Philosophy and the practice of Bayesian statistics

 

This is a 2012 paper by Andrew Gelman and Cosma Rohilla Shalizi on what they view as a misuse of Bayesian statistics in scientific reasoning. I found this interesting because their definition of hypothetico-deductivism closely matches up with Eliezer Yudkowsky's definition of rationalization, and their definition of inductive inference closely matches up with his definition of rationality. The definitions:

 

Eliezer Yudkowsky:

Rationality - Starting from evidence, and then crunching probability flows, in order to output a probable conclusion.

Rationalization - Starting from a conclusion, and then crunching probability flows, in order to output evidence apparently favoring that conclusion.

 

Andrew Gelman and Cosma Rohilla Shalizi:

Inductive Inference - An accretion of evidence is summarized by a posterior distribution, and scientific process is associated with the rise and fall in the posterior probabilities of various models.

Hypothetico-Deductivism - Scientists devise hypotheses, deduce implications for observations from them, and test those implications. Scientific hypotheses can be rejected (i.e., falsified), but never really established or accepted in the same way.

 

Now, what's interesting about the paper is that in contrast to Eliezer Yudkowsky's view they argue that rationalization (hypothetico-deductivism) is the correct analytic method, and rationality as Eliezer Yudkowsky defined it is wrong. They make the following argument:

 

Social-scientific data analysis is especially salient for our purposes because there is general agreement that, in this domain, all models in use are wrong – not merely falsifiable, but actually false. With enough data – and often only a fairly moderate amount – any analyst could reject any model now in use to any desired level of confidence. Model fitting is nonetheless a valuable activity, and indeed the crux of data analysis. To understand why this is so, we need to examine how models are built, fitted, used and checked, and the effects of misspecification on models.

 

They also argue Popper made multiple errors, but that his fundamental view is closer to correct than Kuhn's, and that correct science is about attempting to falsify hypotheses. They simply disagree with how Popper went about doing it.

 

Another interesting issue to me is that if you look at the main post Against Rationalization, Adirian and Vladimir_Nesov both suggested that both forms of analysis are acceptable, but TheAncientGeek was the only one who argued rationalization over rationality, and his comment received multiple downvotes. This also appears to me to have been a major concept central to many parts of the sequences. Andrew Gelman and Eliezer Yudkowsky had a bloggingheads.tv conversation together, b̶̶̶u̶̶̶t̶̶̶ ̶̶̶I̶̶̶'̶̶̶m̶̶̶ ̶̶̶n̶̶̶o̶̶̶t̶̶̶ ̶̶̶s̶̶̶u̶̶̶r̶̶̶e̶̶̶ ̶̶̶i̶̶̶f̶̶̶ ̶̶̶t̶̶̶h̶̶̶i̶̶̶s̶̶̶ ̶̶̶p̶̶̶a̶̶̶r̶̶̶t̶̶̶i̶̶̶c̶̶̶u̶̶̶l̶̶̶a̶̶̶r̶̶̶ ̶̶̶t̶̶̶o̶̶̶p̶̶̶i̶̶̶c̶̶̶ ̶̶̶e̶̶̶v̶̶̶e̶̶̶r̶̶̶ ̶̶̶c̶̶̶a̶̶̶m̶̶̶e̶̶̶ ̶̶̶u̶̶̶p̶̶̶.̶̶̶

 

Thoughts?

 

Edit - Andrew Gelman and Eliezer Yudkowsky discuss this issue at the end of the bloggingheads video.  Click on "The difference between Eliezer and Nassim" for their take.  I also fixed a link.

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13 comments, sorted by Click to highlight new comments since: Today at 4:07 AM

[Edited: Corrected typo] Roughly: You'll have to make a better argument that rationalization and hypothetico-deductivism are the same thing, because one of us is deeply wrong about this, and I don't think it's me.

[-][anonymous]8y00

Possibly... Although my interpretation depends on whether yudkowsky is using the word conclusion to also refer to a hypothesis, I think it's hard to argue that he means something other than inductive inference in his definition of rationality, and so the central issue stands even if rationalization is slightly different.

His definition of rationality is "Bayesian inference."

And rationalization isn't "Everything that isn't rationality", regardless of what rationality refers to.

rationalization (hypothetico-deductivism)

Rationalisation, as defined by Eliezer in the cited posting, consists of selecting evidence for a favoured conclusion and ignoring evidence against. Hypothetico-deductivism, as defined by Gelman and Shalizi in the cited article, consists of looking for evidence bearing on a hypothesis and accepting the evidence whichever way it goes.

In one, you ignore inconvenient evidence; in the other, you accept inconvenient evidence.

These are completely different things. Why do you say they are the same thing?

[-][anonymous]8y00

As I said in response to OrphanWilde, maybe. In that particular instance, the inexactness of his language means it is possible Eliezer meant to use the term under the narrow confines of his example, but several commenters on that post seemed to be using my definition, but it's a largely irrelevant issue as there can be no doubt that Eliezer favors inductive inference, and that the paper favors hypothetico-deductivism. There is a clear dispute here; they even said so in the video. Why is everyone so interested in nitpicking semantics when the relevant issue is well understood? The semantics of rationalization won't change that.

Why is everyone so interested in nitpicking semantics

This is not nitpicking semantics. This is looking at the actual things that are not merely being named by the words, but described at length in the cited sources: selecting only the evidence one likes, versus accepting the evidence whether one likes it or not. When Eliezer talks about rationalisation, he is not talking about hypothetico-deductivism. Gelman and Shalizi talk about hypothetico-deductivism; they do not talk about rationalisation. Their respective definitions do not at all "match up closely".

In that particular instance, the inexactness of his language means it is possible Eliezer meant to use the term under the narrow confines of his example,

There is nothing inexact about his language, and his example is not a narrow confine.

but several commenters on that post seemed to be using my definition

Your definition bears no relationship to anyone else's use of the word "rationalisation". No definition of the word includes the idea of testing a hypothesis; all definitions relevant to the present context include the idea of fitting the evidence to the hypothesis.

there can be no doubt that Eliezer favors inductive inference, and that the paper favors hypothetico-deductivism.

Indeed so, and he has had some things to say about hypothetico-deductivism. But not in the cited article, and he does not call it rationalisation.

[-][anonymous]8y00

As much fun as this argument is, if you think there's a better source that better describes Eliezer's views on hypothetico-deductivism, you could just cite it instead.

I am only aware that he has written on the matter somewhere. The article cited is not a worse source for his views on the subject, it is not a source at all. Its subject matter is completely different and it does not belong in the discussion.

There is a difference between "crunching probability flows, in order to output evidence apparently favoring that conclusion" and testing a hypothesis. Testing a hypothesis is an open-ended process. The tester may do it in order to find evidence in support of it, but that is not necessarily what they'll get.

This exact topic comes up in the discussion you linked to – towards the end under “The difference between Eliezer and Nassim Taleb.” (not a descriptive caption)

[-][anonymous]8y00

You're right. I've updated the post to reflect this. Thanks!

Let's not forget base rates. It is easier to find hundred people willing to do rationalization than one person willing to do LW-style rationality; even among the scientists. Therefore the former will produce more total output.

I don't think the argument is based on the amount of people who succeed with LW-style rationality.

Andrew Gelman is the other of an important book on Bayesian statistics and therefore worthy to be listened to when he says that people draw the wrong conclusions from Bayesianism.