Bayesian Mixed Graphical Model

Implements a Bayesian approach for inference on mixed graphical models. Estimates conditional independencies between variables of mixed types (continuous, discrete, categorical, zero-inflated count data) using an MCMC algorithm for posterior inference.

bmgm(
  X,
  type,
  nburn = 1000,
  nsample = 1000,
  theta_priors,
  v_0 = 0.05,
  v_1 = 1,
  pi_beta,
  seed,
  context_spec = TRUE,
  bfdr = 0.05,
  cont = FALSE,
  verbose = TRUE,
  ...
)

Arguments

X: A numeric matrix or data frame containing the data (mixed type variables). Categorical variables (type "m") must be coded as positive integers (1, 2, ..., K), where K is the number of categories. Category 1 is used as the reference level.
type: A character vector indicating the type of each variable. Options: "c" (continuous), "d" (discrete), "z" (zero-inflated count), "m" (categorical).
nburn: Number of burn-in iterations for MCMC. Default is 1000.
nsample: Number of MCMC samples to collect after burn-in. Default is 1000.
theta_priors: List of priors for node parameters.
v_0: Prior variance for the spike in spike-and-slab. Default is 0.05.
v_1: Prior variance for the slab in spike-and-slab. Default is 1.
pi_beta: Prior probability of edge inclusion. Default is `2/(p-1)`.
seed: Random seed for reproducibility.
context_spec: Logical, whether to compute the context-specific adjacency matrix. Default is TRUE.
bfdr: Bayesian False Discovery Rate threshold for edge selection. Default is 0.05.
cont: Logical, whether to transform continuous variables. Default is FALSE.
verbose: Logical, whether to display a progress bar during MCMC sampling. Default is TRUE.
...: Additional arguments.

Value

A list containing:

post_Beta: Posterior samples of the precision matrix.
post_theta: Posterior samples of node parameters.
post_Z: Posterior samples of edge indicators.
adj_Beta: Estimated adjacency matrix for dependencies.
adj_G: Adjacency matrix for edge selection.
lambda: Estimated transformation parameter.

Examples

# Simulated example data
set.seed(123)
n <- 100
X1 <- rpois(n, lambda = 3)
X2 <- rnorm(n, mean = 5)
X3 <- rnorm(n, mean = X2)
X4 <- rnorm(n, mean = X1)
X <- cbind(X1,X2,X3,X4)
type <- c("d", "c", "c", "c")

# \donttest{
# Fit Bayesian Mixed Graphical Model
fit <- bmgm(X, type, nburn = 1000, nsample = 2000)

# Print adjacency matrix
print(fit$adj_G)
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    1    1
#> [2,]    0    0    1    0
#> [3,]    1    1    0    0
#> [4,]    1    0    0    0
# }