I am seeking an approach to sampling conditional joint distribution (new to probability). I will put my case in a simple way:
Similar question for discrete variables is asked here but not yet answered; I am interested in continuous random variables.
I have observations/ samples (historical synchronized data of forecasted and actual values corresponding to those forecasts) of 6 random variables, i,e. I have 12 random variables [X1 X2... X6, Y1 Y2... Y6] where Xs are the actual values and Ys are the corresponding forecasted values (matrix of 10807*12). So, I am assuming I have enough samples from the joint distribution of the random vector of 12 random variables.
My target is to find the samples from Conditional Error Distribution (error E1=X1-Y1) of the form as in image of the interested conditional distribution for specific forecast values y1 y2... y6 written in word, sorry for image!
I can fit the joint distribution of random vectors [E1 E2... E6, Y1 Y2... y6] (as values calculated for E are also synchronized to the observed data) and [X1 X2... X6, Y1 Y2... Y6] through linear or rank correlation or copula(s). So, basically, I can generate samples from joint distributions of any combination of the random variables, and also from any marginal distribution too.
My question: How to sample from the above conditional joint distribution when specific values of the forecast are provided; I can only generate samples from any joint combination of actual values, forecasted values, and error values? can this be done?