marginalLikelihood_internal: Fast computation of the Normal-IW marginal likelihood.

In lgaborini/bayessource: Bayesian approach to evaluate whether two datasets come from the same population

Description

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

Usage

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 x p): n = observation, p = variables) @param U covariance matrix for the mean (p x 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 x 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 \insertCiteBozza2008Probabilisticbayessource.

Observation level:

• X_{ij} ~ N_p(theta_i, W_i)

  (i = source, j = items from source)

Group level:

• theta_i ~ N_p(μ, B)

• W_i ~ IW_p(n_w, U)

Hyperparameters:

• B, U, n_w, μ

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

See Also

Other C++ functions: chol2inv(), diwishart_inverse(), dmvnorm(), inv_Cholesky_from_Cholesky(), inv_sympd_tol(), inv_triangular(), isCholeskyOn(), ldet_from_Cholesky(), logCummeanExp(), logCumsumExp(), logSumExpMean(), logSumExp(), rmvnorm(), rwish()

Other core functions: bayessource-package, get_minimum_nw_IW(), make_priors_and_init(), marginalLikelihood(), mcmc_postproc(), samesource_C(), two.level.multivariate.calculate.UC()

lgaborini/bayessource documentation built on Nov. 9, 2021, 2:10 p.m.