Hi I’m using the Iris dataset, to try and do inference on the mixtures for each of the 3 species.

I’m using pystan.

They Idea is as followed: the input i the 150x4 matrix, 4d features of the plants. I want to find a 4d beta to get y a 150x1 vector of the new 1d feature, then on this y to do a 3 components gmm.

my stan code is:

```
data {
int<lower=0> N; // number of data points
int<lower=1> K; //initial number of features
matrix[N,K] x; //original features matrix
real pmubeta; // prior mean for beta
real psbeta; // prior std for beta
real psmu; // prior for mu std - for control without recompile model
real pssigma;// prior for sigma std - for control without recompile model
}
parameters {
vector[K] beta;
ordered[3] mu;
real<lower=0> sigma[3];
simplex[3] theta;//prob. of each component of the GMM
}
model {
vector[N] y;
beta ~ normal(pmubeta, psbeta);
mu ~ normal(0, psmu);
sigma ~ lognormal(0, pssigma);
y = x*beta;
for(i in 1:N){
real lp[3];
for (j in 1:3)
lp[j] = log(theta[j]) + normal_lpdf(y[i] | mu[j], sigma[j]);
target += log_sum_exp(lp);
}
}
```

to get the priors for the beta I do PCA and use the mean of the first eigen vector. (for the pmubeta)

for the other priors of psbeta,psmu,pssigma I tried all kind of values.

my Issue is that the fitting/sampling takes for ever and I get this warnings:

WARNING:pystan:n_eff / iter below 0.001 indicates that the effective sample size has likely been overestimated

WARNING:pystan:Rhat above 1.1 or below 0.9 indicates that the chains very likely have not mixed

WARNING:pystan:3902 of 4000 iterations saturated the maximum tree depth of 10 (97.5 %)

WARNING:pystan:Run again with max_treedepth larger than 10 to avoid saturation

WARNING:pystan:Chain 1: E-BFMI = 0.184

WARNING:pystan:Chain 4: E-BFMI = 0.0712

WARNING:pystan:E-BFMI below 0.2 indicates you may need to reparameterize your model

so I guess the problem is with my priors, but I’m not sure…

also I get the following trace plot when using arviz:

Note:

I also tried to use init for the mu values to keep the mixture components identifiable

If anyone can help it will be great!

Thanks a lot!