Bayesian Inference for Stationary Points in Gaussian Process Regression Models for Event-Related Potentials Analysis

TL;DR

This paper introduces a Bayesian approach using Gaussian processes to accurately identify stationary points in functions, specifically applied to EEG data for analyzing age-related changes in speech perception.

Contribution

It presents a novel semiparametric Bayesian model that efficiently infers stationary points without prior knowledge of their number, improving interpretability in EEG analysis.

Findings

Automatically identifies characteristic ERP components and latencies.

Demonstrates age-related differences in speech perception timing.

Avoids excessive averaging by individual-level analysis.

Abstract

Stationary points embedded in the derivatives are often critical for a model to be interpretable and may be considered as key features of interest in many applications. We propose a semiparametric Bayesian model to efficiently infer the locations of stationary points of a nonparametric function, while treating the function itself as a nuisance parameter. We use Gaussian processes as a flexible prior for the underlying function and impose derivative constraints to control the function's shape via conditioning. We develop an inferential strategy that intentionally restricts estimation to the case of at least one stationary point, bypassing possible mis-specifications in the number of stationary points and avoiding the varying dimension problem that often brings in computational complexity. We illustrate the proposed methods using simulations and then apply the method to the estimation of event-related potentials (ERP) derived from electroencephalography (EEG) signals. We show how the proposed method automatically identifies characteristic components and their latencies at the individual level, which avoids the excessive averaging across subjects which is routinely done in the field to obtain smooth curves. By applying this approach to EEG data collected from younger and older adults during a speech perception task, we are able to demonstrate how the time course of speech perception processes changes with age.