HNPE: Leveraging Global Parameters for Neural Posterior Estimation

TL;DR

HNPE introduces a hierarchical neural approach to improve parameter inference in models with indeterminate solutions by leveraging auxiliary observations sharing global parameters, validated on neuroscience data.

Contribution

The paper proposes a novel hierarchical neural posterior estimation method that addresses indeterminacy in parameter inference by utilizing shared global information.

Findings

Successfully applied to a neuroscience model with real EEG data.

Outperforms existing methods in resolving parameter indeterminacy.

Validated on analytical and real-world datasets.

Abstract

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.