DualProbitCDF Repository

The repository DualProbitCDF contains the R package and code implementing the estimation strategy proposed in the article:

“Multivariate Gaussian cumulative distribution functions as the marginal likelihood of their dual Bayesian probit model” by A. Fasano and F. Denti, accepted for publication in Biometrika (2025, In press).

In addition to the package itself, the repository includes all the scripts needed to reproduce the simulation studies and the figures presented in the paper.

Getting Started

1. Open the R Project
   Open the R project file DualProbitCDF.Rproj and set it as your working directory.

2. Install the R Package
   Install the included R package EPmvnCDF, which stands for
   Expectation Propagation for the estimation of Multivariate Normal Cumulative Distribution Functions, via

   install.packages("EPmvnCDF_0.2.0.tar.gz", repos = NULL, type = "source")

   Otherwise open the R project contained in the EPmvnCDF/ folder and build the package from there.

Then you can run the code.

In particular:

• Scripts starting with the letter A contain utility functions that are reused throughout the project.

• Scripts starting with the letter B contain the code to run the four estimation methods described in the main paper:

  • our Expectation Propagation (EP) proposal, implemented using both Cholesky and Eigenvalue decompositions;
  • the method in the TruncatedNormal package;
  • the methods in the tlrmvnmvt package;
  • the Orthant method by Ridgway (2016), implemented in C++ (see the cpp_source/ directory).

  The output of each method is stored in the corresponding subfolder within the RDS/ directory.

• The .Rmd file starting with the letter C extracts and processes the simulation results stored in the .RDS files. It creates summary data frames (saved in RDS/) and saves the figures used in the paper (in NewFigures/).

• Scripts starting with the letter D reproduce an additional simulation study included in the Supplementary Material.