Trans-MCMC for joint space across different models

[hyunjimoon]

Problem: Parameters in model1 do not appear in model2. Exploration happens on joint space of every parameters within the model network.

Suggestion: use transformed parameters block to conditioned parameters as below
From

data {
  int N;
  vector[N] y;
}
parameters {
  real<lower=0> sigma;
}
...

To

data {
  int N;
  vector[N] y;
}
parameters {
  real<lower=0> sigma;
  real<lower=0> mu;
}
transformed parameters{
  real<lower=0> mu;
  mu = 0
}
model {
  sigma ~ lognormal(0, 1);
  y ~ normal(mu, sigma);
}

[rybern]

I can see the argument for this, but I think I'd rather we try to handle the different parameter sets in the wrappers rather than in the core algorithm itself. Do you think that'll be doable?

To me, the issue would be that when any model in the network adds a parameter, all of the models (or I suppose only programs) in the network are affected. That's a sort of unexpected non-local effect to me; I would expected a small change to have a small effect. I think adding parameters may also impact sampling.