Motivational example

[TTitscher]

This motivation is certainly correct, but could be improved by an example to follow along. As @aklawonn wants to tackle this, his current wood compression tests (using dummy data) could be this example. Another idea of mine would be a concrete bridge where one model is the full bridge (1D beam...) with displacement/inclination sensors, another one is a compression test from multiple drilled, cylindrical core samples. Maybe, @aklawonn, you can update us on the general idea here in this issue.

Anyways, we should illustrate:

• the advantages of named parameters
• that not every parameter must be latent
• how one (expensive forward) model can return several outputs in a structured way
• that we can combine multiple model errors (aka experiments?)
• that parameters of multiple experiments can be inferred simultaneously
• the complexity of the example, e.g. by writing down the loglike for the problem (10+ terms! :smile: ) and sketching the laborious and error-prone process of changing things in there
• interface to several solvers (VB algorithm, taralli, pymc3,...)

What else?

IMO the challenge will be to introduce the features above in a reasonable order. I have some kind of multi-step example in mind that increases in complexity. Starting with a simple loglike example that is familiar to the reader, introduce named parameters next, combine two examples and so on and so on.

[joergfunger]

That sounds good, maybe having a notebook type of documentation would be good here.