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Watercressed comments on What Bayesianism taught me - Less Wrong

62 Post author: Tyrrell_McAllister 12 August 2013 06:59AM

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Comment author: Watercressed 11 August 2013 02:24:18AM *  19 points [-]

A related mistake I made was to be impressed by the cleverness of the aphorism "The plural of 'anecdote' is not 'data'." There may be a helpful distinction between scientific evidence and Bayesian evidence. But anecdotal evidence is evidence, and it ought to sway my beliefs.

Anecdotal evidence is filtered evidence. People often cite the anecdote that supports their belief, while not remembering or not mentioning events that contradict them. You can find people saying anecdotes on any side of a debate, and I see no reason the people who are right would cite anecdotes more.

Of course, if you witness an anecdote with your own eyes, that is not filtered, and you should adjust your beliefs accordingly.

Comment author: Kaj_Sotala 11 August 2013 03:44:21AM *  23 points [-]

Of course, if you witness an anecdote with your own eyes, that is not filtered

Unless you too selectively (mis)remember things.

Comment author: wedrifid 11 August 2013 05:14:55AM 21 points [-]

Unless you too selectively (mis)remember things.

Or selectively expose yourself to situations.

Comment author: Pentashagon 13 August 2013 06:26:01PM 2 points [-]

If I can always expose myself to situations in which I anecdotally experience success, isn't that Winning?

Comment author: wedrifid 14 August 2013 05:03:09AM *  0 points [-]

If I can always expose myself to situations in which I anecdotally experience success, isn't that Winning?

Yes. What it isn't is an unbiased scientific study. The anecdotal experience of situations which are selected to to provide success is highly filtered evidence.

Comment author: ChristianKl 11 August 2013 11:44:59AM 8 points [-]

I think the value of anecdotes often doesn't lie so much in changing probabilities of belief but in illustrating what a belief actually is about.

Comment author: Luke_A_Somers 12 August 2013 05:55:47PM 5 points [-]

That, and existence/possibility proofs, and, in the very early phases of investigation, providing a direction for inquiry.

Comment author: Tyrrell_McAllister 11 August 2013 03:33:30AM *  7 points [-]

Anecdotal evidence is filtered evidence.

Right, the existence of the anecdote is the evidence, not the occurrence of the events that it alleges.

You can find people saying anecdotes on any side of a debate, and I see no reason the people who are right would cite anecdotes more.

It is true that, if a hypothesis has reached the point of being seriously debated, then there are probably anecdotes being offered in support of it. (... assuming that we're taking about the kinds of hypotheses that would ever have an anecdote offered in support of it.) Therefore, the learning of the existence of anecdotes probably won't move much probability around among the hypotheses being seriously debated.

However, hypothesis space is vast. Many hypotheses have never even been brought up for debate. The overwhelming majority should never come to our attention at all.

In particular, hypothesis space contains hypotheses for which no anecdote has ever been offered. If you learned that a particular hypothesis H were true, you would increase your probability that H was among those hypotheses that are supported by anecdotes. (Right? The alternative is that which hypotheses get anecdotes is determined by mechanisms that have absolutely no correlation, or even negative correlation, with the truth.) Therefore, the existence of an anecdote is evidence for the hypothesis that the anecdote alleges is true.

Comment author: Anatoly_Vorobey 11 August 2013 06:52:14AM 13 points [-]

A typical situation is that there's a contentious issue, and some anecdotes reach your attention that support one of the competing hypotheses.

You have three ways to respond:

  1. You can under-update your belief in the hypothesis, ignoring the anecdotes completely
  2. You can update by precisely the measure warranted by the existence of these anecdotes and the fact that they reached you.
  3. You can over-update by adding too much credence to the hypothesis.

