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I think you are overstating Judea Pearl's argument. He doesn't claim it is impossible to answer causal questions (on observational data) without resorting to do-calculus. What he does claim is that to answer causal (interventional or counterfactual) questions you need to define a model and reason on that model in a way that transforms the question into conditional probabilities. Do-calculus provides a framework to help you perform that reasoning, but certainly people have been using things like the backdoor criterion before the invention of do-calculus to answer interventional questions.

He might claim that any other method can be reduced to do-calculus. I'm not sure. I do believe at the core of his argument is need for an explicit model.

Yes, that's a better and more accurate phrasing than I used. The issue is that the correctness of the answer depends on the whether the causal structure of the model matches the underlying generative process. Graphs and do-calculus aren't required for this, but can help to make things clearer. In a later comment on the blog post, Pearl links to a paper that describes one of his "toy" examples: http://ftp.cs.ucla.edu/pub/stat_ser/r400-reprint.pdf. Section 3 of page 584 is the beginning of the example. I'm sad to say that I'm sufficiently amateur at this that I found even the "toy" example to be at the limits of my reasoning ability, but I thought it still illustrated the argument Pearl is making.

I absolutely agree if your model is wrong any causal inferences you draw will be wrong. However his framework does provide mechanisms for determining if your data is inconsistent with your model (ie certain independences should or should not exist). So hopefully if your model is wrong your data will tell you so and you can change your model.

That’s my core understanding too, the model is essential and that not only rubs statisticians the wrong way but also the current luminaries in deep learning get visibly irritated by that too. The irony is that JP was very successful with statistics having invented Bayesian Networks, and now has moved on.

Here he asks a very simple question and look at the body language from the panel: https://www.youtube.com/watch?v=mFYM9j8bGtg&t=50m47s

"you'd be doing a great service to encourage him to formulate such a "toy" question that he thinks is unanswerable without resorting to the do-calculus, which you then try to answer to the audiences' satisfaction using more standard techniques."

This would be very helpful indeed.

I think a lot of the issue comes down to how idiosyncratic Pearl's work is. It will have to accumulate quite a lot of victories before enough people will bother with it.

Until then I suspect Causality will remain something of a statistical Finnegan's Wake.

I'll probably read The Book of Why to try and get a better handle on motivation for the technical material.

Thankfully, "Causality: A Primer" is sort of like the CliffNotes to Finnegan's Wake ;)

Thanks, may check it out. This stuff has long been on my to-do list.

I'm not an expert on this stuff at all, but are the toy problems basically formulations of Simpson's paradox? My sense was that if you have a set of a data, where if you cut it into two slices and each slice suggests the same (identical) conclusion, but then if you look at the data overall it suggests a different conclusion, then how do you know which approach is correct? And it seems the only way to know that is to use your judgment about causal factors that generated the data, and the do-calculus helps make that explicit. For instance, when thinking about gender ratios and grad programs, it's more probable that the choice of what grad program to apply to is affected by what gender you are, but it's less probable that the choice of your grad program affects your gender.

Well I just reviewed section 3 of page 584 of that pdf that was shared and it seems different, so I probably have a long way to go before I understand this stuff.

Not all "paradoxes" are similar to Simpson's paradox. See this PDF for more similar "paradoxes":

https://ftp.cs.ucla.edu/pub/stat_ser/r409-corrected-reprint....

(I quote the word paradox, because they aren't really paradoxes once we have an understanding of what's going on.)

> it sure doesn't feel "fine" for the two of you to disagree on what seems like such a fundamental issue. Instead, this seems like a case where two extremely smart individuals should be able to reach an common understanding instead of accepting disagreement as a final outcome.

Once you've reached the limits of what you can know (after examining all data, worked through all arguments, etc.) this is pretty much the only possible outcome. What works in one situation might not work in others. One person's interpretation of our limited knowledge might very well appear implausible to someone else.

I'll admit to being turned off by Pearl's insistence on working with "toy problems". That might be fine for a philosophical discussion, but it's not of much practical value. I want Pearl to write a few empirical papers attacking important issues, then let's have a discussion about putting ideas into practice.

I have much more sympathy for Pearl. He's constructed "toy" problems that yield different answers depending on the hidden causal structure chosen. He then shows that unless one takes account of the causal structure, it's impossible to correctly answer the problem. The logical conclusion of this is that any technique that doesn't use the causal structure as an explicit assumption is instead using it as an hidden implicit assumption. His hope is that anyone who goes through his exercise will come to the same conclusion. Starting with real-world problems is tricky, because one doesn't know the correct answer in advance, thus it's much harder show the reliance on the assumptions.

Consider a parallel with computer programming. A user complains that they fear a program is giving them the wrong answer on a complex real world problem. They report this, and get back the unhelpful answer "Works for me, will not fix". Unable to shake the feeling that the answer is unreliable, they reduce the problem down to a proof of concept that serves as a simple self-contained test case. Two different inputs produce the same answer, but only one of them can be right! But now they are unable to convince the maintainer to even look at the test case, because now the maintainer says "I need to focus on the real world, and don't want to waste my time on toy examples".

It's a discouraging position to find oneself in.

