I am not a Bayesian. In the non-Bayesian case you would use SUR to model both
equations simultaneously. If both use the exact same matrix of data, X
(i.e., the value are numerically absolutely identical), then SUR will
collapse to OLS. In that sense you get a "combined" estimate using SUR
that
respects the correlation of the error terms between equations. However, it
will be efficient to estimate each equation individually if the Xs are
exactly the same.
Daniel
zeec wrote:>
> 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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>
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