Bayesian calibration - input Parameters with known uncertainty


For Bayesian calibration problem, can I specify an input parameter as random (say Gaussian) and not calibrate that parameter. In this case it might be something that is uncertain, but the uncertainty is already known. From the examples, it is clear that defining a parameter as ‘constant’ would use it only for forward problem. Can it be done for a parameter that follows a distribution? Or, do I need to specify such parameters inside the concerned function.

Thank you,

Hi Atma and welcome to UQWorld :smiley:

Yes, these problems can absolutely be handled by the general Bayesian calibration framework. One way to deal with this is presented in this publication or the associated report. What you call known uncertainty is called aleatory uncertainty therein.

The idea, in a nutshell, is to marginalize over all aleatory variables when constructing the likelihood function used in the Bayesian inverse problem. This is not supported out of the box in the current version of the Bayesian module of UQLab but would have to be implemented through the user-defined likelihood feature.

Hope this helps!