Causal Dynamics for Complex Systems

A course in structural causal dynamics

0.1 Preface

Status: In Progress

v0.3

Welcome to Causal Dynamics for Complex Systems. This book develops a unified framework combining causal reasoning with dynamical systems modelling, enabling us to answer questions about what happens when we intervene in complex systems that evolve through time, have feedback loops, are only partially observable, and tend toward equilibria (“attractor states”) that shift with changing environmental conditions.

The book is mostly my attempt to organise my thoughts and align the Julia-native quantitative methods needed to successfully model complex biological systems, specifically to correctly describe them, understand their underlying mechanisms to a depth that is sufficient to inform and predict the effects of interventions on the system. This book will never be complete.

Conceptually, this book is organised around three modelling layers of a data-generating process: Structural (causal structure and invariances), Dynamical (how latent states evolve through time), and Observable (how measurements are generated from latent states, typically with noise). These layers are complemented by Pearl’s Causal Hierarchy of the three levels of Reason, which characterise distinct modes of reasoning: association (perceiving), intervention (doing), and counterfactual (imagining).

More specifically, this books is an effort to implement these notions and methods into a coherent modelling architecture, with code and exercises, which can be followed as a course in structural causal dynamics.

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0.2 Chapter Progress

Introduction

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0.2.1 Part I — Structural

The Causal Hierarchy and Three Worlds

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The Primary Unit: The Dyad

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Graph Theory and Causal Patterns

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Structural Causal Models as Executable Mechanisms

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Identification: When Can We Learn from Data?

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Do-Calculus: Rules for Interventions

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Counterfactuals: Alternative Concrescences at Structural Level

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Transportability: Generalising Structural Claims

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From Structure to Time: FEP and Attractors

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0.2.2 Part II — Dynamical

Deterministic Dynamics: ODEs as Causal Processes

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Stochastic Dynamics: SDEs and Random Processes

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State-Space Models: Inferring Structure from Observations

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Intervening in Deterministic Systems

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Intervening in Stochastic Systems

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Advanced Dynamics: Regimes, Networks, and Resilience

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Counterfactual Dynamics: Alternative Trajectories

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Sensitivity Analysis and Robustness in Dynamics

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From Dynamical to Observable: Measurement and Actualisation

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0.2.3 Part III — Observable

Observational Methods: Learning from Data

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TMLE and Doubly Robust Estimation

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Model Validation with Observable Data

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Interventional Reasoning: Forecasting Under Interventions

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Policy Evaluation and Dynamic Treatment Strategies

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Causal Decision-Making

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Counterfactual Reasoning: Unit-Level Alternatives

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Hypothesis Generation from Counterfactuals

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Experimental Design: Optimal Measurements

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0.2.4 Part IV — Synthesis

CDMs: The Unified Framework

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0.2.5 Appendices

Concept Reference Tables

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Reporting Standards

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Software Patterns

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