Bayesian inference with changing (known) model parameters

UQ with UQLab Community Q&A and How To
1

Hi all,

I have a (maybe simple or silly) question about Bayesian inference for the case that the model is not only depending on the uncertain parameter vector X, but also on (known) operating conditions (let’s say a vector q).
Mathematically speaking, I have:

model: Y_i = M(X,q_i), for i = 1…N_meas; each Y_i is typically a vector
experimental data: d_i, for i=1…N_meas, d_i has the same dimension as Y_i

N_meas is around 28.
I want to calibrate the vector X.
One solution I can think of is to use the ‘multiple forward model’ option in UQLab, in which I effectively have
Y_i = M_i(X) := M(X,q_i)
That would mean that I need to define 28 forward models. Is this the way to go? Or is there another option to do this?

Best regards,

Benjamin

2

Hi @bsanderse

Yes, I think the multiple forward model feature would be the way to go in your case. If you don’t want to go through the hassle of defining 28 models manually, you could also write a simple wrapper model that distributes the experimental conditions q_i to the \mathcal{M}_i forward models and “stitches” their outputs together.

Have fun inferring and let me know how it goes!