Hello,

I have set a Bayesian inversion, with a multiple output model, but the posterior distributions of my inputs raise questions. I am not sure of the relevance of my results.

Here is a description of my analysis:

- I have two inputs, E and c, which follow lognormal distributions.
- My model comes from a finite element software (ZSoil), with two outputs. It is surrogated with a PCK metamodel (Eloo ~ 10^-6 for both outputs).

I use the following code to create my inputs :

InputDist.Marginals(1).Name = āEā;

InputDist.Marginals(1).Type = āLognormalā;

InputDist.Marginals(1).Moments = [8000 2000];

InputDist.Marginals(2).Name = ācā;

InputDist.Marginals(2).Type = āLognormalā;

InputDist.Marginals(2).Moments = [10 ; 2];

myPriorDist = uq_createInput(InputDist);

To perform the inversion :

DiscrepancyOpts.Type = āGaussianā;

DiscrepancyOpts.Parameters = 0.5 ;myData.y = Observation (1,:);

Bayes.Type = āInversionā;

Bayes.Data = myData;

Bayes.Prior = myPriorDist;

Bayes.ForwardModel = my_PCK;

Bayes.Discrepancy = DiscrepancyOpts ;

myBayes_stg3 = uq_createAnalysis(Bayes);

The measurement (25 ; 12) is quite far from the mean predicted value (30,22).

When I look at the prior and posterior distributions of my inputs, I have the following graph:

My question is : is it possible, after a Bayesian inversion, that the standard deviation of an input increases ? On the graph, we can see that the standard deviation of c is higher after the inference. I thought, as the measurement brings information, that the standard deviation should be reduced.

I also have a technical remark : when I set the distribution of c to āconstantā, in order to study only the influence of E on the inference, the Bayesian inversion should run without updating c, as shows the user manual. It seems in this case, the following error appears (before the beginning of AIESās algorithm) :

Unrecognized property āModelā for class āuq_modelā.

Error in uq_initialize_uq_inversion (line 394)

ForwardModel(ii).Model = uq_createModel(ModelOpt,ā-privateā);Error in bayes_biais_uqlab (line 38)

myBayes_stg3 = uq_createAnalysis(Bayes_stage3);

It seems this message also appeared to @olaf.klein : is there something I can do to set c constant, without changing my model ?

Thanks a lot,

Marc Groslambert