Randaly comments on Welcome to Less Wrong! (5th thread, March 2013) - Less Wrong

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Comment author: Randaly 18 September 2013 11:53:54PM *  5 points [-]

Frequentism isn't this view's foil

Err, actually, yes it is. The frequentist interpretation of probability makes the claim that probability theory can only be used in situations involving large numbers of repeatable trials, or selection from a large population. William Feller:

There is no place in our system for speculations concerning the probability that the sun will rise tomorrow. Before speaking of it we should have to agree on an (idealized) model which would presumably run along the lines "out of infinitely many worlds one is selected at random..." Little imagination is required to construct such a model, but it appears both uninteresting and meaningless.

Or to quote from the essay coined the term frequentist:

The essential distinction between the frequentists and the [Bayesians] is, I think, that the former, in an effort to avoid anything savouring of matters of opinion, seek to define probability in terms of the objective properties of a population, real or hypothetical, whereas the latter do not.

Frequentism is only relevant to epistemological debates in a negative sense: unlike Aristotelianism and Anton-Wilsonism, which both present their own theories of epistemology, frequentism's relevance is almost only in claiming that Bayesianism is wrong. (Frequentism separately presents much more complicated and less obviously wrong claims within statistics and probability; these are not relevant, given that frequentism's sole relevance to epistemology is its claim that no theory of statistics and probability could be a suitable basis for an epistemology, since there are many events they simply don't apply to.)

(I agree that it would be useful to separate out the three versions of Bayesianism, whose claims, while related, do not need to all be true or false at the same time. However, all three are substantively opposed to one or both of the views labelled frequentist.)

Comment author: satt 19 September 2013 02:01:13AM 0 points [-]

Err, actually, yes it is. The frequentist interpretation of probability makes the claim that probability theory can only be used in situations involving large numbers of repeatable trials, or selection from a large population.

Depends which frequentist you ask. From Aris Spanos's "A frequentist interpretation of probability for model-based inductive inference":

It is argued that the proposed frequentist interpretation, not only achieves this objective, but contrary to the conventional wisdom, the charges of ‘circularity’, its inability to assign probabilities to ‘single events’, and its reliance on ‘random samples’ are shown to be unfounded.

and

The error statistical perspective identifies the probability of an event A—viewed in the context of a statistical model Mθ(x), x∈R^n_X—with the limit of its relative frequency of occurrence by invoking the SLLN. This frequentist interpretation is defended against the charges of [i] ‘circularity’ and [ii] inability to assign ‘single event’ probabilities, by showing that in model-based induction the defining characteristic of the long-run metaphor is neither its temporal nor its physical dimension, but its repeatability (in principle) which renders it operational in practice.

Comment author: RichardKennaway 19 September 2013 03:48:02PM *  3 points [-]

Depends which frequentist you ask. From Aris Spanos's "A frequentist interpretation of probability for model-based inductive inference":

For those who can't access that through the paywall (I can), his presentation slides for it are here. I would hate to have been in the audience for the presentation, but the upside of that is that they pretty much make sense on their own, being just a compressed version of the paper.

While looking for those, I also found "Frequentists in Exile", which is Deborah Mayo's frequentist statistics blog.

I am not enough of a statistician to make any quick assessment of these, but they look like useful reading for anyone thinking about the foundations of uncertain inference.

Comment author: RobbBB 19 September 2013 12:12:29AM *  0 points [-]

The frequentist interpretation of probability makes the claim that probability theory can only be used in situations involving large numbers of repeatable trials

I don't understand what this "probability theory can only be used..." claim means. Are they saying that if you try to use probability theory to model anything else, your pencil will catch fire? Are they saying that if you model beliefs probabilistically, Math breaks? I need this claim to be unpacked. What do frequentists think is true about non-linguistic reality, that Bayesians deny?

Comment author: Desrtopa 19 September 2013 01:53:07AM 3 points [-]

I don't understand what this "probability theory can only be used..." claim means. Are they saying that if you try to use probability theory to model anything else, your pencil will catch fire? Are they saying that if you model beliefs probabilistically, Math breaks?

I think they would be most likely to describe it as a category error. If you try to use probability theory outside the constraints within which they consider it applicable, they'd attest that you'd produce no meaningful knowledge and accomplish nothing but confusing yourself.

Comment author: RobbBB 19 September 2013 05:02:49AM *  0 points [-]

Can you walk me through where this error arises? Suppose I have a function whose arguments are the elements of a set S, whose values are real numbers between 0 and 1, and whose values sum to 1. Is the idea that if I treat anything in the physical world other than objects' or events' memberships in physical sequences of events or heaps of objects as modeling such a set, the conclusions I draw will be useless noise? Or is there something about the word 'probability' that makes special errors occur independently of the formal features of sample spaces?

Comment author: Desrtopa 19 September 2013 01:44:19PM 2 points [-]

As best I can parse the question, I think the former option better describes the position.

Comment author: nshepperd 19 September 2013 02:18:58AM 2 points [-]

IIRC a common claim was that modeling beliefs at all is "subjective" and therefore unscientific.

Comment author: RobbBB 19 September 2013 05:00:12AM *  0 points [-]

Do you have any links to this argument? I'm having a hard time seeing why any mainstream scientist who thinks beliefs exist at all would think they're ineffable....

Comment author: nshepperd 21 September 2013 12:52:31PM 0 points [-]

Hmm, I thought I had read it in Jaynes' PT:TLoS, but I can't find it now. So take the above with a grain of salt, I guess.

Comment author: Lumifer 19 September 2013 04:53:47PM -1 points [-]

The frequentist interpretation of probability makes the claim that probability theory can only be used in situations involving large numbers of repeatable trials, or selection from a large population.

Yes, but frequentists have zero problems with hypothetical trials or populations.

Do note that for most well-specified statistical problems the Bayesians and the frequentists will come to the same conclusions. Differently expressed, likely, but not contradicting each other.

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