In almost every situation you're likely to encounter, the real danger is 3. Well-known biases are at work pulling you towards 3. These biases are often known to work even when you're aware of them and trying to counteract them. Moreover, the harm from reaching 3 is typically far greater than the harm from reaching 1. This is because the correct added amount of credence in 2 is very tiny, particularly because you're already likely to know that the competing hypotheses for this issue are all likely to have anecdotes going for them. In real-life situations, you don't usually hear anecdotes supporting an incredibly unlikely-seeming hypothesis which you'd otherwise be inclined to think as capable of nurturing no anecdotes at all. So forgoing that tiny amount of credence is not nearly as bad as choosing 3 and updating, typically, by a large amount.

The saying "The plural of anecdotes is not data" exists to steer you away from 3. It works to counteract the very strong biases pulling you towards 3. Its danger, you are saying, is that it pulls you towards 1 rather than the correct 2. That may be pedantically correct, but is a very poor reason to criticize the saying. Even with its help, you're almost always very likely to over-update - all it's doing is lessening the blow.

Perhaps this as an example of "things Bayesianism has taught you" that are harming your epistemic rationality?

A similar thing I noticed is disdain towards "correlation does not imply causation" from enlightened Bayesians. It is counter-productive.

Comment author: Tyrrell_McAllister 11 August 2013 04:23:10PM *  9 points [-]

These biases are often known to work even when you're aware of them and trying to counteract them.

This is the problem. I know, as an epistemic matter of fact, that anecdotes are evidence. I could try to ignore this knowledge, with the goal of counteracting the biases to which you refer. That is, I could try to suppress the Bayesian update or to undo it after it has happened. I could try to push my credence back to where it was "manually". However, as you point out, counteracting biases in this way doesn't work.

Far better, it seems to me, to habituate myself to the fact that updates can by miniscule. Credence is quantitative, not qualitative, and so can change by arbitrarily small amounts. "Update Yourself Incrementally". Granting that someone has evidence for their claims can be an arbitrarily small concession. Updating on the evidence doesn't need to move my credences by even a subjectively discernible amount. Nonetheless, I am obliged to acknowledge that the anecdote would move the credences of an ideal Bayesian agent by some nonzero amount.

Comment author: Lumifer 12 August 2013 05:20:10PM *  2 points [-]

...updates can by miniscule ... Updating on the evidence doesn't need to move my credences by even a subjectively discernible amount. Nonetheless, I am obliged to acknowledge that the anecdote would move the credences of an ideal Bayesian agent by some nonzero amount.

So, let's talk about measurement and detection.

Presumably you don't calculate your believed probabilities to the n-th significant digit, so I don't understand the idea of a "miniscule" update. If it has no discernible consequences then as far as I am concerned it did not happen.

Let's take an example. I believe that my probability of being struck by lightning is very low to the extent that I don't worry about it and don't take any special precautions during thunderstorms. Here is an anecdote which relates how a guy was stuck by lightning while sitting in his office inside a building. You're saying I should update my beliefs, but what does it mean?

I have no numeric estimate of P(me being struck by lightning) so there's no number I can adjust by 0.0000001. I am not going to do anything differently. My estimate of my chances to be electrocuted by Zeus' bolt is still "very very low". So where is that "miniscule update" that you think I should make and how do I detect it?

P.S. If you want to update on each piece of evidence, surely by now you must fully believe that product X is certain to enlarge your penis?

Comment author: 9eB1 12 August 2013 04:28:29AM *  5 points [-]

A typical situation is that there's a contentious issue, and some anecdotes reach your attention that support one of the competing hypotheses.

It is interesting that you think of this as typical, or at least typical enough to be exclusionary of non-contentious issues. I avoid discussions about politics and possibly other contentious issues, and when I think of people providing anecdotes I usually think of them in support of neutral issues, like the efficacy of understudied nutritional supplements. If someone tells you, "I ate dinner at Joe's Crab Shack and I had intense gastrointestinal distress," I wouldn't think it's necessarily justified to ignore it on the basis that it's anecdotal. If you have 3 more friends who all report the same thing to you, you should rightly become very suspicious of the sanitation at Joe's Crab Shack. I think the fact that you are talking about contentious issues specifically is an important and interesting point of clarification.

