FBMS (version 1.3)

fbms.mlik.master: Master Log Marginal Likelihood Function

Description

This function serves as a unified interface to compute the log marginal likelihood for different regression models and priors by calling specific log likelihood functions.

Usage

fbms.mlik.master(
  y,
  x,
  model,
  complex,
  mlpost_params = list(family = "gaussian", beta_prior = list(type = "g-prior"), r =
    NULL)
)

Value

A list with elements:

crit

Log marginal likelihood combined with the log prior.

coefs

Posterior mode of the coefficients.

Arguments

y

A numeric vector containing the dependent variable.

x

A matrix containing the precalculated features (independent variables).

model

A logical vector indicating which variables to include in the model.

complex

A list of complexity measures for the features.

mlpost_params

A list of parameters controlling the model family, prior, and tuning parameters. Key elements include:

• family: "binomial", "poisson", "gamma" (all three referred to as GLM below), or "gaussian" (default: "gaussian")

• prior_beta: Type of prior as a string (default: "g-prior"). Possible values include:

  • "beta.prime": Beta-prime prior (GLM/Gaussian, no additional args)

  • "CH": Compound Hypergeometric prior (GLM/Gaussian, requires a, b, optionally s)

  • "EB-local": Empirical Bayes local prior (GLM/Gaussian, requires a for Gaussian)

  • "EB-global": Empirical Bayes local prior (Gaussian, requires a for Gaussian)

  • "g-prior": Zellner's g-prior (GLM/Gaussian, requires g)

  • "hyper-g": Hyper-g prior (GLM/Gaussian, requires a)

  • "hyper-g-n": Hyper-g/n prior (GLM/Gaussian, requires a)

  • "tCCH": Truncated Compound Hypergeometric prior (GLM/Gaussian, requires a, b, s, rho, v, k)

  • "intrinsic": Intrinsic prior (GLM/Gaussian, no additional args)

  • "TG": Truncated Gamma prior (GLM/Gamma, requires a, s)

  • "Jeffreys": Jeffreys prior (GLM/Gaussian, no additional args)

  • "uniform": Uniform prior (GLM/Gaussian, no additional args)

  • "benchmark": Benchmark prior (Gaussian/GLM, no additional args)

  • "ZS-adapted": Zellner-Siow adapted prior (Gaussian TCCH, no additional args)

  • "robust": Robust prior (Gaussian/GLM, no additional args)

  • "Jeffreys-BIC": Jeffreys prior with BIC approximation of marginal likelihood (Gaussian/GLM)

  • "ZS-null": Zellner-Siow null prior (Gaussian, requires a)

  • "ZS-full": Zellner-Siow full prior (Gaussian, requires a)

  • "hyper-g-laplace": Hyper-g Laplace prior (Gaussian, requires a)

  • "AIC": AIC prior from BAS (Gaussian, requires penalty a)

  • "BIC": BIC prior from BAS (Gaussian/GLM)

  • "JZS": Jeffreys-Zellner-Siow prior (Gaussian, requires a)

• r: Model complexity penalty (default: 1/n)

• a: Tuning parameter for g-prior (default: max(n, p^2))

• a, b, s, v, rho, k: Hyperparameters for various priors

• n: Sample size for some priors (default: length(y))

• var: Variance assumption for Gaussian models ("known" or "unknown", default: "unknown")

• laplace: Logical for Laplace approximation in GLM only (default: FALSE)

Examples

fbms.mlik.master(y = rnorm(100), 
x = matrix(rnorm(100)), 
c(TRUE,TRUE), 
list(oc = 1),
mlpost_params = list(family = "gaussian", beta_prior = list(type = "g-prior", a = 2),
         r = exp(-0.5)))