I am fitting a model where unobserved parameters in a 2-simplex are transformed from a multivariate normal, then they generate the actual data. The relevant lines are not unlike
for (i in 1:N) {
z[i] ~ multi_normal_cholesky(mu, L); // 2-dimensional mv normal
a[i] = inv_logit(z[i][1]); // transform to [0,1]
b[i] = (1-a[i])*inv_logit(z[i][2]); // transform to make a simplex
// ... a[i] and b[i] unobserved, they are parameters to a multinomial
// ... that generates observations, omitted here
}
The multivariate normal is just a modeling device, I care about a
and b
. N
is around 1000, so the questions is how to visualize this. I thought of using HPD regions graphically. I could
- use the posterior mean of
mu
andL
, and visualize the conditionala
andb
based on that, or - I could use all the
a
andb
s, and plot HPD regions for that.
I am wondering which one makes more sense conceptually. (1) does not capture posterior uncertainty, while I think that (2) would overstate it.