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Bayesianism for humans: prosaic priors

22 Post author: BT_Uytya 02 September 2014 09:45PM

 

There are two insights from Bayesianism which occurred to me and which I hadn't seen anywhere else before.
I like lists in the two posts linked above, so for the sake of completeness, I'm going to add my two cents to a public domain. This post is about the second penny, the first one is here.


Prosaic Priors

The second insight can be formulated as «the dull explanations are more likely to be correct because they tend to have high prior probability.»

Why is that? 

1) Almost by definition! Some property X is 'banal' if X applies to a lot of people in an disappointingly mundane way, not having any redeeming features which would make it more rare (and, hence, interesting).

In the other words, X is banal iff base rate of X is high. Or, you can say, prior probability of X is high.

1.5) Because of Occam's Razor and burdensome details. One way to make something boring more exciting is to add interesting details: some special features which will make sure that this explanation is about you as opposed to 'about almost anybody'.

This could work the other way around: sometimes the explanation feels unsatisfying exactly because it was shaved of any unnecessary and (ultimately) burdensome details.

2) Often, the alternative of a mundane explanation is something unique and custom made to fit the case you are interested in. And anybody familiar with overfitting and conjunction fallacy (and the fact that people tend to love coherent stories with blinding passion1) should be very suspicious about such things. So, there could be a strong bias against stale explanations, which should  be countered.

* * *

I fully grokked this when being in process of CBT-induced soul-searching; usage in this context still looks the most natural to me, but I believe that the area of application of this heuristic is wider.

Examples

1) I'm fairly confident that I'm an introvert. Still, sometimes I can behave like an extrovert. I was interested in the causes of this "extroversion activation", as I called it2. I suspected that I really had two modes of functioning (with "introversion" being the default one), and some events — for example, mutual interest (when I am interested in a person I was talking to, and xe is interested in me) or feeling high-status — made me switch between them.

Or, you know, it could be just reduction in a social anxiety, which makes people more communicative. Increased anxiety levels wasn't a new element to be postulated; I already knew I had it, yet I was tempted to make up new mental entities, and prosaic explanation about anxiety managed to avoid me for a while.

2) I find it hard to do something I consider worthwhile while on a spring break, despite having lots of a free time. I tend to make grandiose plans — I should meet new people! I should be more involved in sports! I should start using Anki! I should learn Lojban! I should practice meditation! I should read these textbooks including doing most of exercises! — and then fail to do almost anything. Yet I manage to do some impressive stuff during academic term, despite having less time and more commitments.

This paradoxical situation calls for explanation.

The first hypothesis that came to my mind was about activation energy. It takes effort to go  from "procrastinating" to "doing something"; speaking more generally, you can say that it takes effort to go from "lazy day" to "productive day". During the academic term, I am forced to make most of my days productive: I have to attend classes, do homework, etc. And, already having done something good, I can do something else as well. During spring break, I am deprived of that natural structure, and, hence I am on my own in terms of starting doing something I find worthwhile.

The alternative explanation: I was tired. Because, you know, vacation comes right after midterms, and I tend to go all out while preparing for midterms. I am exhausted, my energy and willpower are scarce, so it's no wonder I am having trouble utilizing it.

(I don't really believe in the latter explanation (I think that my situation is caused by several factors, including two outlined above), so it is also an example of descriptive "probable enough" hypothesis)

3) This example comes from Slate Star Codex. Nerds tend to find aversive many group bonding activities usual people supposedly enjoy, such as patriotism, prayer, team sports, and pep rallies. Supposedly, they should feel (with a tear-jerking passion of thousand exploding suns) the great unity with their fellow citizens, church-goers, teammates or pupils respectively, but instead they feel nothing.

Might it be that nerds are unable to enjoy these activities because something is broken inside their brains? One could be tempted to construct an elaborate argument involving autism spectrum and a mild case of schizoid personality disorder. In other words, this calls for postulating a rare form of autism which affects only some types of social behaviour (perception of group activities), leaving other types unchanged.

Or, you know, maybe nerds just don't like the group they are supposed to root for. Maybe nerds don't feel unity and relationship to The Great Whole because they don't feel like they truly belong here.

As Scott put it, "It’s not that we lack the ability to lose ourselves in an in-group, it’s that all the groups people expected us to lose ourselves in weren’t ones we could imagine as our in-group by any stretch of the imagination"3.

4) This example comes from this short comic titled "Sherlock Holmes in real life".

5) Scott Aaronson uses something similar to the Hanlon's Razor to explain that the lack of practical expertise of CS theorists aren't caused by arrogance or something like that:

"If theorists don’t have as much experience building robots as they should have, don’t know as much about large software projects as they should  know, etc., then those are all defects to add to the long list of their other, unrelated defects.  But it would be a mistake to assume that they failed to acquire this knowledge because of disdain for practical people, rather than for mundane reasons like busyness or laziness."

