# Turing equivalent of Stan/R model from StatisticalRethinking
**URL:** https://discourse.julialang.org/t/turing-equivalent-of-stan-r-model-from-statisticalrethinking/72092
**Category:** General Usage
**Created:** [November 26, 2021, 5:33am UTC](https://discourse.julialang.org/t/turing-equivalent-of-stan-r-model-from-statisticalrethinking/72092 "2021-11-26T05:33:08Z")
**Posts on this page:** 6
**Page:** 1
### Author:  [@amit1](https://discourse.julialang.org/u/amit1)
#### Post date: [November 26, 2021, 5:33am UTC](https://discourse.julialang.org/t/turing-equivalent-of-stan-r-model-from-statisticalrethinking/72092/1 "2021-11-26T05:33:08Z")
Consider the following STAN model from Chapter 12 of book Statistical Rethinking
```R
library(rethinking)
data(UCBadmit)
d <- UCBadmit
d$gid <- ifelse( d$applicant.gender=="male" , 1L , 2L )
dat <- list( A=d$admit , N=d$applications , gid=d$gid )
m12.1 <- ulam(
alist(
A ~ dbetabinom( N , pbar , theta ),
logit(pbar) <- a[gid],
a[gid] ~ dnorm( 0 , 1.5 ),
transpars> theta <<- phi + 2.0,
phi ~ dexp(1)
), data=dat , chains=4 )
```
Below is my equivalent Julia/Turing code:
```julia
using Turing, StatisticalRethinking
d = CSV.read(sr_datadir("UCBadmit.csv"), DataFrame)
d.gid = map((gender) -> (gender == "male" ? 1 : 2) , d.gender)
@model function m121(admit, applications, gid)
a = Vector{Real}(undef, 2)
ϕ ~ Exponential(1)
θ = ϕ + 2.0
a .~ Normal(0, 1.5)
for i = 1:length(gid)
p̄ = logistic(a[gid[i]])
admit[i] ~ BetaBinomial(applications[i], p̄, θ)
end
end
sample121 = sample(m121(d.admit, d.applications, d.gid), NUTS(), 2000)
describe(sample121)
```
However my parameter means are all off
```julia
Parameter Mean logit(mean)
1 :ϕ 0.211097
2 Symbol("a[1]") 1.84039 -
3 Symbol("a[2]") 1.57485 -
```
As opposed to the one given in the book
```julia
ulam posterior: 2000 samples from m12.1
mean sd 5.5% 94.5% histogram
a[1] -0.45 0.41 -1.1 0.21 ▁▁▇▇▂▁
a[2] -0.34 0.40 -1.0 0.27 ▁▁▃▇▂▁
phi 1.05 0.78 0.1 2.44 ▇▇▅▃▂▁▁▁▁▁▁
theta 3.05 0.78 2.1 4.44 ▇▇▅▃▂▁▁▁▁▁▁
```
1. What is wrong in my translation?
2. What is Turing equivalent of `transpars` in STAN?
From the book:
> transpars\> (transformed parameters) so that Stan will return it in the samples.
---
### Author:  [@nilshg](https://discourse.julialang.org/u/nilshg)
#### Post date: [November 26, 2021, 5:57am UTC](https://discourse.julialang.org/t/turing-equivalent-of-stan-r-model-from-statisticalrethinking/72092/2 "2021-11-26T05:57:16Z")
Have you looked at
[https://github.com/StatisticalRethinkingJulia/StatisticalRethinking.jl](https://github.com/StatisticalRethinkingJulia/StatisticalRethinking.jl)
---
### Author:  [@goedman](https://discourse.julialang.org/u/goedman)
#### Post date: [November 26, 2021, 2:11pm UTC](https://discourse.julialang.org/t/turing-equivalent-of-stan-r-model-from-statisticalrethinking/72092/3 "2021-11-26T14:11:42Z")
In particular [here](https://github.com/StatisticalRethinkingJulia/TuringModels.jl).
---
### Author:  [@amit1](https://discourse.julialang.org/u/amit1)
#### Post date: [November 26, 2021, 3:05pm UTC](https://discourse.julialang.org/t/turing-equivalent-of-stan-r-model-from-statisticalrethinking/72092/4 "2021-11-26T15:05:15Z")
While I admit I did miss the `beta-binomial.jl` file at first, it is not the exact model. model 12.1 uses two alpha parameters for males and females separately. Rest of the models use `BinomialLogit` so presume they are from previous chapter.
Also none shows a way to implement transpars equivalent.
---
### Author:  [@trahflow](https://discourse.julialang.org/u/trahflow)
#### Post date: [November 26, 2021, 3:26pm UTC](https://discourse.julialang.org/t/turing-equivalent-of-stan-r-model-from-statisticalrethinking/72092/5 "2021-11-26T15:26:57Z")
> [@amit1](#):
>
> What is Turing equivalent of `transpars` in STAN?
For that question see this discussion (tldr: There is a `generated_quantities()` function) :
> [@Traces of transformed variables within Turing.jl models](https://discourse.julialang.org/t/traces-of-transformed-variables-within-turing-jl-models/53013/7):
>
> Nice and thanks for the quick response @dlakelan! For future reference, here is the example from the [docs](https://docs.juliahub.com/DynamicPPL/2PWyN/0.10.16/autodocs/#DynamicPPL.generated_quantities-Tuple%7BModel,%20AbstractMCMC.AbstractChains%7D) using variational inference: using Turing using Optim using StatsPlots using Turing: Variational @model function demo(xs) s ~ InverseGamma(2, 3) m\_shifted ~ Normal(10, √s) m = m\_shifted - 10 for i in eachindex(xs) xs[i] ~ Normal(m, √s) end return (m, ) end q = vi(model, ADVI(10, 2000)) samples = rand(q, 1000) #NOTE: constructing the chain becomes sligh…
---
### Author:  [@amit1](https://discourse.julialang.org/u/amit1)
#### Post date: [November 26, 2021, 7:56pm UTC](https://discourse.julialang.org/t/turing-equivalent-of-stan-r-model-from-statisticalrethinking/72092/6 "2021-11-26T19:56:18Z")
Solved it. R has somewhat different functional parameters. In R function `dbetabinom` function is parameterized as
p(x) = \frac{C(N,x) \mbox{Beta}(x+\theta p,N-x+\theta(1-p))}% {\mbox{Beta}(\theta p,\theta(1-p))}%
where \theta is given explicitly as “dispersion parameter” and is multiplied to p implicitly. In PyMC3 and Turing, \alpha and \beta are required as shape parameters.
Therefore my implementation should be:
```julia
@model function m121(admit, applications, gid)
a = Vector{Real}(undef, 2)
ϕ ~ Exponential(1)
θ = ϕ + 2.0
a[1] ~ Normal(0,1.5)
a[2] ~ Normal(0,1.5)
for i = 1 : length(gid)
p̄ = logistic(a[gid[i]])
admit[i] ~ BetaBinomial(applications[i], p̄ * θ, (1-p̄) * θ)
end
end
```
which does agree with the book example.