Summary: This book strives to fulfill a three-pronged mission:
- before you in nonmathematical language the intellectual content of the Causal Revolution and how it is affecting our lives as well as our future
- to share with you some of the heroic journeys, both successful and failed, that scientists have embarked on when confronted by critical cause-effect questions.
- Returning the Causal Revolution to its womb in artificial intelligence, I aim to describe to you how robots can be constructed that learn to communicate in our mother tongue—the language of cause and effect.
P(L | do(D))
“if we are interested in the effect of a drug (D) on lifespan (L), then our query might be written symbolically as: P(L | do(D)). In other words, what is the probability (P) ”
counterfactual (plural counterfactuals): A claim, hypothesis, or other belief that is contrary to the facts.
You cannot answer a question that you cannot ask, and you cannot ask a question that you have no words for.
- Knowledge” stands for traces of experience the reasoning agent has had in the past, including past observations, past actions, education, and cultural mores, that are deemed relevant to the query of interest. The dotted box around “Knowledge” indicates that it remains implicit in the mind of the agent and is not explicated formally in the model.
- Scientific research always requires simplifying assumptions, that is, statements which the researcher deems worthy of making explicit on the basis of the available Knowledge. While most of the researcher’s knowledge remains implicit in his or her brain, only Assumptions see the light of day and are encapsulated in the model. They can in fact be read from the model, which has led some logicians to conclude that a model is nothing more than a list of assumptions. Computer scientists take exception to this claim, noting that how assumptions are represented can make a profound difference in one’s ability to specify them correctly, draw conclusions from them, and even extend or modify them in light of compelling evidence.
Various options exist for causal models: causal diagrams, structural equations, logical statements, and so forth. I am strongly sold on causal diagrams for nearly all applications, primarily due to their transparency but also due to the explicit answers they provide to many of the questions we wish to ask. For the purpose of constructing the diagram, the definition of “causation” is simple, if a little metaphorical: a variable X is a cause of Y if Y “listens” to X and determines its value in response to what it hears. For example, if we suspect that a patient’s Lifespan L “listens” to whether Drug D was taken, then we call D a cause of L and draw an arrow from D to L in a causal diagram. Naturally, the answer to our query about D and L is likely to depend on other variables as well, which must also be
“Estimand” comes from Latin, meaning “that which is to be estimated.”
