Looking for a way to specify a truncated lognormal prior to improve performance

[hhau]

Your parameters that have lognormal priors need <lower = 0> bounds, as well as any additional truncation you wish to specify. See here.

@rjc10

it’s completely possible for a draw from the prior for alpha_8_1, alpha_8_4, or both to lie outside the range allowed by the parameter’s constraint.

The MCMC sampler does not draw from the prior distribution. Additionally, I don’t see how the traceplots that follow demonstrate the latter point?

@rjc10

I think that I could deal with the lower bound for alpha_8_4 by writing something like this:

parameters {
  real <lower = 2.2> alpha_8_4;
}

already constraints alpha_8_4 to be greater than 2.2.

@rjc10

But then how do I specify the prior for alpha_8_1 to avoid getting draws greater than the threshold, 2.2?

parameters {
  real <lower = 0, upper = 2.2> alpha_8_1;
}

model {
  alpha_8_1 ~ lognormal(mu_alpha, sigma_alpha);
}

The declared bounds will constrain alpha_8_1 to be between [0, 2.2]. Placing the lognormal distribution on alpha_8_1 just changes the shape of the prior from uniform between [0, 2.2] to having truncated lognormal between [0, 2.2].

@rjc10

Note that to get a model like this one to work, I need to force the initial values to satisfy the constraints. Here’s some R code for that:

You shouldn’t need to do this once you change the parameter declarations to have appropriate bounds.

Higher level thoughts: relabeling quickly becomes infeasible, you need to reparametrize / break the symmetry in the model in order to ensure accurate estimation. Also I’m not sure what you mean by rotational invariance?