A Causal inference developed by Pearl

[jbergman]

I was referring more to framing the concept in ways that are clear and specific enough to be used, applied.

I disagree. Pearl's framework is specific and clear. I think most just have an ignorance of the methods.

 

[Dale]

I disagree. Pearl's framework is specific and clear. I think most just have an ignorance of the methods.

Or, like me, are even aware of the mathematical and statistical methods, but not of the connection to causal inference

 

[Ackbach]

Interesting. I have seen the math in this called structural equation modeling. I never heard of it in terms of causality. So I am aware of the method, but not the causal interpretation.

Structural Equation Modeling is an integral part of the New Causal Revolution. Indeed, it is the glue that shows why Pearl's Directed Acyclic Graph approach and Rubin's Potential Outcomes Framework are equivalent.

Do you agree that P(A | B) is a causal relationship?
That is to say, P(A) given P(B) is a mathematical model of dependence, with a before/after status and causality?

At the intervention level (Pearl's "Second rung"), causality looks like this: $P(Y|do(X))>P(Y).$ In this case, we would say that $X$ causes $Y.$ Here, the $do$ operator means "force the variable $X$ to have the value $x.$ Much of Pearl's framework has to do with eliminating the $do$ expression so that you can get an expression you can evaluate in terms of data (the $do$ operator is not directly measurable). Conditional probability on its own is utterly incapable of expressing the ideas of causality.

 

[Ackbach]

I have some questions about causal inference developed by Pearl. For a background see e.g. the thread https://www.physicsforums.com/threads/the-causal-revolution-and-why-you-should-study-it.987205/
and wikipedia page https://en.wikipedia.org/wiki/Causal_model

Scientists think in causal terms intuitively, even without knowing about formal theory of causal inference. Is there an example of an actual scientific problem that scientist couldn't solve with intuitive causal thinking, but solved it with the use of formal causal inference?

One almost-example is the idea that smoking causes lung cancer. Now this had actually been causally established before Pearl's ideas came out. However, it is possible to show this using the front-door criterion - a dimension of Pearl's framework. Pearl's magnum opus, Causality: Models, Reasoning, and Inference, has been cited thousands of times. If you want examples of how the New Causal Revolution has produced causal information that wouldn't otherwise have been obtained, look at the papers that cite that book.

The fact is this: before the New Causal Revolution, if you wanted to demonstrate causality, you had one and only one tool: the Randomized Controlled Trial (RCT) - the good ol' tried-and-true experiment. This harks back to Mill's Methods for demonstrating causality, as well as Francis Bacon. If you didn't manipulate variables (force them to have particular values), then you didn't have causality. An observational study, in particular, was utterly incapable of demonstrating causality because by definition you don't manipulate variables in an observational study.

However, with the coming of the New Causal Revolution, while you certainly still have the experiment available, you can get causality from an observational study, given the right data and the right model. How does that all work? Study the New Causal Revolution (see link in the OP) to find out! The importance of the New Causal Revolution is that many of the experiments you might like to run are impractical or unethical (smoking, anyone?). So we can still get causality sometimes, even when a RCT is not available.

 

[Ackbach]

I believe at this stage , causation is more a philosophical matter than a scientific one.

I strongly disagree with this. Science has long been concerned with causation - I would say primarily concerned with causation. It's the most important question! Mill's Methods show how an experiment demonstrates causality, but as I have just said in this thread, the New Causal Revolution has demonstrated how you can get causality from an observational study, given the right conditions. This opens up many new possibilities.

The field of statistics, for a long time, distanced itself from causality because it didn't have the vocabulary and tools necessary to deal with it, other than in experiments. But again, the New Causal Revolution has changed all that.

 

[WWGD]

I strongly disagree with this. Science has long been concerned with causation - I would say primarily concerned with causation. It's the most important question! Mill's Methods show how an experiment demonstrates causality, but as I have just said in this thread, the New Causal Revolution has demonstrated how you can get causality from an observational study, given the right conditions. This opens up many new possibilities.

The field of statistics, for a long time, distanced itself from causality because it didn't have the vocabulary and tools necessary to deal with it, other than in experiments. But again, the New Causal Revolution has changed all that.

Please see my reply sbove to Demystifier. That is what I meant. But , yes, @Bergmann , I was not saying Pearl does not provide a clear setup; I am not familiar with it. I meant now science must sbsorb it and work with it. I will read it when I get a chance. I am not saying that the concept is not relevant to science, only that at this point it is at its infancy and hasn't been yet absorbed. Thats all.

 

[Dale]

Science has long been concerned with causation - I would say primarily concerned with causation.

I think that the truth is probably somewhere between your position and @WWGD's position.

Science students tend to dramatically overly apply causation and causality. It is something that has to be corrected frequently.

For example, Newton's 3rd law can be written $\vec F_{ij}=-\vec F_{ji}$. It is common for students to believe that the force on the left is an "action" which causes the "reaction" force on the right. They can then become confused on how to apply Newton's 3rd when the cause and effect is not clear. Since causes precede effects and since the forces in Newton's 3rd law are simultaneous they generally should not be thought of in terms of cause and effect. Even worse is if they do find a pair of causally related forces (one preceding the other) and try to apply Newton's 3rd law across time.

Another example is Maxwell's equations. $$ \nabla \cdot \vec E = \rho $$$$\nabla \cdot \vec B = 0$$$$\nabla \times \vec E = -\partial_t \vec B$$$$\nabla \times \vec B = \vec J + \partial_t \vec E$$ Not just students, but also more experienced scientists will describe the left hand side as effects and the right hand side as causes. They will even describe light as "changing E fields causing changing B fields causing changing E fields and repeating" while referring to these equations. This has the same problem as above: causes precede effects but the things in Maxwell's equations happen at the same time.

