Likelihood-free inference in non-injective models


Séminaire Données et Aléatoire Théorie & Applications

18/11/2021 - 14:00 Pedro L. C. Rodrigues (STATIFY) Salle 106

Inferring the parameters of a stochastic model based on experimental observations is central to the scientific method. A particularly challenging setting is when the model is non-injective, i.e. when distinct sets of parameters yield identical observations. This arises in many practical situations, such as when inferring the distance and power of a radio source (is the source close and weak or far and strong?) or when estimating the amplifier gain and underlying brain activity of an electrophysiological experiment. In this talk, I will present hierarchical neural posterior estimation (HNPE), a novel method for cracking such indeterminacy by exploiting additional information conveyed by an auxiliary set of observations sharing global parameters. Our method extends recent developments in simulation-based inference (SBI) based on normalizing flows to Bayesian hierarchical models. I will show the results of a quantitative validation on a motivating example amenable to analytical solutions and then apply it to invert a well-known non-linear model from computational neuroscience, using both simulated and real EEG data.