Sunday, 14 February 2016

There Probably are Bayesians in Foxholes

Many years ago, I almost fell into bad company.  I frequented a philosophy channel on IRC that included a small, but very vocal band of what I like to call Randians – primarily because they didn’t like being called Randians.  These Randians preferred to be called objectivists and apparently their greatest love in life was sticking it to subjectivists.  Boy, did they hate subjectivism!

(Why Randians?  Because they were devotees of Ayn Rand and her philosophy of "objectivism".  I have, since that time, had an abiding distaste for Ayn Rand and anyone who adores her.  I do understand that in some instances a thoroughly reviled person like Ayn Rand may be misunderstood, or misjudged, and there is the possibility that, despite appearances, such a person does in fact have redeeming features.  For example, they might like puppies and kittens.  Ayn Rand, however, delighted in ripping the legs off puppies and kittens and throwing them at small children that she had cast into a deep well at the bottom of her garden.

If I were given the choice of spending eternity with Ayn Rand or William Lane Craig, I would choose laughing boy, despite being aware that the notion of spending eternity with anyone would indicate that he was right about the whole god thing and he would undoubtably spend some excruciating proportion of that eternity crowing about how he was right and I was wrong.  But at least we would both be in hell.)

The odd thing was that, at the time, when I searched for these subjectivists, they didn't seem to exist.  The Randians appear to have constructed an army of straw men to attack in their objectivistic fervour.  Sure, anyone who crossed them would get labelled as a subjectivist, but this term appeared to be more pejorative than accurate.

A similar sort of one-sided battle appears to be underway between Bayesians and frequentists.  Now perhaps the baying of the Bayesians is a little more accurate than that of those objectivists, perhaps there are people out there carrying the torch for frequentism, but I've not seen any evidence of it.  It seems to me that in some instances a frequentist interpretation of probability is appropriate and in other instances a Bayesian interpretation is appropriate.  See the second last page of this – note however, that the author is a statistician, the sort of person who uses probability all the time.  In other instances, such as the on-going cat fight between Luke Barnes and Richard Carrier, the participants of a recent probability-centred spat are not statisticians – they are a cosmologist and a historian.

What truly boggles the mind is the fact that Barnes has recently devoted an entire post to lambasting Carrier on what started out as a response to short statement from Jeff Lowder in support of a criticism from Barnes, all predicated on one word.  Carrier wrote (in his essay in "The End of Christianity"), my emphasis:

Bayes’ theorem is an argument in formal logic that derives the probability that a claim is true from certain other probabilities about that theory and the evidence.

To say that Bayes' theorem is an argument is possibly a bit of an awkward way of putting it.  It could, possibly, be written as an argument in formal logic, in much the same way as 1+1=2 was by Russell and Whitehead, whose work Carrier references, but that's not really how Bayes' theorem is thought of.  So, Carrier's claim is not worded particularly well.  No big deal.  Barnes however leapt gleefully onto that fact, spending some considerable time in savaging it and Lowder later concurred that Carrier's wording wasn't completely accurate.

Sadly, rather than 'fess up to having (at least) one sentence in his essay that was a tiny bit stilted and moving on, Carrier gracefully conceded that Bayes' theorem might not be an argument per se, but then went on to claim it is the form of an argument (after having claimed, apparently off the cuff, that one simple derivation of Bayes' theorem is the derivation of Bayes' theorem rather than a derivation).  He subsequently went on to point out that the issue is not so much the validity of Bayes' theorem (which no-one appears to be contesting) or the formulation of Bayes' theorem (which, again, no-one appears to be contesting), but rather the issue is what may be input to the equation that is the expression of Bayes' theorem.

In effect this was saying "any argument about Bayes' theorem, the derivation of Bayes' theorem or the description of Bayes' theorem is moot, because the argument isn't about Bayes' theorem itself but rather about what we bring to Bayes' theorem".

So, did Barnes pick up on this implied appeal to stick to what is relevant and not get bogged down in irrelevant detail?  Of course not.  His latest (and perhaps last) attack on Carrier is focussed, laser sharp, on Carrier's use of "the" rather than "a".  In the conclusion, Barnes challenges Carrier to release a new variant of probability or, in effect, choose a side: "Bayesian" or "frequentist".

What I find even more absurd is Barnes' statement in the comments:

(Carrier)’s not a frequentist. Frequentists don’t believe that prior probabilities exist, but Carrier does.

What?  Are alternate interpretations of probability now to be considered as competing ideologies?  Here Barnes appears to either have forgotten what he wrote in his piece 10 Nice things about Bayes' Theorem or he is accusing these mythical frequentists of being complete morons.

Prior probability is a defined term.  It's not something like climate change, free will or the Loch Ness Monster – it's not something that you can really question the existence of (complete morons aside).  Perhaps it's a term that you can, under certain circumstances, question the utility of – like the term "European" (do you mean people who have some combination of the SLC24A5SLC45A2 and HERC2/OCA2 genes or people who currently reside on the continent of Europe, or people who define themselves as members of the European Union, or something else?) – but you'd be crazy to deny that prior probabilities ever exist.

It seems completely bizarre to me that there are these mad keen Bayesians, apparently snug in their foxholes, taking the occasional pot-shots at their enemies, the dastardly frequentists, totally oblivious to the fact that – in the right circumstances – these "frequentists" would be more than happy to utilise a Bayesian interpretation.  It reminds me somewhat of those theists who become defensive at the mere mention of even the mildest expressions of atheism, as if the lack of belief on the part of one were necessarily a full-scale, frontal attack on the other.  (Note that this is a position which only encourages some of the more mildly oriented atheists to move towards the militant position.  It basically becomes a question of self-defence.)

Oh, hang on.  These people, the manic Bayesian defenders and the aggressively defensive apologists, they seem to be one and the same.  What was the likelihood of that!

Anyway, Barnes has stated that he might no longer be attacking Carrier.  I don't know if that will be the case though.  I think I identified a misplaced comma in one of Carrier's latest sentences and that could be strung out into a couple of a rants.  Don't you think so, Dr Barnes?


(Yes, I do appreciate the irony in that final comment, since I have written numerous articles sniping at Barnes, spinning dross from essentially nothing.  But I am small fry, a mere gnat, a bit-part player while Barnes and Carrier are more substantial actors.  That's not to say that my inconsequentiality renders my criticisms invalid though, even if Barnes may well choose to ignore them.

And, again, yes, I do realise that I have a sample size of one here, regarding the correlation between Bayesian defenders [or at least attackers of frequentism] and apologists.  I just provided an example, that was not intended to be conclusive evidence in support of my case.  It happens to be a nice coincidence that the anti-frequentism argument is provided here in the context of a defence of fine-tuning as an argument for god.)

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