Rencontres Statistiques Lyonnaises

Simulation-Based Inference: estimating posterior distributions without analytic likelihoods

by Justine Zeghal

Salle Fokko du Cloux (Bâtiment Braconnier)

Salle Fokko du Cloux

Bâtiment Braconnier


Statistical inference plays a crucial role in numerous scientific fields, providing a framework to draw conclusions from data. In cosmology, galaxy surveys have already made it possible to probe our universe and improve our understanding of it. Upcoming stage IV surveys (such as LSST or Euclid) are expected to be larger and deeper offering the opportunity to refine our estimations even further. To analyze the vast amount of data these surveys will produce and enable new discoveries, we need to update our inference techniques for constraining cosmological parameters. 
To date, inference techniques typically rely on suboptimal compression of data (most of the time, into the power spectrum) and the use of a Gaussian likelihood function.  However, these methods often fail to capture the full richness of the data. Recently, there has been a promising shift from analytical likelihood-based approaches to simulations-based inference. This new paradigm allows for precise inference even when the likelihood of the data given the parameters is unknown. 
In my presentation, I will explain the two ways of performing inference using a simulation model, whether it is explicit (when you can evaluate the likelihood of your simulation model) or implicit (when you only have simulations). I will discuss the pros and cons of these techniques specifically regarding the number of simulations they need. I will use the example of cosmological weak gravitational lensing, but the inference method remains the same in any case!