More on this book
Community
Kindle Notes & Highlights
She must abandon the centuries-old dogma of objectivity for objectivity’s sake.
Unfortunately, the acceptance of Bayesian subjectivity in mainstream statistics did nothing to help the acceptance of causal subjectivity, the kind needed to specify a path diagram.
linguistic barrier. To articulate subjective assumptions, Bayesian statisticians still use the language of probability, the native language of Galton and Pearson. The assumptions entering causal inference, on the other hand, require a richer language (e.g., diagrams) that is foreign to Bayesians and frequentists alike.
On the positive side, causal inference is objective in one critically important sense: once two people agree on their assumptions, it provides a 100 percent objective way of interpreting any new evidence (or data).
“When you have eliminated the impossible, whatever remains, however improbable, must be the truth.”
Not all Bayesian networks are causal, and in many applications it does not matter. However, if you ever want
to ask a rung-two or rung-three query about your Bayesian network, you must draw it with scrupulous attention to causality.
Now, as Euclid said 2,300 years ago, two things that each equal a third thing also equal one another. That means it must be the case that P(S | T) P(T) = P(T | S) P(S) (3.1)
This is perhaps the most important role of Bayes’s rule in statistics: we can estimate the conditional probability directly in one direction, for which our judgment is more reliable, and use mathematics to derive the conditional probability in the other direction, for which our judgment is rather hazy.
we need to know P(T | D) and P(T). In the medical context, P(T | D) is the sensitivity of the mammogram—
In many ways, Bayes’s rule is a distillation of the scientific method.
Unfortunately, although ingenious, these approaches suffered a common flaw: they modeled the expert, not the world, and therefore tended to produce unintended results.
finally realized that the messages were conditional probabilities in one direction and likelihood ratios in the other.
The arrow merely signifies that we know the
“forward” probability, P(scones | tea) or P(test | disease). Bayes’s rule tells us how to reverse the procedure, specifically by multiplying the prior probability by a likelihood ratio.
The process of looking only at rows in the table where Smoke = 1 is called conditioning on a variable. Likewise, we say that Fire and Alarm are conditionally independent, given the value of Smoke.
randomization is a way of simulating Model 2. It disables all the old confounders without introducing any new confounders.
procedure known as double blinding).
the do-operator gives us scientifically sound ways of determining causal effects from nonexperimental studies, which challenge the traditional supremacy of RCTs.
The reason for the difficulty is that confounding is not a statistical notion. It stands for the discrepancy between what we want to assess (the causal effect) and what we actually do assess using statistical methods.
This is a general theme of Bayesian analysis: any hypothesis that has survived some test that threatens its validity becomes more likely.
We do not need to argue about whether such worlds exist as physical or even metaphysical entities.
fraction of attributable risk (FAR)
It turns out, however, that under two mild causal assumptions, it is identical to the probability of necessity.
But there is a second version of the “Why?” question, which we ask when we want to better understand the connection between a known cause and a known effect.
The word that scientists use for the second type of “Why?” question is “mediation.”
They can be quantified only after we have reached the third rung of the Ladder of Causation, and that is why I have placed them at the end of this book.
Mediation has flourished in its new habitat and enabled us to quantify, often from the bare data, the portion of the effect mediated by any desired path.
They tell us that bias is a phenomenon on rung one of the Ladder of Causation.
discrimination as “the exercise of decision influenced by the sex of the applicant when that is immaterial to the qualifications for entry.”
Discrimination, unlike bias, belongs on rung two or three of the Ladder of Causation.
I cannot stress enough how often this blunder has been repeated over the years—conditioning on the mediator instead of holding the mediator constant. For that reason I call it the Mediation Fallacy.
261 Yerushalmy, Jacob, 167–169, 174, 183–184 Yule, George
