Are Monte Carlo methods considered Bayesian or Frequentist?

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I went down the Frequentist vs Bayesian rabbit hole. I was searching for specific examples and I came across this question. Is sampling with Monte Carlo techniques a Bayesian or a Frequentist approach to statistics?

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Since Monte Carlo techniques are methodologies that draw samples from any probability distribution, they can't really be categorized as Bayesian or Frequentist. However, since these methods, especially Markov chain Monte Carlo methods (MCMC), are particularly well suited for and predominantly applied to Bayesian posteriors, I would slightly lean towards "Bayesian" as an answer, but only if someone really forced me to choose. :-)