* * *

...and after this the word "prosaic" quickly turned into an awesome compliment. Like, "so, this hypothesis explains my behaviour well; but is it boring enough?", or "your claim is refreshingly dull; I like it!".


1. If you had read Thinking: Fast and Slow, you probably know what I mean. If you hadn't, you can look at narrative fallacy in order to get a general idea.
2. Which was, as I now realize, an excellent way to deceive myself via using word with a lot of hidden assumptions. Taboo your words, folks!
3. As a side note, my friend proposed an alternative explanation: the thing is, often nerds are defined as "sort of people who dislike pep rallies". So, naturally, we have "usual people" who like pep rallies and "nerds" who avoid them. And then "nerds dislike pep rallies" is tautology rather than something to be explained.

Comments (11)

Comment author: Lumifer 03 September 2014 07:05:33PM 3 points [-]

The second insight can be formulated as «the dull explanations are more likely to be correct because they tend to have high prior probability.»

That needs a LOT of caveats.

A counter-quote: "For every complex problem there is an answer that is clear, simple, and wrong." - H. L. Mencken

Comment author: Lunin 03 September 2014 06:37:03PM *  1 point [-]

Some property X is 'banal' if X applies to a lot of people in an disappointingly mundane way, not having any redeeming features which would make it more rare (and, hence, interesting). In the other words, X is banal iff base rate of X is high. Or, you can say, prior probability of X is high.

I doubt that (widespread belief) <=> (high prior probability). If a statement is believed and considered obvious by a lot of people, it can be really obvious and true. Or it can be a wrong cached thought. Or just a common misconception.

If you are proficient in some area, your feeling of prior probabilities in this area is better than average, because you are already used to some counterintuitive facts of that field, and you have some idea about how proper 'counterintuitive-ness' looks like. In fact, you update your intuition. If you already believe General Relativity, you will be more apt to believe counterintuitive facts from Quantum Mechanics. Probably the same holds true if you are on the right side of the Bell Curve.

By the way, Boring Advice Repository seems not boring at all. It's more like a collection of 'lifehacks' and advices aimed to shoot blind spots and ugh fields

Comment author: Mizue 03 September 2014 04:52:39AM 2 points [-]

Ooh, I get to comment.

A particular dull explanation is more likely than a particular exciting one. But it is possible that dull explanations, in general, are not more likely than exciting ones, in general, because there might be more of the exciting explanations even though each individual one is less likely.

(This is not typical--if you have cold symptoms, you probably have a cold and not an exotic disease--but it's possible.)

Comment author: ishi 03 September 2014 10:21:39AM 1 point [-]

Comments---

  1. 2 sayings i like (relevant to the nerd issue) are 'I love humanity, i just hate people' and (for those of use who could be called 'elites' as distinct from the commoners ) 'I wouldn't me a member of any group that would me as a member' (Mark Twain). I'm not that convinced of the 'broken brain theory'. I tend to think in terms like 'frequency dependence' in biology or 'division of labor' in economics. Not everyone is the same, and there are reasons for that. (This is related also to the 'pigeonhole principle' and things like the existance of 'runts' in dog litters, various forms of hierarchies----in the real world, not everyone is in reaching distance of the same set of resources. Some don't get to sit in a warm place next to the fire, and so adapt to the cold. (And, very often, when occassionaly they get invited to be in the heat, since they have learned to live in, and even enjoy the cold, they are considered antisocial, rude and disturbed if they don't accept the invitation (eg 'you can take this job, or seat, and shove it'). Or if you invite people to consider coming into the cold, that will be considered insanity.

    (This goes for other things too---if you decide religion is very narrow, boring, intolerant etc. but then one day the confgregation decides that, since they are losing members and tithes, they will 'lighten up' and invite you back (but again on their slightly revised terms---eg they won't preach that you are going to hell, but will still tell you to shut up why they preach to you the truth which you know nothing about). If you decide your peer group who does nothing but bar hop is boring and find new activities, when they see you again and say 'hey come on, lets party' they will say 'you've really changed and are no fun anymore, unlike us party animals'. Darwin was probably a nerd and didnt attend church (or half heartedly, mostly for show). Einstein wasn't a big zionist type studying the torah and waiting to return to the promised land, but was interested in larger parts of the space of possibilities. He also wasn't much of a family man it seems, preferring to do stuff like EPR rather than like mowing the lawn, going to July 4 fireworks etc. (He did sign a letter written to Joe McCarthy (congressman) supporting Paul Robeson who was being accused of being a communist, and he helped get Godel citizenship, so that may have some relation to being a patriot).

