It calculates the value of the integral defined in Definition 11 from references. It implements Theorem 8 from references and uses the formula (19) from references.
Arguments
- perm
An object of a
gips_perm
class. It can also be of agips
class, but it will be interpreted as the underlyinggips_perm
.- lambda
A positive real number.
Value
Returns the value of the Gamma function of the colored cone (for the definition of the colored cone, see the Basic definitions
section in vignette("Theory", package = "gips")
or in its
pkgdown page).
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
get_structure_constants()
- The function useful inside thecalculate_gamma_function()
.log_posteriori_of_gips()
- The function that uses the values of the gamma function.vignette("Theory", package = "gips")
or its pkgdown page - A place to learn more about the math behind thegips
package.
Examples
id_perm <- gips_perm("()", 2)
calculate_gamma_function(id_perm, 0.5001) # 10.7...
#> [1] 10.70139
calculate_gamma_function(id_perm, 0.50000001) # 19.9...
#> [1] 19.91198
calculate_gamma_function(id_perm, 0.500000000001) # 29.1...
#> [1] 29.12235
oldw <- getOption("warn")
options(warn = -1)
calculate_gamma_function(id_perm, 0.5) # Inf
#> [1] Inf
# Integral diverges; returns Inf and warning
options(warn = oldw)