Oh, I'm completely on board with being explicit about any assumptions you're making, and for thinking deeply about the causal relations, and for thinking about the reliability of the analysis. I've been critical of economists for not thinking things through. And I'm definitely on board with teaching using toy problems.

The problem is that, as far as I can tell, Pearl doesn't go beyond making points with toy problems. He hasn't done much empirical work (has he published a single empirical paper?) or even read much of the empirical literature he's criticizing as worthless. Ultimately, the question is whether policy and other decisions will be better using a particular framework. The fact that Pearl writes with the aggressive confidence of a Hacker News commenter does not mean he's right.

But from a mathematical point of view this insistence of focusing on empirical work is a little bit disheartening isn’t it?

And frankly Judea Pearl is hardly a random internet tinfoil hat guy, nor is he asking people to invest a massive effort checking his looong work (as we eg often see with random NP-completeness “proofs”, or was discussed with the time investment needed to check Mochizuki’s ABC proof - no, he just asks Gellman to apply his own familiar techniques to a toy problem. It does not sound unreasonable at all.

> But from a mathematical point of view this insistence of focusing on empirical work is a little bit disheartening isn’t it?

Why? The only thing that matters is the quality of the empirical work. You can get caught up in philosophical debates about the best way to do research. If it has no impact on empirical work, it's useless.

That's not to say Pearl's arguments are wrong or that his work is useless. The problem is the incompleteness of his arguments. You can't arrogantly dismiss empirical work just because it's imperfect. There's no reason a priori to expect that Pearl's approach will lead to better decisions.

There are many self-proclaimed experts who can point out the flaws in programming language designs, but that doesn't mean they can design a better language, and it doesn't mean existing programming languages are useless. Pearl's approach is not some kind of magic pixie dust that suddenly guarantees your empirical work is more trustworthy. It's unfortunate that Pearl thinks it is, and it prevents him from having a reasonable conversation about the topic.

Well from my point of view when I read the link, I see (with a little bit of characterization) two academics, one of them points at an issue on the standard statistical approach and tools, provides a reproduceable way to showcase that answer, and the other one answers “not interesting - i’ll go now to do real work”. And I found that avoidance of a discussion of a shared example disheartening.

And Pearl isnt just complaining - the provided an alternative. So it seems that one side identified a problem, curated examples, delivered a solution, and now the other side doesnt care about the problem - and causality is not a trivial problem. As academic discussion, not a business meeting, to me thats subpar.

That’s only my view from the outside, it may well be the case that it is wrong and I just need to review more in depth Pearl to see that he does not bring anything useful.

They've been debating this for many years, and Gelman is a coauthor and student of Rubin, who has been debating with Pearl for decades. Gelman is saying he doesn't want to debate the same issues yet again.

The primary message of Pearl is "all other methods are trash and all empirical work done using those methods is trash." My interpretation of the post is that Gelman is arguing other methods are not trash.

I probably agree more with Pearl than Gelman on the details, but Pearl's approach is just not appropriate for an academic setting.

What they are really fighting about is who gets to reference colloquial notions of causality when discussing their work. I don't think it's fair to say that Pearl treats the rest of stats as trash, but he is saying that they are misleading folks by describing their inference as evidence of cause and effect - which is about as bad for most academics and especially for the Rubin crew who have often policed integrity of other inference regimes (like less rigorous ML).

Debating who gets to use which words is a great way to make sure your debate only matters to other academics. I'd love to see the causality camp make their point by unlocking some great new applied results instead!

Refusing to provide a demonstration of the statistical technique on a toy example constructed for pedagogic purpose, hardly constitutes as a "debate". I would file that under: using a lot of words to avoid answering a direct and fundamental question

http://causality.cs.ucla.edu/blog/index.php/2016/02/01/works...

Is this sufficiently applied for you? Pearl may not apply his work on causality often, but there are a lot of people who are on the applied side who do.

Some of these "toy" problems have had pretty major practical effects. For example, reconciling the disagreement between cohort studies and RCTs, in many medical contexts, come down to remarkably simple causal diagrams.

I don't disagree. I'm not debating the value of Pearl's approach. I'm saying other methods can also be helpful. Pearl does not accept that.

What methods?

His main point is that "To properly define causal problems, let alone solve them, requires a vocabulary that resides outside the language of probability theory. This means that all the smart and brilliant statisticians who used joint density functions, correlation analysis, contingency tables, ANOVA, Entropy, Risk Ratios, etc., etc., and did not enrich them with either diagrams or counterfactual symbols have been laboring in vain — orthogonally to the question — you can’t answer a question if you have no words to ask it." http://causality.cs.ucla.edu/blog/index.php/2018/06/11/stati...

I think Pearl is more a theoretician. I believe some of his descendants have done some work that might qualify.

But, I agree that it would be nice if Pearl used real world problems using his methodology.

Why does JP have to be the one to write the empirical papers? Why is that a prerequisite here?

Judea Pearl is attempting to develop (or has developed) and evangelize the approach for others to use it on empirical problems.

So it seems the response is to be in favor of anyone (not just JP) to use it for empirical work.

Do we expect every developer of a theory to put it into practice before it is found convincing? Shouldn't the reasoned explanation of a theory be sufficient for someone else to understand and attempt it?