AIC and BIC Comparison

This example compares two manually specified vines on the same data. In real workflows, the compared models might come from different structures, truncation levels, or candidate family sets.

using VineCopulas
using Distributions: fit
using Random

truth = DVineCopula(
    [1, 2, 3],
    [[GaussianCopula(2, 0.55), ClaytonCopula(2, 1.5)],
     [FrankCopula(2, 2.0)]],
)

U = rand(MersenneTwister(44), truth, 250)

candidate_a = fit(DVineCopula, U; order=[1, 2, 3], family_set=:default)
candidate_b = fit(DVineCopula, U; order=[1, 3, 2], family_set=:default)

(
    aic_a = aic(candidate_a, U),
    aic_b = aic(candidate_b, U),
    bic_a = bic(candidate_a, U),
    bic_b = bic(candidate_b, U),
)

(aic_a = -286.3593418939181, aic_b = -285.65498911074366, bic_a = -275.79495914033134, bic_b = -275.0906063571569)

Smaller AIC/BIC is preferred for the corresponding criterion.

Warning

AIC and BIC are model-selection scores for a fitted candidate on a fixed dataset. They are not a guarantee that sequential vine fitting found a global full-vine optimum.