  2. To me the 'dull prior' is similar to the 'maximum entropy' postulate in statistical mechanics (which Jaynes i think identified with bayesianism). There are (as a caveat) in my view many ways of applying this postulate, so there can be a hierarchy of 'dullness' ---its what you call dull, or what your information is. (This is why i personally don't really consider bayesianism distinct from frequentism, any more than i consider so called 'linear' sciences as distinct from 'nonlinear' ones. (The former just comes usually by truncating your equation, or changing coordinates,, or aggregating). This is also why I am highly skeptical of many applications of maximum entropy especially in fields like economics or other social sciences. The formalism is so general that you can find any result you want, or fit any distribution (with your prior 'principle of impotence'---equal a priori probability ---like 'overfitting' (eg Norbert Weiner on elephants) .). EG just because someone fits the description, doesn't mean they did the crime though this sort of 'prior' is often used since it seems to work (eg you solve the crime, case closed, god said it, i believe it and that is all there is to it, qed.).

Comment author: [deleted] 03 September 2014 10:27:18PM 1 point [-]

Einstein wasn't a big zionist type studying the torah and waiting to return to the promised land,

Just some historical nitpicking, but "Zionist" is a political descriptor, not a religious one. Particularly in Einstein's time, the word would have meant something more like "socialist commune member" than "observantly religious person".

In fact, most usages of the term "Zionist" today are wrong, since the word is used more often by its enemies than by its supporters.

Comment author: ishi 05 September 2014 05:11:41PM 0 points [-]

I agree with you on this---its a political term nowadays , and im in DC so i fairly commonly come across all the uses (and i even have distant cousins in Israel, my closer ones came through ellis island from russia around 1910, have some distant ones who died in the holocaust, etc.). but technically i'm goy through genetics and/or descent. (other half of my family were essentially expelled from britain because they were a dissident protestant sect---the brethren, related in a way to the mennonites. they werent involved in salem witch trials, nor indigenous genocide, though did get their 40 acre farm in north dakota---before fracking ). (I gather Herzl (sic) maybe wrote early ideas on zionism for various reasons (religion, political persecution---russia had pogroms (see 'fiddler on a roof' movie i think )). Einstein does have an essay 'why i am a socialist' (one can also consider bertrand russel's 'why i am not a christian' (he was, like me, agnostic) . kibbutz idea. Sorin Solomon of Weiszmann Inst and NewInstitute for Economic thinking is one prof there (writes on statistical mechanics of income distribution); i think he was in Peace Now. Einstein was on first board of Hebrew U.

Comment author: RichardKennaway 26 August 2014 02:35:57PM 8 points [-]

I find it hard to do something I consider worthwhile while on a spring break, despite having lots of a free time.

Perhaps it is because you have no deadlines, no compelling reason to complete something specific?

I tend to make grandiose plans — I should meet new people! I should be more involved in sports! I should start using Anki! I should learn Lojban! I should practice meditation! I should read these textbooks including doing most of exercises!

Those aren't plans.

— and then fail to do almost anything.

This is the retrospective evidence that they weren't plans.

Yet I manage to do some impressive stuff during academic term, despite having less time and more commitments.

There you are—commitments, and a structure, in this case externally imposed, once you've made the decision to go to college.

If when you have a wish such as "I should meet new people!", your thinking does not immediately proceed to considering what sort of people, where to find them, when to do it, and what the effort will look like, then it's just daydreaming.

Comment author: Bobertron 25 August 2014 11:18:33AM 4 points [-]

I know it's just an example, but concerning

I find it hard to do something I consider worthwhile while on a spring break

maybe you have learned to be lazy on spring break? I mean, the theory that it's a habit seems more prosaic to me than being tired or something about "activasion energy".

Comment author: BT_Uytya 25 August 2014 12:18:46PM 2 points [-]

Good call!

Yes, your theory is more prosaic, yet it never occured to me. I wonder whether purposefully looking for boring explanations would help with that.

Also, your theory is actually plausible, fits with some of my observations, so I think that I should look into it. Thanks!

Comment author: Bobertron 26 August 2014 08:43:54AM 4 points [-]

The idea that it's a habit is, in a way, boring, true.

But when I read that industriousness and creativity can be learned like described in the learned industriousness wikipedia article, I was quite surprised. So the iedea isn't boring to me at all.

Comment author: evand 26 August 2014 01:30:47AM 3 points [-]

Also beware of comparing a one week Spring break with a particularly memorable or otherwise highly available sample of a week from other times, rather than an actually "typical" week.