Bayesian Inverse Problems, GPUs, and AI

GLITTER Training School Workshop

University of Luxembourg, 15 April 2026

Will Handley (University of Cambridge / PolyChord Ltd)

Workshop Notebook

Click the badge above to open the workshop notebook in Google Colab.

Talk slides: [PDF] [source]

What this workshop covers

Part 1: Bayesian Inference via Line Fitting

Starting from least-squares fitting (which you already know), we show that $\chi^2$ minimisation is equivalent to maximum likelihood, and that Bayes' theorem extends this to give:

• Parameter estimation with proper error bars (posterior distributions)
• Predictive posteriors showing model uncertainty in data space
• Model comparison via the Bayesian evidence (automatic Occam's razor)

All inference is done with BlackJAX nested sampling, visualised with anesthetic.

Part 2: Satellite Orbit Determination

The same framework applied to a GNSS-relevant problem: inferring orbital elements from noisy satellite position observations using jaxsgp4, a differentiable SGP4 propagator in JAX.

• 2 parameters: infer inclination and RAAN, visualise the posterior and predictive orbits
• 4 parameters: add eccentricity and mean motion, see parameter degeneracies
• Model comparison: circular vs elliptical orbit -- can the data detect eccentricity?

Part 3: Extensions

Open-ended exploration: change noise levels, add parameters, or apply the framework to your own forward model.

Local installation

If not using Colab:

pip install "blackjax @ git+https://github.com/handley-lab/blackjax.git"
pip install "jaxsgp4 @ git+https://github.com/cmpriestley/jaxsgp4.git" anesthetic fgivenx tqdm matplotlib

Then open workshop_glitter.ipynb in Jupyter.

Key resources

• jaxsgp4 -- differentiable SGP4 in JAX (arXiv:2603.27830)
• BlackJAX -- GPU-native nested sampling
• Nested Sampling Book -- tutorial and reference
• anesthetic -- nested sampling visualisation