evidence {graphicalEvidence}R Documentation

Compute Marginal Likelihood using Graphical Evidence

Description

Computes the marginal likelihood of input data xx under one of the following priors: Wishart, Bayesian Graphical Lasso (BGL), Graphical Horseshoe (GHS), and G-Wishart, specified under prior_name. The number of runs is specified by num_runs, where each run is by default using a random permutation of the columns of xx, as marginal likelihood should be independent of column permutation.

Usage

evidence(
  xx,
  burnin,
  nmc,
  prior_name = c("Wishart", "BGL", "GHS", "G_Wishart"),
  runs = 1,
  print_progress = FALSE,
  permute_columns = TRUE,
  alpha = NULL,
  lambda = NULL,
  V = NULL,
  G = NULL
)

Arguments

xx

The input data specified by a user for which the marginal likelihood is to be calculated. This should be input as a matrix like object with each individual sample of xx representing one row

burnin

The number of iterations the MCMC sampler should iterate through and discard before beginning to save results

nmc

The number of samples that the MCMC sampler should use to estimate marginal likelihood

prior_name

The name of the prior for which the marginal should be calculated, this is one of 'Wishart', 'BGL', 'GHS', 'G_Wishart'

runs

The number of complete runs of the graphical evidence method that will be executed. Specifying multiple runs allows estimation of the variance of the estimator and by default will permute the columns of xx such that each run uses a random column ordering, as marginal likelihood should be independent of column permutations

print_progress

A boolean which indicates whether progress should be displayed on the console as each row of the telescoping sum is computed and each run is completed

permute_columns

A boolean which indicates whether columns of xx for runs beyond the first should be randomly permuted to ensure that marginal calculation is consistent across different column permutations

alpha

A number specifying alpha for the priors of 'Wishart' and 'G_Wishart'

lambda

A number specifying lambda for the priors of 'BGL' and 'GHS' prior

V

The scale matrix when specifying 'Wishart' or 'G_Wishart' prior

G

The adjacency matrix when specifying 'G_Wishart' prior

Value

A list of results which contains the mean marginal likelihood, the standard deviation of the estimator, and the raw results in a vector

Examples

# Compute the marginal 10 times with random column permutations of xx at each
# individual run for G-Wishart prior using 2,000 burnin and 10,000 sampled
# values at each call to the MCMC sampler
g_params <- gen_params_evidence('G_Wishart')
marginal_results <- evidence(
  g_params$x_mat, 2e3, 1e4, 'G_Wishart', 3, alpha=2, 
  V=g_params$scale_mat, G=g_params$g_mat
)

[Package graphicalEvidence version 1.1 Index]