Approximate Bayesian Computation Made Easy: A Practical Guide to ABC-SMC for Dynamical Systems with \texttt{pymc}

TL;DR

This paper provides a practical, example-driven guide to implementing Approximate Bayesian Computation with Sequential Monte Carlo (ABC-SMC) for dynamical systems using Python and PyMC, making likelihood-free inference more accessible.

Contribution

It offers a comprehensive tutorial with code examples demonstrating how to apply ABC-SMC to various mechanistic models in ecology and epidemiology, emphasizing ease of use and interpretability.

Findings

ABC-SMC effectively infers parameters in intractable likelihood models.

Partial observability impacts parameter identifiability.

Hierarchical structures naturally emerge in Bayesian ABC-SMC.

Abstract

Mechanistic models are essential tools across ecology, epidemiology, and the life sciences, but parameter inference remains challenging when likelihood functions are intractable. Approximate Bayesian Computation with Sequential Monte Carlo (ABC-SMC) offers a powerful likelihood-free alternative that requires only the ability to simulate data from mechanistic models. Despite its potential, many researchers remain hesitant to adopt these methods due to perceived complexity. This tutorial bridges that gap by providing a practical, example-driven introduction to ABC-SMC using Python. From predator-prey dynamics to hierarchical epidemic models, we illustrate by example how to implement, diagnose, and interpret ABC-SMC analyses. Each example builds intuition about when and why ABC-SMC works, how partial observability affects parameter identifiability, and how hierarchical structures naturally emerge in Bayesian frameworks. All code leverages PyMC's modern probabilistic programming interface, ensuring reproducibility and easy adaptation to new problems. The code its fully available for download at \href{https://github.com/mariocastro73/ABCSMC_pymc_by_example}{mariocastro73/ABCSMC\_pymc\_by\_example}