Diagnostic plots for detecting autoregressive and non-stationary noise

[rccreswell]

@ben18785 and I have been looking at some additional diagnostic plots for residuals. These are helpful for detecting when an IID noise process is inadequate and correlation or non-stationary behaviour is present. Functionality for these plots could be added to Pints in the pints.residuals_diagnostics module.

Three diagnostics which could be added are:

1. The residuals are divided into bins, and the lag 1 autocorrelation within each bin is calculated. The binned autocorrelations are plotted over time.
2. Same as above, but looking at the variance within each bin.
3. A distance matrix between the residuals. When a banded structure appears in the distance matrix, this suggests that the true noise process may be autocorrelated.

[MichaelClerx]

Are these new ideas, or are they commonly used plots?

I think this is great work, but a bit worried how we're going to write documentation etc. without papers to refer to for details.

[ben18785]

@MichaelClerx these will be in Richard's paper that will be submitted soon. I don't think we should be too led by publications for what to include / not though; otherwise, the whole of Pints wouldn't really be in there ;)

[MichaelClerx]

Haha, fair enough! As long as the end result makes sense to outsiders I'm happy. (I guess the notebooks take care of that!)