When you do a Monte-Carlo simulation with several fluctuating input parameters, do you vary all inputs separately or at once?

So if I want to vary 10 parameters in my model and let's say for all the individual parameters, I have 100 different values. So shall I perform 100*10 simulations or 100 simulations for one parameter and then for the next one and so on? Maybe I am unclear about the aim of the mc simulation here.

  • $\begingroup$ What you suggest is an exhaustive map of the "estimated cost" over the entire parameter space. That may not be practical. If it is your goal to characterise the influence of a certain parameter "locally", you may have a look at sensitivity analysis. This gets you the influences at a certain point in the parameter space. If you need a more global view of the parameters' influences over a certain region, you could consider doing a designed experiment (see theory of Design of Experiments, DOE, with ANOVA analysis). $\endgroup$ – StijnDeVuyst Apr 18 '18 at 9:25

In general the added value of MC simulations is to be able to vary all of the uncertain input parameters at the same time. Otherwise, you might as well use other forms of one-way sensitivity analysis. So you probably want run the simulation varying all parameters simultaneously for 1000 or actually 10000 times or greater (more is generally better but with diminishing marginal returns for each additional simulation, and some practical considerations on computational time).

A word of caution: You say you have various parameters, and each of those parameters can take 100 values. Do each of those 100 values have the same 1% chance of occurring, i.e. a uniform distribution? If not, it’s much more appropriate to apply some parametric assumptions, eg normal or beta or whatever of various distributions most accurately describes the situation you are modelling. If you truly have uniform distributions across all the input parameters, your final MC simulation is most likely going to give you a linear pattern from lowest to highest possible outcome, which doesn’t really add much value beyond a deterministic analysis that could be done with arithmetic.

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  • $\begingroup$ Thanks a lot. I did beta random distribution of my parameters and changed all of them together. Performed 20000 runs and got the outputs changing in the same trend as my input (beta or normally distributed) errors are negligible according to MC formula and hence did not increase the number of runs further. Thanks :) $\endgroup$ – Neje Apr 26 '18 at 12:04

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