Gibbs Sampler for Bayesian Mixed Graphical Models

Implements a Gibbs sampler for Bayesian inference on Mixed Graphical Models.

sampler_bmgm(
  n = 1,
  Beta,
  theta,
  type,
  categories,
  lambda,
  M = 1000,
  X_new,
  variables,
  std
)

Arguments

n: Number of samples to generate.
Beta: Precision matrix of the graphical model.
theta: A list of parameters for each node.
type: Character vector indicating variable types.
categories: Vector indicating the number of categories (for categorical variables).
lambda: Transformation parameter.
M: Number of Gibbs sampler iterations. Default is 1000.
X_new: Vector of known values for imputation. Default is `c(0,0,0)`.
variables: Indicator vector specifying which variables to update.
std: Standard deviation used in the transformation.

Value

A matrix containing the sampled data.

Examples

# Simulate example data
set.seed(123)
Beta <- diag(4)  # Identity precision matrix
theta <- list(c(0,1), c(0,1), c(0.5,1), c(0.5,1))
type <- c("c", "c", "d", "d")
categories <- c(1,1,1,1)
lambda <- 1

# Run the Gibbs sampler
samples <- sampler_bmgm(n = 10, Beta = Beta, theta = theta, type = type,
                        categories = categories, lambda = lambda, M = 500)

# View first few samples
head(samples)
#>            [,1]       [,2] [,3] [,4]
#> [1,]  0.1174596 -0.3315458    1    0
#> [2,] -0.6580102  0.8552022    1    0
#> [3,]  1.4046843  0.3870831    0    1
#> [4,] -0.1852022  1.2209637    2    1
#> [5,]  0.5577310  1.4819340    1    1
#> [6,] -0.5973301  0.7894599    0    0