Update to Turing 0.38

[penelopeysm]

generated_quantities was deprecated quite a few DPPL versions ago, so I replaced it with returned, and also added a section talking about :=.

Also replaced TuringBenchmarking with in-house DPPL benchmarking.

Also removed Zygote from the list of 'officially supported'. Technically, this would have been done in #595, but I'm slow on getting that merged.

Also added a reference to ADTests.

Also fixed some other dead links.

[github-actions]

Preview the changes: https://turinglang.org/docs/pr-previews/599
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[mhauru]

Looks great, only a couple of optional-to-attend-to suggestions.

[penelopeysm]

Moving on, we generate samples from the posterior using the default NUTS sampler. We’ll make use of ReverseDiff.jl, as it has better performance than ForwardDiff.jl on this example. See Turing.jl’s docs on Automatic Differentiation for more info.

I just benchmarked this one, interesting - cc @willtebbutt as you might like this example where Mooncake absolutely blows RD out of the water

distances = [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]
ns = [1443, 694, 455, 353, 272, 256, 240, 217, 200, 237, 202, 192, 174, 167, 201, 195, 191, 147, 152, ]
ys = [1346, 577, 337, 208, 149, 136, 111, 69, 67, 75, 52, 46, 54, 28, 27, 31, 33, 20, 24]

using AbstractGPs, LogExpFunctions, Turing
@model function putting_model(d, n; jitter=1e-4)
    v ~ Gamma(2, 1)
    l ~ Gamma(4, 1)
    f = GP(v * with_lengthscale(SEKernel(), l))
    f_latent ~ f(d, jitter)
    y ~ product_distribution(Binomial.(n, logistic.(f_latent)))
    return (fx=f(d, jitter), f_latent=f_latent, y=y)
end
m = putting_model(Float64.(distances), ns)

ForwardDiff 17.60233918128655
ReverseDiff 120.82069565217394
ReverseDiffCompiled 31.189760856427522
Mooncake 5.9673639441020745

(Enzyme forward and reverse both error)