Fast computation of the Normal-IW marginal likelihood.

This is the numerator of the Bayes factor: assume that all observations come from the same source. To be called by the R wrapper.

marginalLikelihood_internal(
  X,
  n_iter,
  B_inv,
  W_inv,
  U,
  nw,
  mu,
  burn_in,
  chain_output = FALSE,
  verbose = FALSE,
  Gibbs_only = FALSE
)

Arguments

X	the observation matrix ($n \times p$: n = observation, p = variables) @param U covariance matrix for the mean ($p \times p$)
n_iter	number of MCMC iterations excluding burn-in
B_inv	prior inverse of between-source covariance matrix
W_inv	initialization for prior inverse of within-source covariance matrix
nw	degrees of freedom
mu	prior mean ($p \times 1$)
burn_in	number of MCMC burn-in iterations
chain_output	if true, output the entire chain as a list (ML-value, samples from theta, samples from W_inv)
verbose	if TRUE, be verbose
Gibbs_only	if TRUE, only return the Gibbs posterior samples. Implies `chain_output = TRUE`.

Normal-Inverse-Wishart model

Described in (Bozza et al. 2008) .

Observation level:

$$X_{ij} \sim N_p(\theta_i, W_i)$$ (i = source, j = items from source)

Group level:

$$\theta_i \sim N_p(\mu, B)$$
$$W_i \sim IW_p(\nu_w, U)$$

Hyperparameters:

$$B, U, \nu_w, \mu$$

Posterior samples of $\theta$, $W^{(-1)}$ can be generated with a Gibbs sampler.

X	the observation matrix (\(n \times p\): n = observation, p = variables) @param U covariance matrix for the mean (\(p \times p\))
n_iter	number of MCMC iterations excluding burn-in
B_inv	prior inverse of between-source covariance matrix
W_inv	initialization for prior inverse of within-source covariance matrix
nw	degrees of freedom
mu	prior mean (\(p \times 1\))
burn_in	number of MCMC burn-in iterations
chain_output	if true, output the entire chain as a list (ML-value, samples from theta, samples from W_inv)
verbose	if TRUE, be verbose
Gibbs_only	if TRUE, only return the Gibbs posterior samples. Implies `chain_output = TRUE`.

Arguments

Normal-Inverse-Wishart model

See also