Use `filldist` in coinflip example

[devmotion]

When updating some other tutorials, I noticed that maybe we should use (and hence somewhat promote) filldist already in the coinflip example.

I think it should be more well-known and used (even though I would still like to unify and extend it in Distributions), since it

• makes it easier to sample from the prior (without having to use missing and/or type parameters),
• should be efficient regardless of the AD backend (since it does not enforce the use of for loops but allows AD backends to use an optimized implementation)

[devmotion]

e.g. using arraydist and filldist

We could deprecate filldist right away and instead use arraydist(Fill(dist, N)) but it's a bit more (too?) verbose. Internally, actually Distributions.product_distribution(Fill(dist, N)) will result in exactly the same objects and behaviour as filldist(dist, N) for almost all distributions: https://github.com/TuringLang/DistributionsAD.jl/blob/48c43f8e8062ba95542330735593b5275117e592/src/filldist.jl#L9-L12

[yebai]

Personally, I'd depreciate filldist and encourage users to use arraydist(Fill(dist, N)) from now. If it is too verbose, we can perhaps consider sugar syntax like arraydist(dist, IID, N) where IID indicate the relationship between elements in the array?

[devmotion]

IMO arraydist(Fill(...)) would be a bit simpler and more consistent API. And also closer to something like product or product_distribution that we (hopefully) will use at some point.