Validation of inverse problem solution based on Bayesian method

Question

Recently, I read a paper about the inverse problem and parameter estimation. The main approach of the paper is based on the Bayesian method. The answer in this method is a posterior probability density function.

Part of the paper describes: "The validation of obtained results is important. We have to verify that they make sense and don't simply trust our results."

There is no more information due to results validation is out of paper scope. I searched and found some articles. But the math of articles is above my knowledge.

Can someone illustrate the results validation concept in a simple way?

I want to know simply what it said and how it works.

Link of article

Answer 1

As a concept, the idea is pretty simple. Do the results make sense? Creating a numerical example, or doing it for that matter, isn't trivial.

Bayesian hypotheses are combinatoric. While Frequentist methods only have a null and an alternative, Bayesian hypotheses are mutually exclusive and exhaustive. That can lead to many potential models to test.

Now imagine that you are testing a physical process, and the dense region of your estimate for some parameter is $9.1<\mu_x<9.9.$ You know that if $\mu_x\approx{9.1}$, or greater, then the object you are using should tear apart because the tensile strength of the materials wouldn't handle that. Nonetheless, the object you are testing is in good shape.

That would imply that this model is wrong. If that is your best model, then all may be wrong, and you need to consider models in addition to the models you have already built.

That type of reality check requires a domain expert. If you were testing the object and were not an engineer or materials scientist, then you need to get one and find out what you are doing wrong.