A few years ago, Weisberg’s Willful ignorance  distinguished two facets of uncertainty: doubt, which is the focus of modern statistics, and ambiguity about the causal structure of the world, which researchers in many domains have not addressed systematically. Statistics formalizes the manipulation of the data obtained from experiments and observations, and has for over a hundred years spurned causal claims on the grounds that they are subjective and not grounded in data. But causality lies at the heart of resolving ambiguity. The concept is complex and must be approached from multiple perspectives. Several recent works on causality promise to remedy this problem computationally, philosophically, and psychologically.
Readers of Computing Reviews may be most familiar with causality in the work of computer scientists such as Judea Pearl. This body of work is the most direct challenge to statisticians’ characterization of causality as subjective and ungrounded. It is based on the representation of causal structures as directed graphs, whose nodes are variables and whose edges indicate that the destination node is “caused by” the source node, in a sense to be discussed later in this review. Pearl teamed with science writer Dana Mackenzie to produce The book of why . This volume is not only an introduction to Pearl’s highly technical earlier works that will be accessible to the general public, but also an engaging history of why causal claims have been avoided by statistical purists and how early work by Sewell Wright, neglected for years except in the form of structural equation modeling, has been revived by Pearl and others and is now claiming a growing following. Pearl grants that the structure of a causal graph is subjective in the sense that it reflects the causal hypotheses of its author. But it makes these hypotheses explicit and yields mathematically rigorous guidance in experimental design and data analysis to evaluate those hypotheses. The book is organized around what Pearl calls “the ladder of causation.” The idea is that analysis of association, understanding of experimental intervention, and reasoning about counterfactuals are qualitatively distinct rungs. While each rung rests on those below it, it cannot be defined by it. Classical statistical analysis, which deals with the rung of association, in principle cannot predict the result of interventions. Moving to this rung requires introduction of the do-calculus, a way to reason about what will happen if a variable in the graph is forced to take a specific value. Similarly, the do-calculus alone cannot enable us to reason counterfactually about what would have happened if we had not done something, which requires further analysis of the causal graph. Successive sections of the book work their way up this ladder, with many examples of how the techniques were (or could have been) applied to real research problems (such as the health effects of smoking, or the nature-nurture debate, or educational policy decisions).
Pearl’s work has led to a plethora of other research. One particularly important recent example is Peters et al.’s Elements of causal inference . This volume extends the causal graph approach to more complex statistical situations (such as when a joint distribution suffices to resolve causal direction between variables). It also explores how causal models can enhance machine learning, and brings together important results on how to learn causal models from data.
Pearl explicitly leaves the meaning of “cause” on the edges of his graphs undefined, saying only that the destination variable “listens to” the value of the source variables in setting its value. Mathematically, this relation may be characterized in some cases as a conditional probability table (as in a Bayesian belief network), or as a deterministic regression equation, but the deeper issue of just what causality is remains ambiguous. Philosophers have probed this question at least since the time of Aristotle, who distinguished four kinds of cause in his Physics and Metaphysics. While the philosophical literature on causation is vast, Mumford and Anjum’s Causation is an excellent and succinct summary . This slender volume walks the reader through a wide range of philosophical approaches to causation, from Hume’s reduction of the notion to the regularity of a sequence of actions, through counterfactual dependence, physicalism (transfer of some property from the cause to the effect), pluralism (the view that the concept of “cause” confounds multiple fundamentally distinct things), primitivism (which rejects definitions of causality by making it an axiom), and dispositionalism (the view that certain objects have a disposition to cause certain effects). Mumford and Anjum discuss Pearl’s causal graphs in the broader statistical context as yet another approach to defining causality: interventionism, the idea that causality is defined by what happens to a system when we take an action upon it.
One reason that philosophers have been so fascinated by causality, and a powerful motive for scientists to go beyond correlation and begin to formalize the concept, is that people inevitably rationalize their thoughts in causal terms. So understanding causality requires not just philosophical distinctions and appropriate mathematical formalisms, but also a psychological explanation of just what people are doing in their heads when they make causal claims. Michael Waldman’s encyclopedic The Oxford handbook of causal reasoning brings together 35 well-edited and integrated chapters by 61 researchers exploring causal reasoning from the standpoint of experimental psychology and cognitive science. After the editor’s introduction, 12 chapters introduce various theories of causal cognition, defining them and summarizing experimental evidence that illuminates them. Some of these chapters explicitly draw on the work of Pearl and others in modeling causal reasoning as a graph structure. An important trend in recent psychological studies of causation is its role in a wide range of cognitive functions, explored in the next 13 chapters, ranging from vision through planning and control, learning, categorization, induction, explanation, diagnosis, argumentation, and decision-making. The third part of the book offers six chapters describing different domains in which humans reason causally, including intuitive theories, space and time, legal and moral questions, psychiatric diagnosis, natural language, and social processes. The last three chapters explore the development of causal reasoning, including evidence for its presence in other species and its role in culture.
Pearl describes the recent willingness of scientists to speak openly about causality as the “causal revolution.” Work by him and his associates equips us to compute in a rigorous way about an undefined “causality,” but full appreciation of what it is we are analyzing requires grappling with the philosophical and psychological dimensions of the subject. Happily, readers who wish to probe further have an abundance of excellent material available.