Rcode README (Figures + Monte Carlo)

This folder contains:

• my_functions.R: core functions used by all scripts (do not edit unless you intend to change the methods).
• Figure_*.R: scripts that generate the paper figures into Figures/.
• mc_interpolate_BB_*.R: Monte Carlo scripts that benchmark the rejection samplers used by interpolate_BB_*.

Requirements

• R (recent version recommended)
• Packages used across scripts:
  • ggplot2, latex2exp
  • patchwork (used by Figure_005.R, Figure_006.R, Figure_007.R, Figure_008.R)
  • gridExtra (used by Figure_002.R)

Install packages in R if needed:

install.packages(c("ggplot2", "latex2exp", "patchwork", "gridExtra"))

Figure scripts (Figure_*.R)

Run from this directory (so relative paths like Figures/... resolve):

Rscript Figure_001.R

To (re)generate all figures:

for f in Figure_*.R; do Rscript "$f"; done

Outputs

• Most scripts write .png files to Figures/ via ggsave().
• Some scripts also save plot objects as .rds in Figures/ (e.g., Figures/p_005a.rds).

Monte Carlo scripts (mc_interpolate_BB_*.R)

These scripts report, for each scenario:

1. Acceptance rate of the rejection sampler inside interpolate_BB_*, estimated as:
   • acceptance_rate = B_accept / total_proposals
   • where total_proposals is counted by temporarily wrapping the proposal generator (extrapolate_bm_I or extrapolate_bm_II).
2. Elapsed wall-clock time to generate B_time = 10000 accepted draws, using system.time(...)[["elapsed"]].

Run individually:

Rscript mc_interpolate_BB_I.R
Rscript mc_interpolate_BB_II.R
Rscript mc_interpolate_BB_III.R
Rscript mc_interpolate_BB_IV.R

What varies in each script

• mc_interpolate_BB_I.R: fixes a=2, T=3, uses t ∈ {0.2, 1.5, 2.8}, varies x and z over grids in (0,a).
• mc_interpolate_BB_II.R: fixes a=2, T=3, uses t ∈ {0.2, 1.5, 2.8}, varies z over a grid in (0,a).
• mc_interpolate_BB_III.R: fixes a=2, T=3, uses t ∈ {0.2, 1.5, 2.8}, varies x over a grid in (0,a).
• mc_interpolate_BB_IV.R: fixes a=2, T=3, uses t ∈ {0.2, 1.5, 2.8} (no endpoint grid in this case).

Outputs Each script writes two CSV files with a timestamped run_id:

• mc_interpolate_BB_*.csv: per-scenario results (includes acceptance rate and elapsed seconds for 10,000 draws).
• mc_interpolate_BB_*_summary_by_t_<run_id>.csv: a simple summary by t.
  • For mc_interpolate_BB_I.R, the summary is averaged over the (x,z) grid:
    • mean acceptance rate over (x,z)
    • median elapsed time (over (x,z)) to generate 10,000 draws

Customizing the experiments

In each mc_interpolate_BB_*.R file you can edit:

• grid sizes (x_grid_n, z_grid_n) and the boundary buffer eps
• B_accept (acceptance-rate accuracy)
• B_time (timed number of accepted draws; currently 10,000)
• timing_reps (set >1 to repeat timings and take the median across repeats)