Diagnosing Robustness of Decomposability in Gaussian Graphical Models

Reproducible code, data, and writeup for the paper Diagnosing Robustness of Decomposability in Gaussian Graphical Models by Juan Carlos Cisneros and Erik Solé (Universitat Pompeu Fabra, 2026).

The paper assesses the empirical-Bayes SAEM-MCMC procedure of Donnet and Marin (2012) for decomposable Gaussian graphical models and characterizes the regimes in which its central decomposability assumption is, and is not, costly. We propose using the two-stage output (Stage 1 decomposable + Stage 2 unrestricted via BDgraph) as a diagnostic for misspecification of the decomposable family, and apply the procedure to the Demirer-Diebold-Liu-Yilmaz (2018) global bank-volatility panel ($n = 2{,}676$, $p = 106$).

Repository layout

1_data/        DDLY raw CSV + bank-name lookup; wrangling script
2_analysis/    Three R scripts: simulation grid, DDLY application, lambda-sensitivity sweep
3_slides/      Beamer source for the conference deck
4_paper/       LaTeX source for the paper, plus bibliography and section files
utils/         R helpers actually sourced by the analysis (SAEM-MCMC, two-stage wrapper, comparators)
lib/           Shell helpers used by the per-module make.sh scripts

Reproducing the paper and slides

The build is orchestrated by per-module make.sh scripts and a top-level run_all.sh. The R environment is pinned via micromamba and conda-lock.yml; LaTeX uses tectonic plus biber for the bibliography.

One-time setup

bash setup.sh         # installs micromamba, R, tectonic into .micromamba/
bash setup_biber.sh   # installs biber binary (tectonic does not ship it)

Full rebuild

bash run_all.sh

This runs, in order:

1. 1_data/make.sh — wrangle the raw DDLY CSV into 1_data/output/ddly_clean.rds
2. 2_analysis/make.sh — run the simulation grid, DDLY application, and lambda-sensitivity sweep; write figures and LaTeX tables under 2_analysis/output/
3. 3_slides/make.sh — compile the slides → 3_slides/output/slides.pdf
4. 4_paper/make.sh — compile the paper → 4_paper/output/paper.pdf

Compile only the writeup

If you just want the PDFs and trust the precomputed analysis outputs that ship with the repo (2_analysis/output/figures/ and 2_analysis/output/tables/):

bash 3_slides/make.sh    # → 3_slides/output/slides.pdf
bash 4_paper/make.sh     # → 4_paper/output/paper.pdf

Runtime budget

The simulation grid in 2_analysis/source/run_simulations_extended.r is the expensive step (~30 minutes on 8 cores). The DDLY application (run_ddly_application.r) is ~25 minutes for the full $p = 106$ panel. The lambda-sensitivity sweep is ~10 minutes. The LaTeX build is under a minute end-to-end.

Data

• DDLY bank-volatility panel — 1_data/source/raw/ddly/ddly-data.csv: ninety-six bank stocks plus ten ten-year sovereign bond series, daily log range volatilities from 12 September 2003 to 7 February 2014 ($n = 2{,}676$, $p = 106$). Distributed alongside Demirer, Diebold, Liu, and Yilmaz (2018); the cleaned long-format ddly_clean.rds is rebuilt by 1_data/make.sh.
• Bank-name lookup — 1_data/source/raw/ddly/bank_names.csv: ticker → bank name mapping parsed from the DDLY data appendix.

Citation

If you use this code or build on the diagnostic, please cite the paper:

@unpublished{cisneros_sole_2026_diagnosing,
  title  = {Diagnosing Robustness of Decomposability in Gaussian Graphical Models},
  author = {Cisneros, Juan Carlos and Sol{\'e}, Erik},
  year   = {2026},
  note   = {Universitat Pompeu Fabra}
}

License

MIT — see LICENSE.

Contact

Juan Carlos Cisneros — juancarlos.cisneros@upf.edu