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I have drawn X-many samples from a population. I want to use this data to drive inputs for a Monte Carlo simulation (or similar). The population may be a real world measurement, or it could be the output of another computer model.

There are two ways I could go about this:

  • I could use the samples to estimate a population distribution and sample from the estimated distribution within the Monte Carlo simulation.
  • I could randomly draw from the samples that I have already collected from the population.

Both of these approaches have strengths and weaknesses and are appropriate in some situations and less useful in others.

Is there better terminology that I can use if/when I want to discuss the distinction?

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Both these approaches are considered two different versions of the bootstrap

In the case that we are fitting the distribution to a parametric model and then sampling from the model, this is called the parametric bootstrap. If we simply resample the raw data directly, this is referred to the non-parametric bootstrap.

In practice, the non-parametric bootstrap is used much more often, due to being simpler and having less assumptions attached. As such, when people refer to simply "bootstrap", they usually mean the non-parametric approach.

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This is called an Empirical distribution function. You can check out this.

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  • $\begingroup$ Super, thanks! That gives me two straightforward ways to describe the difference: "Empirical distribution vs Estimated distribution" and "parametric vs non-parametric bootstrap". $\endgroup$ May 6, 2023 at 14:49
  • $\begingroup$ I marked the other answer as correct but if I could then I'd have ticked both. $\endgroup$ May 6, 2023 at 14:52

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