HNPE: Leveraging Global Parameters for Neural Posterior Estimation
This addresses parameter inference challenges in scientific domains like radio astronomy and neuroscience, though it is an incremental extension of existing simulation-based inference methods.
The paper tackles the problem of inferring parameters in strongly indeterminate stochastic models by introducing hierarchical neural posterior estimation (HNPE), which leverages global parameters from auxiliary observations to resolve indeterminacy, validated on analytical examples and applied to a computational neuroscience model with simulated and real EEG data.
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 strongly indeterminate, 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 work, we 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. We validate quantitatively our proposal 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.