Prior of matrix expressed as vector : lead to the degradation of the n_eff

Modeling
1

Hi everyone!
I would like to optimize my code but I don’t succeed for now :

I my current code, I have a parameter that is expressed as a matrix, and I specify the prior of each component of the matrix using a loop : but it’s pretty slow. It looks like that :


parameters{
matrix[N,L]  mu; 
...
}

model{
    for(i in 1:N){
        for(j in  1:L){
        mu[i,j] ~ normal(0,1);
        ...
  }
 }   
}

I read in Specifying priors for a matrix that I could use the function to_vector to express the prior of a matrix in a quicker way. So It would be :


parameters{
matrix[N,L]  mu; 
...
}

model{
    for(i in 1:N){
        for(j in  1:L){
        ...
  }
 }
 to_vector(mu) ~ normal(0,1);
}

The code do compile and is way faster, however the n_eff are way smaller. So I was wondering if the code was correct? And If there is another way to optimize the run time without damaging the n_effective,

Thank you in advance for the help!

2

I don’t think it should have an effect. How smaller? Have you tried running it multiple times? If the model has a problematic posterior, some runs might be much worse than others even of the same model depending the initial values.

3

For both code, I had 500 iterations with 250 warm-up and 4 chains.

For the first code with the loop, I obtained those n_eff
image

For the second code with the to_vector prior, I obtained those n_eff
image

(the codes that I posted is a simplyfication of the actual code, as it’s the only part that is modified from the “loop code” to the “to_vector code”. The initial values and the data are the same).

I’m going to try to run those code with other initial values to see if the issue remains

4

That’s very likely not enough warmup iterations for the adaptation to complete, which would explain the unstable results. Can you try running it with the default 1000+1000 iterations?

5

Running the same code with 2000 iterations and 1000 warm-up with 4 chains also lead to quite different n_eff :
For the first code with the loop, I obtained those n_eff :
image
For the second code with the to_vector prior, I obtained those n_eff:
image