samesource_C: Fast computation of the Bayes Factor (same source v....

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

Description

Implemented in C.

Usage

samesource_C(
  quest,
  ref,
  n.iter,
  B.inv,
  W.inv.1,
  W.inv.2,
  U,
  nw,
  mu,
  burn.in,
  verbose = FALSE,
  marginals = FALSE
)

Arguments

quest	the questioned dataset (a n_q x p matrix)
ref	the reference dataset (a n_r x p matrix)
n.iter	number of MCMC iterations excluding burn-in
B.inv	prior inverse of between-source covariance matrix
W.inv.1	prior inverse of within-source covariance matrix (questioned items)
W.inv.2	prior inverse of within-source covariance matrix (reference items)
nw	degrees of freedom
mu	prior mean (p x 1)
burn.in	number of MCMC burn-in iterations
verbose	if TRUE, be verbose
marginals	if TRUE, also return the marginal likelihoods in the LR formula (default: FALSE)

Details

The hypothesis pair is:

• H_p: all ref and quest come from the same source

• H_p: quest comes from source 1, ref comes from source 2

See diwishart_inverse for the parametrization of the Inverted Wishart. See marginalLikelihood_internal for further documentation.

Value

the log-BF value (base e), or a list with the log-BF and the computed marginal likelihoods:

• value: the log-BF value (base e)

• log_ml_Hp: log-BF numerator (from reference = questioned source)

• log_ml_Hd_ref: log-BF denominator from reference source

• log_ml_Hd_quest: log-BF denominator from questioned (!= reference) source

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.

Inverted Wishart parametrization (Press)

Uses \insertCitePress2012Appliedbayessource parametrization.

X ~ IW(v, S)

with S is a p x p matrix, v > 2p (the degrees of freedom).

Then:

E[X] = S/(n - 2(p + 1))

References

\insertAllCited

See Also

marginalLikelihood

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

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