Default chains backend

[penelopeysm]

As I mentioned in #16 (review), Turing's default chain backend is now FlexiChains.jl rather than MCMCChains.jl. There are many reasons for this -- I am biased because I wrote FlexiChains ;) but I do think it's better.

There is absolutely no obligation for you to follow suit of course. I think it would be good to ensure that the package does work with FlexiChains, but whether you want it to be a default or not is a stronger question, and that is completely up to you. I see three possible pathways that ParallelMCMC could take:

1. Keep MCMCChains as the default, and make things work with FlexiChains. This would just entail adding a FlexiChainsExt, and probably also a DynamicPPLFlexiChainsExt. (We'd need two different extensions unfortunately to deal with the different cases where people sample either an arbitrary LogDensityProblems.jl-compatible model, or a DynamicPPL model.)

2. Make FlexiChains the default, and move the MCMCChains code to an MCMCChainsExt + DynamicPPLMCMCChainsExt.

3. Be completely agnostic, and have a zoo of extensions for each chains backend! This sounds silly, and it is probably a bit silly, but it does mean that your dependency chain will be slimmer. Both MCMCChains and FlexiChains will pull in some deps that you probably don't care about.

As mentioned I am biased and I would say my order of preference is (2) > (1) > (3), but it is very much up to you :)

[rsenne]

I looked through FlexiChains.jl and the reasons why its better--and I agree. Let's make FlexiChains.jl the default :)

[penelopeysm]

I just wanted to say this is still on my radar and I can do a PR for this some time, however I want to sort out penelopeysm/FlexiChains.jl#181 first as it should give us a nicer API to work with!

[rsenne]

Thanks so much! I really appreciate the help--and no worries, your projects take priority :)

I will shamelessly ask however, if its alright if i ask you to review code periodically? You're more than welcome to say no, (i'd even encourage you to say no if you have too much on your plate!), but right now this is a one-person show, so I'd have greater piece of mind knowing at least someone has looked over what I've done (e.g., the current draft PR that overhauls the AD of this package).

In return I'm happy to help out on FlexiChains, I like the project, and have had the opportunity to use it when I fit some Bayesian models this weekend, and overall I like contributing to the ecosystem where i can. Food for thought!

[penelopeysm]

I can't guarantee a thorough review or indeed any review, but you can always ping and ask, there is no problem with that :) Generally I've found that the Julia community is really nice and you can usually ask people who know the relevant packages to take a look. So it doesn't just have to be me!