Single MCMC update to Student's t-distribution

Samples the degrees of freedom parameter of standardized and homoskedastic t-distributed input variates. Marginal data augmentation (MDA) is applied, tau is the vector of auxiliary latent states. Depending on the prior specification, nu might not be updated, just tau.

update_t_error(
  homosked_data,
  tau,
  mean,
  sd,
  nu,
  prior_spec,
  do_tau_acceptance_rejection = TRUE
)

Arguments

homosked_data	de-meaned and homoskedastic observations
tau	the vector of the latent states used in MDA. Updated in place
mean	the vector of the conditional means // TODO update docs in R
sd	the vector of the conditional standard deviations
nu	parameter nu. The degrees of freedom for the t-distribution. Updated in place
prior_spec	prior specification object. See type_definitions.h
do_tau_acceptance_rejection	boolean. If TRUE, there is a correction for non-zero mean and non-unit sd, otherwise the proposal distribution is used

Details

The function samples tau and nu from the following hierarchical model: homosked_data_i = sqrt(tau_i) * (mean_i + sd_i * N(0, 1)) tau_i ~ InvGamma(.5*nu, .5*(nu-2)) Naming: The data is homoskedastic ex ante in the model, mean_i and sd_i are conditional on some other parameter in the model. The prior on tau corresponds to a standardized t-distributed heavy tail on the data.

See also

Other stochvol_cpp: update_fast_sv(), update_general_sv(), update_regressors()