There is a causal formulation of electromagnetism called Jefimenko's equations (or rather the retarded potentials): $$\phi(\vec r,t)=\int\frac{\rho(\vec r',t_r)}{|\vec r-\vec r'|} d^3\vec r'$$$$ \vec A(\vec r,t)=\int \frac{\vec J(\vec r',t_r)}{|\vec r-\vec r'|} d^3\vec r'$$$$t_r=t-\frac{\vec r-\vec r'}{c}$$In this formula causes on the right side of the equations precede effects on the left side. This does express a true causaul relationship, but such equations are actually rather uncommon so I wouldn't say that science is primarily concerned with causation. It is certainly a topic of some concern, but not so ubiquitously as you imply. Even when causal relations do exist, they are often not the most convenient or useful approach to a phenomenon.

 

[Ackbach]

Please see my reply sbove to Demystifier. That is what I meant. But , yes, @Bergmann , I was not saying Pearl does not provide a clear setup; I am not familiar with it. I meant now science must sbsorb it and work with it. I will read it when I get a chance. I am not saying that the concept is not relevant to science, only that at this point it is at its infancy and hasn't been yet absorbed. Thats all.

Yes, I agree. The New Causal Revolution needs to make significant inroads on traditional statistics and science education, and it hasn't, yet.

I think that the truth is probably somewhere between your position and @WWGD's position.

Science students tend to dramatically overly apply causation and causality. It is something that has to be corrected frequently.

For example, Newton's 3rd law can be written $\vec F_{ij}=-\vec F_{ji}$. It is common for students to believe that the force on the left is an "action" which causes the "reaction" force on the right. They can then become confused on how to apply Newton's 3rd when the cause and effect is not clear. Since causes precede effects and since the forces in Newton's 3rd law are simultaneous they generally should not be thought of in terms of cause and effect. Even worse is if they do find a pair of causally related forces (one preceding the other) and try to apply Newton's 3rd law across time.

Another example is Maxwell's equations. $$ \nabla \cdot \vec E = \rho $$$$\nabla \cdot \vec B = 0$$$$\nabla \times \vec E = -\partial_t \vec B$$$$\nabla \times \vec B = \vec J + \partial_t \vec E$$ Not just students, but also more experienced scientists will describe the left hand side as effects and the right hand side as causes. They will even describe light as "changing E fields causing changing B fields causing changing E fields and repeating" while referring to these equations. This has the same problem as above: causes precede effects but the things in Maxwell's equations happen at the same time.

There is a causal formulation of electromagnetism called Jefimenko's equations (or rather the retarded potentials): $$\phi(\vec r,t)=\int\frac{\rho(\vec r',t_r)}{|\vec r-\vec r'|} d^3\vec r'$$$$ \vec A(\vec r,t)=\int \frac{\vec J(\vec r',t_r)}{|\vec r-\vec r'|} d^3\vec r'$$$$t_r=t-\frac{\vec r-\vec r'}{c}$$In this formula causes on the right side of the equations precede effects on the left side. This does express a true causaul relationship, but such equations are actually rather uncommon so I wouldn't say that science is primarily concerned with causation. It is certainly a topic of some concern, but not so ubiquitously as you imply. Even when causal relations do exist, they are often not the most convenient or useful approach to a phenomenon.

Perhaps. But I can't help thinking that most scientists want to know why something is happening. They see a phenomenon and want to explain it - that is, they want to explain why. That's causal language.

 

[FactChecker]

Perhaps. But I can't help thinking that most scientists want to know why something is happening. They see a phenomenon and want to explain it - that is, they want to explain why. That's causal language.

Yes, but that is much trickier than many realize. When forces are in balance, it is often true that they coexist and neither can be said to cause the other. They are just in balance and may remain stable that way for a long time.

 

[Dale]

Perhaps. But I can't help thinking that most scientists want to know why something is happening. They see a phenomenon and want to explain it - that is, they want to explain why. That's causal language.

Not always. "Why" is broader than causality.

Scientifically "why" can also refer to implication. E.g. you might ask "Why does a fast moving clock tick slower than coordinate time in a given reference frame?" The answer could reasonably be Einstein's two postulates, but the two postulates are not causes that precede effects, they are logical principles from which physical phenomena can be deduced. So it is not a causal relationship that is sought with this "why" question.

"Why" can also signal a request for an explanation in terms of a different theory. Especially when asking about why some classical behavior occurs in terms of some underlying quantum mechanical phenomena. Or when asking about some Newtonian gravitational behavior in terms of general relativity. A more general theory does not precede an approximate theory in any meaningful sense, and in fact historically usually the approximate theory precedes the general theory. So again, it is not a causal relationship that is sought with this "why" question.

Non scientifically "why" can also refer to motivation. In psychology motivations could be considered causes of behaviors, but in physics we try to avoid motivation-based why questions.

So "explain", "why" and even "want to explain why" are not always causal language. The non-causal "why" questions in physics are very important, and perhaps even dominant. In particular, theoretical physics is almost always focused on the non-causal meanings of "why". Which is why (implication) I think that your "primarily" assertion is overly broad.

Not that you are wrong that causality is important nor are you wrong that finally having a framework for causality is very cool, but I think you are overstating your case. This causal inference stuff is interesting enough on its own that it is not necessary to overstate and oversell it.

 

[WWGD]

I was surprised recently, finding out the extensive role that Category Theory plays in the causation layout.