Please apologise my likely ignorance of the correct terminology and notation. Any edits and suggestions to improve the question are very much appreciated.
I want to perform a Monte Carlo simulation with a simple computational model. That means I want to random sample the model's input variables and later analyse the sensitivity of the inputs for the results. Let's say the model uses the variables $a,b,c,$ and $d$ as inputs. However, the model only accepts a cumulated input of 1.0, i.e. $a+b+c+d=1.0$.
The input variables are random sampled from a uniform distribution with individual ranges $\mathcal{U}(y,z)$ for each.
My first (innocent) thought was to simply random sample, sum the variables and divide each by their sum to normalise them to 1.0. However, this will effectively change the bounds of each variable $y,z$ and also distort the uniform distribution.
Now, I am at a loss how I should correctly approach this issue. I feel like I am not the first person that wants to run a Monte Carlo model using conditional inputs, but I could not find any useful pointers in the literature so far. Can anybody help, please?
