I have a very simple Turing model where all variables are Normal or TruncatedNormal. For some reason, the summary statistics of the model are not the ones I expected. Can you please help with this MWE?

```
using Turing
using Distributions
using LinearAlgebra
using Random
@model function Model(X, Y, params)
# size of design matrix
n, p = size(X)
# hyperparameters
σF = params.σF
σP = params.σP
σM = params.σM
τF = params.τF
τP = params.τP
τM = params.τM
cF = params.cF
cP = params.cP
cM = params.cM
αF ~ Normal(cF, σF)
αP ~ Normal(cP, σP)
αM ~ Normal(cM, σM)
βF ~ MvNormal(τF^2 * I(p))
βP ~ MvNormal(τP^2 * I(p))
βM ~ MvNormal(τM^2 * I(p))
for i in 1:n
x = view(X, i, :)
NF = Normal(αF + βF⋅x, σF)
NP = Normal(αP + βP⋅x, σP)
NM = Normal(αM + βM⋅x, σM)
Y[i, 1] ~ Truncated(NF, 1000.0, 4000.0)
Y[i, 2] ~ Truncated(NP, 0.0, Y[i, 1])
Y[i, 3] ~ Truncated(NM, 0.2, 1.8)
end
end
# ------------
# MAIN SCRIPT
# ------------
Random.seed!(2021)
X = randn(100, 10)
Y = [2200 80 1] .+ randn(100, 3)
params = (
σF=80.0, σP=3.0, σM=0.07,
τF=80.0, τP=3.0, τM=0.07,
cF=2365.67, cP=81.86, cM=0.93,
A=106.0
)
model = Model(X, Y, params)
prior = sample(model, Prior(), MCMCThreads(), 125, 8)
```

The summary statistics say that the betas have non-zero mean:

```
Summary Statistics
parameters mean std naive_se mcse ess rhat ess_per_sec
Symbol Float64 Float64 Float64 Float64 Float64 Float64 Float64
αF 2367.5469 77.2003 2.4413 1.9845 1050.1537 0.9952 252.4408
αP 81.8590 3.0893 0.0977 0.1060 970.1233 0.9982 233.2027
αM 0.9303 0.0677 0.0021 0.0025 943.5514 1.0003 226.8152
βF[1] 1.6034 80.3508 2.5409 2.2824 1023.2686 0.9990 245.9780
βF[2] -3.7451 82.0924 2.5960 2.5802 961.3972 1.0008 231.1051
βF[3] 1.1207 80.0799 2.5323 2.7361 1018.4947 0.9976 244.8304
βF[4] -1.6076 78.7029 2.4888 2.3270 1082.2488 0.9969 260.1560
βF[5] -2.7930 79.1165 2.5019 2.5547 893.2253 0.9989 214.7176
βF[6] -2.7102 79.5150 2.5145 1.8956 986.7812 0.9955 237.2070
βF[7] -2.7330 80.4840 2.5451 2.4614 1180.3496 1.0000 283.7379
βF[8] -0.6590 79.4045 2.5110 2.6443 1043.9858 1.0049 250.9581
βF[9] -3.1116 82.5449 2.6103 2.4207 1066.4970 0.9977 256.3695
⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮
21 rows omitted
```

Am I missing something? I’ve been debugging this code for hours and can’t find out why it is not producing betas with zero mean.