cat_glm_bayes_joint_gibbs: Bayesian Estimation with Gibbs Sampling for Catalytic...

In catalytic: Tools for Applying Catalytic Priors in Statistical Modeling

Bayesian Estimation with Gibbs Sampling for Catalytic Generalized Linear Models (GLMs) Binomial Family for Coefficients and tau

Description

This function uses Gibbs sampling to estimate a Bayesian GLMs Binomial Family, where both the coefficients and tau parameter are jointly sampled. tau is updated via a gamma distribution, while coefficients are updated using Hamiltonian Monte Carlo (HMC) sampling. The model allows for progress updates, warm-up iterations, and initial coefficient estimation based on initial tau value.

Usage

cat_glm_bayes_joint_gibbs(
  formula,
  cat_init,
  iter = 1000,
  warmup = 500,
  coefs_iter = 5,
  tau_0 = NULL,
  tau_alpha = 2,
  tau_gamma = 1,
  refresh = TRUE
)

Arguments

formula	A formula specifying the GLMs. Should at least include response variables (e.g. ~.).
cat_init	A list generated from cat_glm_initialization.
iter	Integer; the number of Gibbs sampling iterations (default = 1000).
warmup	Integer; the number of initial iterations for warm-up (default = 500).
coefs_iter	Integer; the number of iterations for the HMC step to update coefficients.
tau_0	Initial value for tau; defaults to the number of predictors / 4 if NULL.
tau_alpha	Shape parameter for the gamma distribution when updating tau. Default is 2.
tau_gamma	Scale parameter for the gamma distribution when updating tau. Default is 1.
refresh	Logical; if TRUE, displays sampling progress. Default is TRUE.

Value

A list containing the values of all the arguments and the following components:

gibbs_iteration_log	Matrix containing the coefficients and tau values from each Gibbs iteration.
inform_df	Summary statistics of each parameter, including mean, standard error, quantiles, and effective sample size.
tau	Mean of sampled tau values.
coefficients	Mean of sampled coefficient values.

Examples

binomial_data <- data.frame(
  X1 = stats::rnorm(10),
  X2 = stats::rnorm(10),
  Y = stats::rbinom(10, 1, 0.5)
)

cat_init <- cat_glm_initialization(
  formula = Y ~ 1, # formula for simple model
  data = binomial_data,
  family = binomial,
  syn_size = 100, # Synthetic data size
  custom_variance = NULL, # User customized variance value
  gaussian_known_variance = FALSE, # Indicating whether the data variance is unknown
  x_degree = c(1, 1), # Degrees for polynomial expansion of predictors
  resample_only = FALSE, # Whether to perform resampling only
  na_replace = stats::na.omit # How to handle NA values in data
)

cat_model <- cat_glm_bayes_joint_gibbs(
  formula = ~.,
  cat_init = cat_init, # Only accept object generated from `cat_glm_initialization`
  iter = 10, # Number of Gibbs sampling iterations
  warmup = 5, # Number of warm-up (or burn-in) iterations for initial iterations
  coefs_iter = 2, # Number of iterations for the HMC step to update coefficients
  tau_alpha = 1, # Shape parameter for the gamma distribution when updating tau
  tau_gamma = 2, # Scale parameter for the gamma distribution when updating tau
  refresh = TRUE # Indicator for displaying sampling progress
)
cat_model

catalytic documentation built on April 4, 2025, 5:51 a.m.