compare_posteriories_of_perms {gips}

Compare the posteriori probabilities of 2 permutations

Description

Check which permutation is more likely and how much more likely.

Usage

compare_posteriories_of_perms(
  perm1,
  perm2 = "()",
  S = NULL,
  number_of_observations = NULL,
  delta = 3,
  D_matrix = NULL,
  was_mean_estimated = TRUE,
  print_output = TRUE,
  digits = 3
)

compare_log_posteriories_of_perms(
  perm1,
  perm2 = "()",
  S = NULL,
  number_of_observations = NULL,
  delta = 3,
  D_matrix = NULL,
  was_mean_estimated = TRUE,
  print_output = TRUE,
  digits = 3
)

Arguments

perm1, perm2

Permutations to compare. How many times perm1 is more likely than perm2? Those can be provided as the gips objects, the gips_perm objects, or anything that can be used as the x parameter in the gips_perm() function. They do not have to be of the same class.

S, number_of_observations, delta, D_matrix, was_mean_estimated

The same parameters as in the gips() function. If at least one of perm1 or perm2 is a gips object, they are overwritten with those from the gips object.

print_output

A boolean. When TRUE (default), the computed value will be printed with additional text and returned invisibly. When FALSE, the computed value will be returned visibly.

digits

Integer. Only used when print_output = TRUE. The number of digits after the comma to print. It can be negative, can be +Inf. It is passed to base::round().

Value

The function compare_posteriories_of_perms() returns the value of how many times the perm1 is more likely than perm2.

The function compare_log_posteriories_of_perms() returns the logarithm of how many times the perm1 is more likely than perm2.

Functions

• compare_log_posteriories_of_perms(): More stable, logarithmic version of compare_posteriories_of_perms(). The natural logarithm is used.

See Also

• print.gips() - The function that prints the posterior of the optimized gips object compared to the starting permutation.

• summary.gips() - The function that calculates the posterior of the optimized gips object compared to the starting permutation.

• find_MAP() - The function that finds the permutation that maximizes log_posteriori_of_gips().

• log_posteriori_of_gips() - The function this compare_posteriories_of_perms() calls underneath.

Examples

require("MASS") # for mvrnorm()

perm_size <- 6
mu <- runif(6, -10, 10) # Assume we don't know the mean
sigma_matrix <- matrix(
  data = c(
    1.05, 0.8, 0.6, 0.4, 0.6, 0.8,
    0.8, 1.05, 0.8, 0.6, 0.4, 0.6,
    0.6, 0.8, 1.05, 0.8, 0.6, 0.4,
    0.4, 0.6, 0.8, 1.05, 0.8, 0.6,
    0.6, 0.4, 0.6, 0.8, 1.05, 0.8,
    0.8, 0.6, 0.4, 0.6, 0.8, 1.05
  ),
  nrow = perm_size, byrow = TRUE
) # sigma_matrix is a matrix invariant under permutation (1,2,3,4,5,6)
number_of_observations <- 13
Z <- MASS::mvrnorm(number_of_observations, mu = mu, Sigma = sigma_matrix)
S <- cov(Z) # Assume we have to estimate the mean

g <- gips(S, number_of_observations)
g_map <- find_MAP(g, max_iter = 10, show_progress_bar = FALSE, optimizer = "Metropolis_Hastings")

compare_posteriories_of_perms(g_map, g, print_output = TRUE)
exp(compare_log_posteriories_of_perms(g_map, g, print_output = FALSE))