao Du Feb 07 '18 at 17:17
  • @hxd1011 In that case it's just very imprecise for lecturers to use the term Monte Carlo method in various cases, because it doesn't really tell what the method is used for. – mavavilj Feb 07 '18 at 17:34
  • 1
    Monte Carlo methods are a generic hat for evaluations involving simulation from a fixed distribution and it is not naturally associated with Statistics (or only with Statistics). Sampling with replacement seems connected with the bootstrap method, which means simulating from the empirical cdf of an iid sample. This is a fairly special case of Monte Carlo. – Xi'an Feb 07 '18 at 17:58
  • @mavavilj humans use many imprecise, general words. It is easier to say "flowers" then "a set containing roses, tulips, orchids, lilys, ..." don't you think? Monte Carlo is basically a synonym for simulation. – Tim Feb 07 '18 at 18:03
  • @Tim - I almost agree. There are creations such as flight simulators that create an experience, a set of sensory stimuli, rather than a set of quantitative findings to analyze. – rolando2 Feb 07 '18 at 21:00

0 Answers0