Methane PoD — thinned marked temporal point processes

Methane PoD¶

A self-contained sub-project on methane retrieval from satellite observations, treated as a thinned marked temporal point process (TMTPP). It packages:

• A library of 13 intensity kernels λ(t) for satellite-visible methane sources (wells, compressors, mines, landfills, wetlands, feedlots, offshore platforms), each as an equinox.Module with a NumPyro prior factory.
• A library of 10 probability-of-detection (POD) models P_d(·), spanning logistic → varying-coefficient → spectral-aware → full GLM, each exposing the same __call__ + sample_priors interface.
• A Monte Carlo proof of the “missing mass paradox”: a PoD-thinned sampler simultaneously overestimates the average emission rate and underestimates the total emitted mass. Pure-NumPy library plus a notebook driver.
• A NumPyro NUTS fitter for a POD-modified power-law model — invert noisy observed-flux histograms for (α, x₀, σ).

Layout¶

projects/methane_pod/
├── pyproject.toml          # standalone package "methane_pod"
├── src/methane_pod/
│   ├── intensity.py        # λ(t) equinox modules + INTENSITY_REGISTRY
│   ├── pod_functions.py    # P_d(·) equinox modules + POD_REGISTRY
│   ├── paradox.py          # Monte Carlo simulation (pure NumPy)
│   └── fitting.py          # NumPyro NUTS fitter (pure library — no I/O)
├── tests/                  # pytest suite, ~80 fast tests + 1 MCMC smoke test
└── notebooks/              # jupytext .py + executed .ipynb + prose .md

Running¶

The parent research_notebook pixi file defines a methane-pod feature / environment with the right pins (jax <0.9 for numpyro compatibility, equinox, numpyro, corner).

# install + open a shell in the env
pixi install -e methane-pod
pixi shell -e methane-pod

# fast library tests (no MCMC)
pixi run -e methane-pod test-methane-pod

# full suite (includes a ~11s NUTS smoke test)
pixi run -e methane-pod test-methane-pod-all

# re-execute all code notebooks in-place
pixi run -e methane-pod execute-methane-pod

Notebooks¶

See the notebooks/ directory and the MyST toc entry Methane PoD in the parent myst.yml. Prose-only .md files cover the theory; .ipynb files (with their .py jupytext source alongside) are executed end-to-end with outputs committed.

Reading order¶

1. 01_mttpp_theory — point-process foundations
2. 02_intensity_zoo — the λ(t) catalog
3. 03_missing_mass_paradox — MC proof
4. 04_intensity_gallery — λ(t) code gallery
5. 05_pod_gallery — P_d(·) code gallery
6. 06_stationary_numpyro_mcmc — NUTS fit
7. 07_pod_fitting_mcmc.ipynb — placeholder; real-data CSV-driven NUTS fit (pending)
8. 08_persistency — operational predictions