Comment author: cousin_it 11 August 2013 01:02:26PM *  3 points [-]

Thanks for that comment! Eliezer often says people should be more sensitive to evidence, but an awful lot of real-life evidence is in fact much weaker, noisier, and easier to misinterpret than it seems. And it's not enough to just keep in mind a bunch of Bayesian mantras - you need to be aware of survivor bias, publication bias, Simpson's paradox and many other non-obvious traps, otherwise you silently go wrong and don't even know it. In a world where most published medical results fail to replicate, how much should we trust our own conclusions?

Would it be more honest to recommend people to just never update at all? But then everyone will stick to their favorite theories forever... Maybe an even better recommendation would be to watch out for "motivated cognition", try to be more skeptical of all theories including your favorites.

Comment author: Lumifer 12 August 2013 05:10:01PM *  1 point [-]

The alternative is that which hypotheses get anecdotes is determined by mechanisms that have absolutely no correlation, or even negative correlation, with the truth.

Doesn't look implausible to me. Here's an alternative hypothesis: the existence of anecdotes is a function of which beliefs are least supported by strong data because such beliefs need anecdotes for justification.

In general, I think anecdotes are way too filtered and too biased as an information source to be considered serious evidence. In particular, there's a real danger of treating a lot of biased anecdotes as conclusive data and that danger, seems to me, outweighs the miniscule usefulness of anecdotes.

Comment author: Tyrrell_McAllister 13 August 2013 10:06:32PM 1 point [-]

In general, I think anecdotes are way too filtered and too biased as an information source to be considered serious evidence.

We may agree. It depends on what work the word "serious" is doing in the quoted sentence.

Comment author: Lumifer 14 August 2013 01:11:29AM 0 points [-]

In this context "serious" = "I'm willing to pay attention to it".

Comment author: Watercressed 11 August 2013 04:53:42AM *  0 points [-]

I would raise a hypothesis to consideration because someone was arguing for it, but I don't think anecdotes are good evidence in that I would have similar confidence in a hypothesis supported by an anecdote, and a hypothesis that is flatly stated with no justification. The evidence to raise it to consideration comes from the fact that someone took the time to advocate it.

This is more of a heuristic than a rule, because there are anecdotes that are strong evidence ("I ran experiments on this last year and they didn't fit"), but when dealing with murkier issues, they don't count for much.

Comment author: Tyrrell_McAllister 11 August 2013 05:13:34AM 2 points [-]

The evidence to raise it to consideration comes from the fact that someone took the time to advocate it, not the anecdote.

Yes, it may be that the mere fact that a hypothesis is advocated screens off whether that hypothesis is also supported by an anecdote. But I suspect that the existence of anecdotes still moves a little probability mass around, even among just those hypotheses that are being advocated.

I mean, if someone advocated for a hypothesis, and they couldn't even offer an anecdote in support of it, that would be pretty deadly to their credibility. So, unless I am certain that every advocated hypothesis has supporting anecdotes (which I am not), I must concede that anecdotes are evidence, howsoever weak, over and above mere advocacy.

Comment author: Watercressed 11 August 2013 03:48:50PM 2 points [-]

Here's a situation where an anecdote should reduce our confidence in a belief:

  • A person's beliefs are usually well-supported.
  • When he offers supporting evidence, he usually offers the strongest evidence he knows about.

If this person were to offer an anecdote, it should reduce our confidence in his proposition, because it makes it unlikely he knows of stronger supporting evidence.

I don't know how applicable this is to actual people.

Comment author: JoshuaZ 11 August 2013 07:19:28PM *  1 point [-]

I don't think this is necessarily valid, because people also know that anecdotes can be highly persuasive. So for many people, if you have an anecdote it will make sense to say so, since most people argue not to reach the truth but to persuade.

