Multi-variate half-normal or half-student-t distribution

Hi, is it possible to specific a multi-variate half-normal or half-student-t distribution? As a matter of fact, is the uni-variate half-N(0,1) a real Stan syntax? I saw it in the Prior Recommendation page but I cannot find it in the manual to learn more about it. Thanks.

data {
  int <lower = 1> N;
}
parameters {
  vector <lower = 0> [N] x;
}
model {
  target += normal_lpdf(x | 0.0, 1.0);
}

specifies an N-dimensional half-normal prior on x.

Hi, this is not what I was after. I am looking for a correlated half-normal or correlated half-student-t distribution in N-dimensional space. Sorry for not being clear.

Is the covariance matrix of the half-(normal | Student-t) distribution a parameter or is it part of the prior?

If it is a parameter, then a multivariate normal, defined in terms of the Cholesky factor of its covariance matrix, truncated at 0 can be coded as:

data {
  int <lower = 1> N;
}
transformed data {
  vector [N] zero_vec = rep_vector(0.0, N);
}
parameters {
  vector <lower = 0> [N] x;

  // Cholesky
  cholesky_factor_corr [N] L_omega;
  // vector of prior standard deviations
  vector <lower=0> [N] L_sigma;
}
model {
  target += multi_normal_cholesky_lpdf(x | zero_vec, diag_pre_multiply(L_sigma, L_omega));
  target += lkj_corr_cholesky_lpdf(L_omega | 5.0);
  target += normal_lpdf(L_sigma | 0.0, 1.0);
}

If it is part of the prior, then L_omega and L_sigma could be computed in the transformed data block, or outside of Stan.

I don’t actually know how to answer your question. But I have duration data on the individuals, but for multiple events. My analysis is to model the each time-to-event using exponential or Weibull distribution. However, the parameters for distributions between events are correlated. Since the parameters are positive for exponential or Weibull distribution, I believe I need to use a multi-variate distribution restricted to the positive numbers. Thanks

Tricky! Some follow up questions (though I think we are getting a bit off topic here):

  • Do you have any covariates? Or just the individual, event type, and time from study entry to event?
  • Is the set of events the same for all individuals? Perhaps you could build some kind of model?

If you want to ask more questions about your data / possible model, then I’d recommend starting a new topic :)

2 Likes

Hey there, check out the link above. Maybe that’s what you need?

Cheers,
Max