library(rstan)

# sim observations
library(gtools)
y <- rdirichlet(50,c(10,2,5))

# model
dir_model <- "
data{
    int N;
    matrix[N,3] y;
}
parameters{
    vector<lower=0>[3] alpha;
}
model{
    alpha ~ normal(10,1);
    for ( i in 1:N ) y[i,]' ~ dirichlet(alpha);
}
"

m0 <- stan( model_code=dir_model , data=list(N=50,y=y) )