Comment author: Tyrrell_McAllister 11 August 2013 04:26:43PM 1 point [-]

I agree that it is at least hypothetically possible that the offering of an anecdote should reduce our credence in what the anecdote claims.

Comment author: Tyrrell_McAllister 13 August 2013 10:10:24PM 2 points [-]

... For example, if you told me that you once met a powerful demon who works to stop anyone from ever telling anecdotes about him (regardless of whether the anecdotes are true or false), then I would decrease my credence in the existence of such a demon.

Comment author: Kawoomba 11 August 2013 06:35:17AM 5 points [-]

Anecdotal evidence is filtered evidence.

Still evidence.

Comment author: RichardKennaway 11 August 2013 08:26:29AM 4 points [-]

After accounting for the filtering, which way does it point? If you're left with a delta log-odds of zero, it's "evidence" only in the sense that if you have no apples you have "some" apples.

Comment author: Kawoomba 11 August 2013 11:36:26AM 2 points [-]

Yes, "Daaad, Zeus the Greek god ate my homework!" isn't strong evidence, certainly.

But the way it points (in relation to P(Zeus exists)) is clear. I agree with your second sentence, but I'm not sure I understand your first one.

Comment author: RichardKennaway 12 August 2013 01:50:20PM 7 points [-]

Yes, "Daaad, Zeus the Greek god ate my homework!" isn't strong evidence, certainly.

But the way it points (in relation to P(Zeus exists)) is clear.

I don't think it is. If Zeus really had eaten the homework, I wouldn't expect it to be reported in those terms. Some stories are evidence against their own truth -- if the truth were as the story says, that story would not have been told, or not in that way. (Fictionally, there's a Father Brown story hinging on that.)

And even if it theoretically pointed in the right direction, it is so weak as to be worthless. To say, "ah, but P(A|B)>P(A)!" is not to any practical point. It is like saying that a white wall is evidence for all crows being black. A white wall is also evidence, in that sense, for all crows being magenta, for the moon being made of green cheese, for every sparrow falling being observed by God, and for no sparrow falling being observed by God. Calling this "evidence" is like picking up from the sidewalk, not even pennies, but bottle tops.

Comment author: [deleted] 12 August 2013 06:25:54PM 2 points [-]

I don't think it is. If Zeus really had eaten the homework, I wouldn't expect it to be reported in those terms. Some stories are evidence against their own truth -- if the truth were as the story says, that story would not have been told, or not in that way. (Fictionally, there's a Father Brown story hinging on that.)

What I was just about to say. See also Yvain on self-defeating arguments.

A white wall is also evidence, in that sense, for all crows being magenta, for the moon being made of green cheese,

Okay, but...

for every sparrow falling being observed by God, and for no sparrow falling being observed by God.

How so?

Comment author: RichardKennaway 12 August 2013 07:50:37PM 2 points [-]

for every sparrow falling being observed by God, and for no sparrow falling being observed by God.

How so?

Every white wall is a non-sparrow not observed by God, hence evidence for God observing every sparrow's fall. It is also a, um, no, you're right, the second one doesn't work.

Comment author: [deleted] 12 August 2013 10:27:58PM 2 points [-]

Every white wall is a non-sparrow not observed by God

How do we know that the wall is not observed by God?

Comment author: RichardKennaway 13 August 2013 07:44:54AM 2 points [-]

Ah, quite so. God sees all, sparrows and walls alike. Both of those examples are broken.

Comment author: Kawoomba 13 August 2013 07:50:55AM 6 points [-]

An omnipotence-omniscience paradox: "God, look away!" - "I can't!"

Comment author: Jiro 12 August 2013 08:55:14PM 1 point [-]

If sparrows do not exist, then "every sparrow falling is observed by God" and "no sparrow falling is observed by God" are both true. (And of course, every white wall is a tiny bit of evidence for "sparrows do not exist", although not very good evidence since there are so many other things in the universe that also need to be checked for sparrow-ness.)

