Quantitative indices for low-curvature likelihood profiles in practical identifiability

Develop quantitative indices that rigorously characterize low-curvature (flat) likelihood profiles in profile likelihood–based practical identifiability analysis, enabling reliable resolution of parameter coordinates whose conditional loss surfaces exhibit near-flat behavior without relying solely on calibrated statistical thresholds.

Background

The paper discusses limitations of traditional profile likelihood methods for practical identifiability, noting that parameters with relatively flat likelihood profiles are difficult to resolve using standard curvature-based diagnostics. While threshold calibration can sometimes recover identifiability, the absence of rigorously defined quantitative indices to capture such low-curvature cases hinders robust inference.

Motivated by recurring flatness across diverse biological models, the authors argue for scaling laws of identifiability and introduce higher-order metrics as part of their framework. The quoted sentence explicitly identifies the lack of quantitative indices for low-curvature profiles as an open challenge.