mdgc_log_ml: Evaluate the Log Marginal Likelihood and Its Derivatives

Description

Approximates the log marginal likelihood and the derivatives using randomized quasi-Monte Carlo. The method uses a generalization of the Fortran code by Genz and Bretz (2002).

Mean terms for observed continuous variables are always assumed to be zero.

The returned log marginal likelihood is not a proper log marginal likelihood if the ptr object is constructed from a mdgc object from get_mdgc as it does not include the log of the determinants of the Jacobians for the transformation of the continuous variables.

Usage

mdgc_log_ml(
  ptr,
  vcov,
  mea,
  rel_eps = 0.01,
  n_threads = 1L,
  comp_derivs = FALSE,
  indices = NULL,
  do_reorder = TRUE,
  maxpts = 100000L,
  abs_eps = -1,
  minvls = 100L,
  use_aprx = FALSE
)

Arguments

ptr

object returned by get_mdgc_log_ml.

vcov

covariance matrix.

mea

vector with non-zero mean entries.

rel_eps

relative error for each marginal likelihood factor.

n_threads

number of threads to use.

comp_derivs

logical for whether to approximate the gradient.

indices

integer vector with which terms (observations) to include. Must be zero-based. NULL yields all observations.

do_reorder

logical for whether to use a heuristic variable reordering. TRUE is likely the best option.

maxpts

maximum number of samples to draw for each marginal likelihood term.

abs_eps

absolute convergence threshold for each marginal likelihood factor.

minvls

minimum number of samples.

use_aprx

logical for whether to use an approximation of pnorm and qnorm. This may yield a noticeable reduction in the computation time.

Value

A numeric vector with a single element with the log marginal likelihood approximation. Two attributes are added if comp_derivs is TRUE: "grad_vcov" for the derivative approximation with respect to vcov and "grad_mea" for the derivative approximation with respect to mea.

References

Genz, A., & Bretz, F. (2002). Comparison of Methods for the Computation of Multivariate t Probabilities. Journal of Computational and Graphical Statistics.

Genz, A., & Bretz, F. (2008). Computation of Multivariate Normal and t Probabilities. Springer-Verlag, Heidelberg.

Examples

Run this code

# NOT RUN {
# randomly mask data
set.seed(11)
masked_data <- iris
masked_data[matrix(runif(prod(dim(iris))) < .10, NROW(iris))] <- NA

# use the functions in the package
library(mdgc)
obj <- get_mdgc(masked_data)
ptr <- get_mdgc_log_ml(obj)
start_vals <- mdgc_start_value(obj)
mdgc_log_ml(ptr, start_vals, obj$means)
mdgc_log_ml(ptr, start_vals, obj$means, use_aprx = TRUE)
mdgc_log_ml(ptr, start_vals, obj$means, use_aprx = TRUE, comp_derivs = TRUE)

# }