Comment author: Kawoomba 12 August 2013 04:53:34PM *  0 points [-]

Well, we could use the word "evidence" in different ways (you requiring some magnitude-of-prior-shift).

But then you'd still need a word for "that-which-[increases|decreases]-the-probability-you-assign-to-a-belief". Just because that shift is tiny doesn't render it undefined or its impact arbitrary. You can say with confidence that 1/x remains positive for any positive x however large, and be it a googolplex (btw, TIL in which case 1/x would be called a googolminex).

Think of what you're advocating here: whatever would we do if we disallowed strictly-speaking-correct-nitpicks on LW?

Comment author: RichardKennaway 12 August 2013 05:01:49PM *  1 point [-]

Well, we could use the word "evidence" in different ways (you requiring some magnitude-of-prior-shift).

There's a handy table, two of them in fact, of terminology for strength of evidence here. Up to 5 decibans is "barely worth mentioning". How many microbans does "Zeus ate my homework" amount to?

Think of what you're advocating here: whatever would we do if we disallowed strictly-speaking-correct-nitpicks on LW?

You may be joking, but I do think LW (and everywhere else) would be improved if people didn't do that. I find nitpicking as unappealing as nose-picking.

Comment author: Kawoomba 12 August 2013 08:09:03PM 2 points [-]

How many microbans does "Zeus ate my homework" amount to?

Few enough that it's in the "barely worth mentioning" bracket, of course. (Under any kind of resource constraint, it wouldn't be mentioned at all, however that only relates to its infinitesimal weight, not the nature of what it is (evidence).)

You say that shouldn't be classified as evidence, I say it should. Note that the table is about strength of evidence.

Comment author: DSherron 12 August 2013 08:26:57PM 3 points [-]

Nitpicking is absolutely critical in any public forum. Maybe in private, with only people who you know well and have very strong reason to believe are very much more likely to misspeak than to misunderstand, nitpicking can be overlooked. Certainly, I don't nitpick every misspoken statement in private. But when those conditions do not hold, when someone is speaking on a subject I am not certain they know well, or when I do not trust that everyone in the audience is going to correctly parse the statement as misspoken and then correctly reinterpret the correct version, nitpicking is the only way to ensure that everyone involved hears the correct message.

Charitably I'll guess that you dislike nitpicking because you already knew all those minor points, they were obvious to anyone reading after all, and they don't have any major impact on the post as a whole. The problem with that is that not everyone who reads Less Wrong has a fully correct understanding of everything that goes into every post. They don't spot the small mistakes, whether those be inconsequential math errors or a misapplication of some minor rule or whatever. And the problem is that just because the error was small in this particular context, it may be a large error in another context. If you mess up your math when doing Bayes' Theorem, you may thoroughly confuse someone who is weak at math and trying to follow how it is applied in real life. In the particular context of this post, getting the direction of a piece of evidence wrong is inconsequential if the magnitude of that evidence is tiny. But if you are making a systematic error which causes you to get the direction of certain types of evidence, which are usually small in magnitude, wrong, then you will eventually make a large error. And unless you are allowed to call out errors dealing with small magnitude pieces of evidence, you won't ever discover it.

I'd also like to say that just because a piece of evidence is "barely worth mentioning" when listing out evidence for and against a claim, does not mean that that evidence should be immediately thrown aside when found. The rules which govern evidence strong enough to convince me that 2+2=3 are the same rules that govern the evidence gained from the fact that when I drop an apple, it falls. You can't just pretend the rules stop applying and expect to come out ok in every situation. In part you can gain practice from applying the rules to those situations, and in part it's important to remember that they do still apply, even if in the end you decide that their outcome is inconsequential.

Comment author: RichardKennaway 15 August 2013 12:00:38PM 1 point [-]

Nitpicking is absolutely critical in any public forum .

