[R] Multi-output regression

[zeec at gmx.net]

Hi,

I have a question regarding the modeling methodology of the following problem:

* I have two data sets {X_i,y_i} {X_i,z_i}, i=1..N,
  where y_i = f(X_i) + i.i.d. Gaussian noise 
  and   z_i = g(X_i) + i.i.d. Gaussian noise
* I apply bayesian linear regression to each of them and obtain
  p(y|X) and p(z|X)
  
I would like to improve the prediction of the two models using the knowledge that
f and g are related (for example f(X_i) = g(X_i) - 1). I can obtain a model p(y,z).

I know that there are methods for multi-output regression, but I hope both can be modeled independently and then combined. 

Thank you for your help!
Steffan
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