Hierarchical Bayesian inference

Behavioral Mapping of Hierarchical Dynamical Models Accelerates Bayesian Parameter Inference

Learning behavioral compatibility across hierarchical dynamical models to accelerate Bayesian parameter inference.

Dynamical systems Bayesian inference Model reduction

Paper Code Participant

Behavioral compatibility region for the linear-system example, with baseline and GP-guided MCMC samples, the compatibility ellipse, and the true parameter — Behavioral compatibility for the illustrative linear system, with baseline and GP-guided MCMC samples overlaid. The compatibility ellipse is evaluated at the reduced-posterior mean. Panel (a) from the paper.

Project overview

Bayesian parameter inference for complex nonlinear dynamical models is often limited by the cost of repeated model simulation. We present a behavioral mapping framework that uses the inferred posterior of a higher-level model to accelerate inference of a lower-level model without requiring state or parameter correspondence between them.

Building on approximate simulation relations for hierarchically related models, we define the notion of behavioral compatibility and quantify the behavioral support of detailed model parameters using the reduced model posterior. We learn a level set of behavioral support using a Gaussian process and use it to filter detailed model parameter proposals before expensive simulations during Markov Chain Monte Carlo (MCMC) inference. We derive conditions under which the behavioral support level set retains all detailed model parameters that fit the experimental data within a prescribed tolerance.

We apply this method to a hierarchy of gene-expression models fitted to cell-free experimental data. After initial setup costs, our approach speeds up MCMC by 8.02% for the phenomenological model and 15.21% for the mechanistic model.

Paper

Behavioral Mapping of Hierarchical Dynamical Models Accelerates Bayesian Parameter Inference
Jingsong Bai and Ayush Pandey. arXiv:2610.30683 (2026). DOI: 10.48550/arXiv.2610.30683.

Code

Hierarchical inference examples and methods
The hierarch-inf repository contains the linear-system example, hierarchical inference of phenomenological and mechanistic gene-expression models, and model construction with SBML export.

Current participants

Jingsong Bai

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