Bug? - or at least curious behaviour (different behaviour from trivially different implementations of the same model)

General
1

I have just noticed a bit of curious behaviour, and I would be interested to know what is going on.
I have a model (for fitting a Poisson process) that runs cleanly implemented one way but generates a slew of warnings (though the final result is no different) when implemented another so far as I can see trivially different way.

The core of the model is W, a vector of Gaussians, with variance W_s.

If I implement this as:

transformed parameters {
…[W[i] * W_s…
}
model {
…
W_s ~ normal(A, B);
W ~ std_normal();
…
}

Then everything is fine. If instead, I implement

transformed parameters {
…[W[i]]…
}
model {
…
W_s ~ normal(A, B);
W ~ normal(0, W_s);
…
}

I get a slew of warnings (Bayesian Fraction of Missing Information was low, Bulk effective samples size too low, tail effective sample size too low), and obvious linear correlation between W_s and energy__ in the pairs plot.

As far as I can see, the two implementations should be identical, so can anybody tell me what I am missing.

1 Like
2

You’ve rediscovered the centered/non-centered parameterization issue. There should be a section on it in the modeling manual.

1 Like
3

Thanks - learn something every day - I didn’t realise it applied in that circumstance.
Very interesting.

4

See here for thorough discussion of the centered/non-centered distinction.