How to define prior for inferences-for-correlations ?

[math4mad]

Follow Bayesian Cognitive Modeling_ A Practical Course

I want to try to define a turing model for correlations inference like this :
Correlation_1_Stan.R

using Turing , Random
using RCall

R"""
ma <- matrix(c( .8, 102, 
1.0,  98, 
 .5, 100,
 .9, 105, 
 .7, 103, 
 .4, 110,
1.2,  99, 
1.4,  87,
 .6, 113,
1.1,  89,
1.3,  93), nrow=11, ncol=2, byrow=T)
"""
ma=@rget ma

@model function cor_infer(df)
    n=11
    μ₁~Normal(1,30)
    μ₂~Normal(100,30)
    s ~ Gamma(1,1)
    σ = sqrt(s)
    
    r~Uniform(-1,1)
    for idx in 1:n 
         data=df[idx,1:2]
         data~ MvNormal([μ₁,μ₂] ,[σ^2 r*σ*σ; r*σ*σ  σ^2])
         
    end
end

model= cor_infer(ma)
chns = sample(model, NUTS(), 3_000)

but seems covariance matrix is not correctly, how to define covariance matrix with r?
I try prior using InverseGamma then sqrt, it is not working