Dependent Covariance Matrix in Bayesian Inversion/Multiplicative Discrepancy Error

Hello UQlab,

I am working on a bayesian inversion problem.

  1. Consisting of different forward models (\mathbf{u^+} \mathbf{y^+}, c_f etc).
  2. I have figured how to make room for different forward models, on the assumption that the model discrepancy is independent and unrelated.
  3. However, I would like to toy around with the possibility of a dependent covariance matrix. The Question;
  • I found one example for a user-defined likelihood function. In the same way I define multiple forward models, can I define multiple user-defined likelihood functions?
  • is it possible to go about this differently? i.e. instead of a user-defined likelihood function, my forward model would take the discrepancy “kernel” into consideration (and to close it out, I add a model discrepancy term)
  1. In (Bayesian Uncertainty Quantification applied to RANS turbulence models), a multiplicative discrepancy is assumed by the authors for the velocity term. I would like to replicate this example. I would like tips on how this can be done.
    thank you very much for the kind assistance.

Hi! Uche_A. I am also pretty new in this area but very interested in your problem.

When you mentioned different forward models, that means considering different sources of monitored data, right? So you will have different discrepancies models in your user-defined loglikelihood function. So, how you exactly define different discrepancy in your user-defined loglikelihood? is that just simply multiplying them together in the likelihood (or add them together in the log space)?