1# Local Bias Correction versus Global Synchronization in Distributed Maximum Likelihood23Authors listed in the working paper: **Simon-Pierre Boucher and GPT-6.1** (AI designation requested by the user).45This is a *working research note*, not a peer-reviewed or priority-validated paper. The theorem assumptions, limits of the exponential illustration, and computational scope are explained inside the PDF.67## Files89- `pamle.tex` - LaTeX source (16-page article)10- `references.bib` - machine-readable bibliography (the article also contains manual bibliography entries, so BibTeX is **not** required for compilation)11- `figures/mc_comparison.pdf` - vector chart included in the article12- `figures/mc_comparison.png` - preview version of the chart13- `monte_carlo.py` - exact-Gamma reproducible simulation14- `simulation_summary.csv` - reported statistics for 500 replications per partition count15- `simulation_replicates.csv` - 10,500 method/replication rows, across 3 designs x 500 replications x 7 estimators1617## Build the LaTeX article1819```bash20pdflatex -interaction=nonstopmode pamle.tex21pdflatex -interaction=nonstopmode pamle.tex22```2324Requirements: pdfLaTeX and standard LaTeX packages (amsmath, amsthm, microtype, hyperref, cleveref, natbib, tikz, listings, etc.). The project uses relative paths, so compile from this directory.2526## Reproduce Monte Carlo2728```bash29pip install numpy matplotlib30python monte_carlo.py31```3233Seed: 20261028. Total observations in each replication: 1,048,576. Partition sizes: m=256, m=64, m=16. Repetitions: 500 per design. Exponential rate=1. The script draws exact block-wise Gamma sufficient statistics rather than materializing every individual observation.3435**No physical cluster was benchmarked** and no numerical speedup is claimed. All simulations are synthetic and measure scaled estimator gaps relative to the centralized MLE.36