pMFMC

parametric multi-fidelity Monte Carlo estimation methods

Supplementary Code Submission

This supplementary package includes R scripts, generated figures, and a technical derivation document that support the results in the manuscript. Each script corresponds to a specific experiment or case study described in the paper.

Prerequisites

R Version

This code has been tested with R version 4.0.0 or higher.

Required R Packages

Before running the scripts, install the following R packages:

install.packages(c(
  "tidyverse",    # Data manipulation and visualization
  "ggplot2",      # Plotting (included in tidyverse)
  "evd",          # Extreme value distributions
  "MASS",         # Statistical functions
  "mvtnorm",      # Multivariate normal distribution
  "qqplotr",      # Enhanced Q-Q plots
  "stats"         # Statistical functions (base R)
))

Installation

1. Clone this repository:

   git clone https://github.com/mjkim1001/pMFMC.git
   cd pMFMC

2. Install required packages using the command above

3. Run the R scripts in the scripts/ directory

Folder Structure

├── data/                           # Real data used for ship application
├── scripts/                        # R scripts for each analysis
│   ├── BernoulliAnalysis.R         # Bernoulli model
│   ├── Gumbel_muOnly.R             # Gumbel: estimation of mu only
│   ├── Gumbel_jointEstimation.R    # Gumbel: estimation of mu and sigma jointly
│   └── Ship_application.R          # Application to ship data
├── images/                         # Generated PNG figures
└── derivations/                    # Technical derivation document
    └── Gumbel_supplementary.pdf    # Derivations to help understand the code for Gumbel estimation

Usage

Each script can be run independently. Navigate to the scripts/ directory and run:

# For Bernoulli analysis
source("BernoulliAnalysis.R")

# For Gumbel estimation (mu only)
source("Gumbel_muOnly.R")

# For joint Gumbel estimation
source("Gumbel_jointEstimation.R")

# For ship application
source("Ship_application.R")

Notes

• All code is self-contained and does not rely on any external data files beyond what's included in the data/ directory.
• Each R script automatically saves the corresponding figures in .png format to the images/ folder.
• All plots are reproducible by running the scripts in the scripts/ folder.
• Scripts should be run from the project root directory to ensure correct relative paths.