update example to the latest microphysics

[trontrytel]

Hi. I have updated the example code to the latest CM.jl version. The example runs, but the convergence of the calibration is not as good as it used to be.

I'll take another look at the microphysics code. But @odunbar could you also look at how we use the EKP package? Maybe something needs to be changed there as well?

Not-sure-if-closes #306

[trontrytel]

Here are the old plots:

And here are the new: molar_mass_average.pdf molar_mass_scatter.pdf osmotic_coeff_average.pdf osmotic_coeff_scatter.pdf

[odunbar]

I think that the EKP tools are working fine. I'm confident that the issue is that the data is uninformative about the osmotic coefficient. Thus the inverse problem can only learn about the molar mass. This is true even in the original code.

To express this, by shrinking the data noise standard deviation by a factor of 100 the molar mass converges always to the true value, while the osmotic coefficient varies and drifts around whatever the prior mean was set to.

To go back to the original plots, we see that the osmotic coeff wasn't really converging either, I think it was just a coincidence it looked like convergence, by playing with random seed I have also got plots where it looks like its going to the truth over many iterations, but drift away afterwards, this illusion is strengthened when the prior mean was set quite close to the truth.

[odunbar]

PS Here is one with the prior mean increased to 2.0 (spread 0-100) or with prior mean decreased to 0.1 spread (0-5) In all these plots the covariance-weighted data-misfit was decreasing by a lot

[odunbar]

@trontrytel any movement on this one?