I have a question regarding Monte Carlo simulation (direct simulation), applied to propagation of uncertainties.
From what I understand Monte Carlo accepts random numbers of each input variable of the model.
These random numbers are generated with the mean, standard deviation and type of PDF (normal, triangular, uniform, etc.)
But the question is: I have 2 input variables in my model:
x: mean=30.5 std=0.001 <- calculated with 95% confidence.
y: mean=2 std=0.1 <- calculated with 99% confidence
with z = x*y
What confidence interval will z be generated? How do I know which uncertainty (standard deviation) of z is correspondent to a 95% confidence level?
Best Answer
Finish 10.000 MC runs and then start computing your confidence intervals. Compute e.g. the median value, which divides your probability distribution (PD) into two parts, where each part corresponds to 50% probability or area of your PD. Integrate your PD from -infinity to the z value covering 2.5% area of your PD, and integrate from zero to the z value covering 97.5% area of your PD. In total you then have the z values, which enclose 95% of your PD. This is denoted the 95 percentile. You can then compute something like a standard deviation by: z1=z975-median and z2=median-z025. Maybe have a look at "confidence.pro" (IDL language).