thamesmix (version 0.1.3)

compute_nobile_identity: Nobile's identity for the marginal likelihood

Description

This function uses the identity from Nobile (2004, 2007) to compute an estimate of the marginal likelihood for a mixture model with G components given an estimate of the marginal likelihood for a mixture model with G-1 components and an estimate of the proportion of empty components.

Usage

compute_nobile_identity(logZhatGminus1, p0hat_value, G, dirichlet_vec, n)

Value

estimate of the marginal likelihood for G

Arguments

logZhatGminus1

estimate of the marginal likelihood for G-1

p0hat_value

estimate of the proportion of empty components

G

number of components

dirichlet_vec

hyperparameter-vector of the dirichlet prior

n

size of the data

References

Nobile, A. (2004). On the posterior distribution of the number of components in a finite mixture. The Annals of Statistics 32(5), 2044–2073.

Nobile, A. (2007). Bayesian finite mixtures: a note on prior specification and posterior computation.arXiv preprint arXiv:0711.0458.

Martin Metodiev, Nicholas J. Irons, Marie Perrot-Dockès, Pierre Latouche, Adrian E. Raftery. "Easily Computed Marginal Likelihoods for Multivariate Mixture Models Using the THAMES Estimator." arXiv preprint arXiv:2504.21812.

Examples

# computes log marginal likelihood of the Swiss banknote dataset
# for G=4, given the settings in Metodiev et al. (2025)
compute_nobile_identity(logZhatGminus1 = -909.49,
p0hat_value = 1/4,
dirichlet_vec = rep(1,4),
n=200)