> Monte Carlo simulation - estimating uncertainty.
By definition, "uncertainty" is the thing that does not have a PDF ... You can quantify risk based on assumptions you make about underlying probability distributions from which you are drawing. Far too often, even in Monte Carlo, people decide to work with the easy distributions instead of the most appropriate distributions.
The "easy" distributions tend to admit actual mathematical solutions which means Monte Carlo is helpful if you can't do the math but not strictly necessary.
Monte Carlo shines when you cannot get nice solution and there is your opportunity to not be constrained by the need to do so: Draw from appropriate distributions.
Also, know the difference between LLN and CLT and when to appeal to which to justify your methods.
I would think that you could have "uncertainty" even if you do have a PDF. Maybe there is a formal definition of uncertainty that I am not aware of. The PDF can describe the uncertainty for every outcome.
Risk is what you can put a probability on (i.e., quantify). Uncertainty is what you can't. Uncertainty encompasses unknown unknowns. See Knight[1] and Keynes[2].
Good rule of thumb even if it sounds overly simplified.
By definition, "uncertainty" is the thing that does not have a PDF ... You can quantify risk based on assumptions you make about underlying probability distributions from which you are drawing. Far too often, even in Monte Carlo, people decide to work with the easy distributions instead of the most appropriate distributions.
The "easy" distributions tend to admit actual mathematical solutions which means Monte Carlo is helpful if you can't do the math but not strictly necessary.
Monte Carlo shines when you cannot get nice solution and there is your opportunity to not be constrained by the need to do so: Draw from appropriate distributions.
Also, know the difference between LLN and CLT and when to appeal to which to justify your methods.