• Nested sampling

  Bayesian inference requires reliable Monte Carlo methods.

  I enjoy studying various algorithms for their performance and limitations, including Markov Chain Monte Carlo, Variational Bayes and Importance Sampling and Nested Sampling. For example: limitations of MultiNest and a more robust alternative.

  I am the author of two popular nested sampling packages: PyMultiNest and the newer UltraNest.

• Bayesian population inference

  Hierarchical Bayesian models are a powerful, self-consistent way to infer population distributions from uncertain measurements. They have wide applicability in astronomy.

  At the limit of our telescope's ability, faint and obscured sources are missing. Modeling the selection bias (sample truncation) enables unbiased inference up to the detection limit.

  I have successfully used these approaches in large surveys, to infer the abundance of Active Galactic Nuclei over cosmic time, luminosity and obscuration, and the obscuration of gamma-ray bursts.

• Big Data

  How can we analyse large survey datasets while still inserting and gaining physical insights? A new inference algorithm can simultaneously analyse many datasets with arbitrarily complex physical models.

  I have extensive knowledge of neural networks, random forests and other machine learning techniques, as well as non-parametric inference. These are useful to infer models when the data are better than our physical understanding. A recent application is the development of spectral models for X-ray telescopes and robust Gaussian processes for exoplanet detection.

Getting statistics right

• Minimal statistics checklist to help you identify and fix common errors/misinterpretation in your analysis, or of a paper you are refereeing.
• Lectures and books can be found on that page too.
• Jupyter notebooks illustrating Bayesian inference in practice, including parameter estimation and model comparison.