Get Structure Constants

Finds constants necessary for internal calculations of integrals and eventually the posteriori probability in log_posteriori_of_gips().

Usage

get_structure_constants(perm)

Arguments

perm

An object of a gips_perm class. It can also be of a gips class, but it will be interpreted as the underlying gips_perm.

Value

Returns a list of 5 items: r, d, k, L, dim_omega - vectors of constants from Theorem 1 from references and the beginning of section 3.1. from references.

Details

Uses Theorem 5 from references to calculate the constants.

References

Piotr Graczyk, Hideyuki Ishi, Bartosz Kołodziejek, Hélène Massam. "Model selection in the space of Gaussian models invariant by symmetry." The Annals of Statistics, 50(3) 1747-1774 June 2022. arXiv link; doi:10.1214/22-AOS2174

See also

• calculate_gamma_function(), log_posteriori_of_gips() - The functions that rely heavily on get_structure_constants().

Examples

perm <- gips_perm("(1)(2)(3)(4,5)", 5)
get_structure_constants(perm)
#> $r
#> [1] 4 1
#> 
#> $d
#> [1] 1 1
#> 
#> $k
#> [1] 1 1
#> 
#> $L
#> [1] 2
#> 
#> $dim_omega
#> [1] 10  1
#>