I disagree. Not all things that are true are either relevant or important. Irrelevancies and trivialities lower discussion quality, however impeccable their truth. There is practically nothing that anyone can say, that one could not find fault with, given sufficient motivation and sufficient disregard for the context that determines what matters and what does not.

In the case at hand, "evidence" sometimes means "any amount whatever, including zero", sometimes "any amount whatever, except zero, including such quantities as 1/3^^^3", and sometimes "an amount worth taking notice of".

In practical matters, only the third sense is relevant: if you want to know the colour of crows, you must observe crows, not non-crows, because that is where the value of information is concentrated. The first two are only relevant in a technical, mathematical context.

The point of the Bayesian solution to Hempel's paradox is to stop worrying about it, not to start seeing purple zebras as evidence for black crows that is worth mentioning in any other context than talking about Hempel's paradox.

Comment author: elharo 13 August 2013 08:55:21PM -1 points [-]

Yes, in a world in which Zeus existed, people would not proclaim the importance of faith in Zeus, anymore than they proclaim the importance of faith in elephants or automobiles. Everyone would just accept that they exist.

Comment author: Lumifer 13 August 2013 09:12:16PM 1 point [-]

Yes, in a world in which Zeus existed, people would not proclaim the importance of faith in Zeus

I don't know: consider the classic cargo cult. It proclaims the importance of faith in airplanes.

Or consider Christianity: people who fully believe in Jesus Christ (=from their point of view they live in the world in which Jesus exists) tend to proclaim the importance of faith in Jesus.

Comment author: ArisKatsaris 23 August 2013 02:10:11PM -1 points [-]

tend to proclaim the importance of faith in Jesus

Yes, that's the point - people don't tend to proclaim the importance of faith in things that actually exist. You won't hear them say "have faith in the existence of tables" or "have faith in the existence of chairs".

Comment author: AndHisHorse 23 August 2013 02:40:36PM 5 points [-]

I would suspect that this is because a) everybody believes in tables and chairs (with the exception of a few very strange people, who are probably easy enough to spot), and b) nobody (again with a few odd exceptions) believes in any sort of doctrine or plan of action for chair-and-table-believers, so faith doesn't have many consequences (except for having somewhere to sit and place things on).

We, on the other hand, proclaim the importance of confidence in rational thought, for the same reasons that theists proclaim the importance of belief in their god: it is a belief which is not universal in the population, and it is a belief which we expect to have important consequences and prescriptions for action.

Comment author: Lumifer 12 August 2013 06:17:51PM 1 point [-]

If you look into your spam folder you'll find plenty of evidence for penis extension pills and the availability of large amount of money in abandoned accounts at Nigerian banks.

Comment author: sketerpot 13 August 2013 10:13:46PM *  2 points [-]

This is actually a really tidy example of Bayesian thinking. People send various types of emails for a variety of reasons. Of those who send penis extension pill emails, there are (vaguely speaking) three possible groups:

  1. People who have invented penile embiggening pills and honestly want to sell them. (I've never confirmed anybody to be in this group, so it may be empty.)

  2. Scammers trying to find a sucker by spamming out millions of emails.

  3. Trolls.

If you see emails offering to "Eml4rge your m3mber!!", this is evidence for the existence of someone from one or more of these groups. Which group do you think is largest? Those spam emails are evidence for all of these, but not such strong evidence for choosing between them.

Comment author: JQuinton 16 August 2013 04:46:12PM 1 point [-]

Don't spam algorithms actually use Bayes rule to filter spam from non-spam, updating when you click "this is spam" or "this is not spam"?

Comment author: Jayson_Virissimo 16 August 2013 11:25:54PM 1 point [-]

Yes, this is exactly how Paul Graham went about solving the spam problem.

Comment author: Eugine_Nier 15 August 2013 02:31:48AM 0 points [-]

The value of anecdotal evidence on a subject depends on how good the other sources are. For example, in something like medicine where something like 1 in 5 studies wind up retracted, anecdotal evidence is reasonable useful. To say nothing of the social "sciences".