Plotting credible intervals in Julia from Turing model - julia

Question

Ok so I figured out how to plot the credible intervals for a univariate linear model in Turing.jl using the following code (I'm replicating Statistical rethinking by McElreath) This particular exercise is in chapter 4. If anyone has already plotted these types of models with Turing and can give me a guide, it would be great!!!
Univariate model code:
using Turing
using StatsPlots
using Plots
height = df2.height
weight = df2.weight
#model heightmodel(y, x) = begin
#priors
α ~ Normal(178, 100)
σ ~ Uniform(0, 50)
β ~ LogNormal(0, 10)
x_bar = mean(x)
#model
μ = α .+ (x.-x_bar).*β
y ~ MvNormal(μ, σ)
end
chns = sample(heightmodel(height, weight), NUTS(), 100000)
## code 4.43
describe(chns) |> display
# covariance and correlation
alph = get(chns, :α)[1].data
bet = get(chns, :β)[1].data
sigm = get(chns, :σ)[1].data
vecs = (alph[1:352], bet[1:352])
arr = vcat(transpose.(vecs)...)'
ss = [vec(alph + bet.*(x)) for x in 25:1:70]
arrr = vcat(transpose.(ss)...)'
plot([mean(arrr[:,x]) for x in 1:46],25:1:70, ribbon = ([-1*(quantile(arrr[:,x],[0.1,0.9])[1] - mean(arrr[:,x])) for x in 1:46], [quantile(arrr[:,x],[0.1,0.9])[2] - mean(arrr[:,x]) for x in 1:46]))
Credible interval Univariate:
However, when I try to replicate it with a multivatiate function, very strange things are drawn:
Multivariate model code:
weight_s = (df.weight .-mean(df.weight))./std(df.weight)
weight_s² = weight_s.^2
#model heightmodel(height, weight, weight²) = begin
#priors
α ~ Normal(178, 20)
σ ~ Uniform(0, 50)
β1 ~ LogNormal(0, 1)
β2 ~ Normal(0, 1)
#model
μ = α .+ weight.*β1 + weight².*β2
height ~ MvNormal(μ, σ)
end
chns = sample(heightmodel(height, weight_s, weight_s²), NUTS(), 100000)
describe(chns) |> display
### painting the fit
alph = get(chns, :α)[1].data
bet1 = get(chns, :β1)[1].data
bet2 = get(chns, :β2)[1].data
vecs = (alph[1:99000], bet1[1:99000], bet2[1:99000])
arr = vcat(transpose.(vecs)...)'
polinomial = [vec(alph + bet1.*(x) + bet2.*(x.^2)) for x in -2:0.01:2]
arrr = vcat(transpose.(polinomial)...)'
plot([mean(arrr[:,x]) for x in 1:401],-2:0.01:2, ribbon = ([-1*(quantile(arrr[:,x],[0.1,0.9])[1] - mean(arrr[:,x])) for x in 1:46], [quantile(arrr[:,x],[0.1,0.9])[2] - mean(arrr[:,x]) for x in 1:46]))
Credible interval Univariate:

Answer 1

In the Julia Slack channel (https://slackinvite.julialang.org/) Jens was kind enough to give me the answer. The credit goes to him --He doesn't have a SO account.
The main problem was that I was lacking simplicity and was trying to plot the mean the wrong way --in a very inefficient and strange way might I add. Each parameter has a vector which corresponds to 99000 draws from the posterior distribution, I was trying to draw the mean through the matrix but it's much easier to define the median first and then plot it, then you don't make mistakes as I did calculating the mean.
old code
vecs = (alph[1:99000], bet1[1:99000], bet2[1:99000])
arr = vcat(transpose.(vecs)...)'
[mean(arrr[:,x]) for x in 1:401]
can be written as:
testweights = -2:0.01:2
arr = [fheight.(w, res.α, res.β1, res.β2) for w in testweights]
m = [mean(v) for v in arr]
Moreover, the way Jens defined the Credible intervals is much more elegant and Julianic:
Jens' code:
quantiles = [quantile(v, [0.1, 0.9]) for v in arr]
lower = [q[1] - m for (q, m) in zip(quantiles, m)]
upper = [q[2] - m for (q, m) in zip(quantiles, m)]
My code:
ribbon = ([-1*(quantile(arrr[:,x],[0.1,0.9])[1] - mean(arrr[:,x])) for x in 1:46], [quantile(arrr[:,x],[0.1,0.9])[2] - mean(arrr[:,x]) for x in 1:46]))
Complete Solution:
weight_s = (d.weight .-mean(d.weight))./std(d.weight)
height = d.height
#model heightmodel(height, weight) = begin
#priors
α ~ Normal(178, 20)´
σ ~ Uniform(0, 50)
β1 ~ LogNormal(0, 1)
β2 ~ Normal(0, 1)
#model
μ = α .+ weight .* β1 + weight.^2 .* β2
# or μ = fheight.(weight, α, β1, β2) if we are defining fheigth anyways
height ~ MvNormal(μ, σ)
end
chns = sample(heightmodel(height, weight_s), NUTS(), 10000)
describe(chns) |> display
res = DataFrame(chns)
fheight(weight, α, β1, β2) = α + weight * β1 + weight^2 * β2
testweights = -2:0.01:2
arr = [fheight.(w, res.α, res.β1, res.β2) for w in testweights]
m = [mean(v) for v in arr]
quantiles = [quantile(v, [0.1, 0.9]) for v in arr]
lower = [q[1] - m for (q, m) in zip(quantiles, m)]
upper = [q[2] - m for (q, m) in zip(quantiles, m)]
plot(testweights, m, ribbon = [lower, upper])