Scaling of ppc_dens_overlay for prior predictive distribution

Modeling
1

Hi all,

I’m using the following code to generate a prior predictive distribution

priorpred<-"

data {
int n;
}
parameters {
real<lower=0> mu;
real<lower=0> sigma;
}

model {
// priors
mu ~ normal(400,10);
sigma ~ cauchy(0,3);
}

generated quantities {
vector[n] prior_rep;

// prior predictive

for(i in 1:n) {
prior_rep[i] = normal_rng(mu,sigma);
  }
}

"
m1priorpred<-stan(model_code=priorpred,
                  data=data.list,
                  chains = 4,
                  iter = 5000)


prior_rep <- as.matrix(m1priorpred,pars="prior_rep")
plot <- ppc_dens_overlay(data.list$readscore,prior_rep[1:50,])
plot + lims(x=c(300,800),y=c(0,.009))

Everything seems to be fine, but when using ppc_dens_overlay, I get the plot as shown in the attachment.
Rplot.pdf (44.1 KB)

The plot is sensible give the parameters of the prior, but the height of the plot seems strange and I have tried many values for the ylim to correct this to no effect. I’m probably missing something and would appreciate any advise.

Thanks in advance,

David

2

Note that your observed data ranges from ~300 to ~800, but your model priors are implying that the SD around the mean is given by a cauchy(0,3) distribution - which is comparatively very narrow.

This is why your prior predictive plots have such large ‘heights’ - the prior on sigma implies that all observations should be very narrowly distributed around the mean mu, resulting in the density being concentrated in a narrow range and giving such a tall plot