Tools of Composition
Causal inference requires two kinds of knowledge: knowledge of what to estimate, and knowledge of when that estimate is trustworthy. But before we can probe causal claims, we need the tools to articulate them. These foundations provides those tools: a modelling workflow, a causal estimation strategy, a graphical language for causal reasoning, and the structural patterns that make that language tractable.
Why These Tools, in This Order
Bayesian Inference. We begin with the modelling workflow itself. The habits established here carry the rest of the book. Demonstrating concrete and repeatable model-building patterns, we establish that probabilistic programming gives us an expressive capacity that formula-based syntax alone cannot reach. We need that expressiveness to explore the posterior distributions of complex data-generating processes.
Causal Inference. A fitted model is not yet a causal claim. The coefficients of a well-specified regression describe association; they do not, by themselves, license intervention or assert causal effect. Causal inference must ask what additional machinery is needed to move from “these variables are related” to “changing this variable would change that one”. For computing answers to these intervention questions, this chapter provides a general-purpose algorithm called g-computation. Change the assumptions you feed it, or the contrast you ask it for, and the same algorithm returns a different causal quantity. The question of if we have the right assumptions is deliberately left open. That is the work of the next two chapters.
Causal Identification. To justify a causal reading of any statistical estimate, we need a language for encoding what we believe about which variables affect which. The third chapter introduces that language. Directed acyclic graphs make causal assumptions visible, auditable and crucially, falsifiable through their implied conditional independencies. The chapter builds the full graphical toolkit introducing: paths, probabilistic factorisation, d-separation and the adjustment formula. These tools are then applied in the next chapter.
Composition of Causal Models. The final chapter in this part shows that complex causal structures are not as daunting as they first appear. They decompose into core atomic patterns: the fork, the chain, and the collider. Compose those, and you get mediation and moderation DAGs. Each distinct pattern comes with its own rules about what to condition on, and why. Every identification strategy in the rest of the book is, at bottom, an argument about which pattern applies and what to do about it.
What These Tools Enable
Together, these four chapters outline a routine: specify a model, compute causal contrasts for a target causal quantity, reason about the graph using its atomic structure, and justify the resulting claim. Applied causal inference is a species of argumentation. Critics of causal claims will target the model-encoded assumptions. To participate in these debates we need first to know how to express causal claims in the language of statistical modelling.
Verlyn Klinkenborg’s advice to writers is to know what each sentence says, what it doesn’t say, and what it implies (Klinkenborg 2012). The advice applies to models too. A model says something concrete; hours of study predict exam scores, treatment shifts an outcome. It doesn’t say other things; every omitted variable, every distributional choice is a silence that shapes the meaning of what remains. A model implies consequences that are unclear until exposed to the stress test of data. Knowing what your model actually says, as distinct from what you intended it to say, is the skill these chapters aim to build.