Implement vb and adapt interface

[seabbs]

This PR combines updating the package interface (based on #73 and feedback from @pearsonca) with added support for variational inference (#72). It contains breaking changes that will impact all downstream users but substantially simplify the end-user experience whilst adding the ability for future extensions. See the updated readme and examples for new implementation details.

Changes

• stan arguments now passed using stan_args with defaults from create_stan_args
• generation times and incubation periods now stored in a generalised package data table
• Added access functions for the generation time and incubation period to smooth access
• Removed spurious arguments in examples
• Removed testing arguments and embedded in stan_args as undocumented features (i.e stuck_chains).
• Add support for variational bayes (method = "approximate").

Relevant to: @kathsherratt @pearsonca @joeHickson @jhellewell14

[seabbs]

Example using variational inference with standard defaults (but using 10 trials in case of algorithm failure). It is likely that there are better defaults (i.e slower but more conservative) but no info on what these are at the moment.

Via NUTs (run time 100 ~ 200 times longer).

[joeHickson]

I'm starting a review on this one but it seems to be a lot of tickets joined into one PR. @seabbs please can you try and keep them to separate branches for future changes? 48 files, +1018 lines, -101,232 lines is not a good sign for me being able to hold it all in my head (even if -100,001 is one file being removed) ;)

edit - I can see they may be intertwined so hard to split

[seabbs]

Unfortunately, supporting VB required a large-scale interface change so this is a minimal PR.

[seabbs]

Any issues with this @joeHickson or happy for me to merge in?

[joeHickson]

still reviewing!

[joeHickson]

(and yes, I have left comments but because it's mid-review I don't think it's exposed them to you yet)

[joeHickson]

We should have a chat about code styling standards on the call later - there's a few bits in here that change from one style to another with regards line breaks and it slows down the review a bit.

one or two minor bits and a couple of larger ones, notably:

The stan_args generation method is a bit wierd in the way some properties are native arguments and others are a list that is passed in (as stan_args), and then the calling places treat both the original stub list and the returning object as stan_args. I can see this is to do with how you pass the list of user defined options in to where it's generated. I have suggested some R6 objects but there are other ways around this one (including other structures of R6 objects), but if the current structure is kept some renaming should be done to clarify when the list is a stan_args stub and when it's a full stan_args list.

The use of magic strings is something that I spotted whilst reviewing - this task adds a few more. Suggestions as to how can be found on incubation-period.R but again there are multiple ways to crack this nut.

[seabbs]

Thanks for the review @joeHickson.

Addressed the minor issue with stan_args and opened a few issues based on review comments that I think warrant further discussion/there own PR. Happy to see an issue on the magic strings comment as well.

Merging this now as I think the main features are in place and will bring some solid user benefits.