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Comment author: James_Miller 31 July 2015 03:23:47PM 4 points [-]

Something is causing a huge number of Americans to " receive a motor vehicle induced traumatic brain injury every year." I agree with you about a helmet's mass being a problem, but the Crasche hat is very light.

Comment author: RichardKennaway 31 July 2015 03:31:52PM 0 points [-]

Something is causing a huge number of Americans to " receive a motor vehicle induced traumatic brain injury every year."

Do Americans wear seatbelts much? Especially by passengers.

Comment author: IlyaShpitser 30 July 2015 10:14:50PM 1 point [-]

As I recall, Teddy Seidenfeld is a fan of finite additivity. He does decision theory work, also.

Comment author: RichardKennaway 30 July 2015 11:01:57PM *  1 point [-]

As I recall, Teddy Seidenfeld is a fan of finite additivity.

Do you know why?

The recent thread on optional stopping and Bayes led me to this paper, which I see Seidenfeld is one of the authors of, which argues that countable additivity has bad consequences. But these consequences are a result of improper handling of limits, as Jaynes sets forth in his chapter 15. Seidenfeld and his coauthors go to great lengths (also here) exploring the negative consequences of finite additivity for Bayesian reasoning. They see this as a problem for Bayesian reasoning rather than for finite additivity. But I have not seen their motivation.

If you're going to do probability on infinite spaces at all, finite additivity just seems to me to be an obviously wrong concept.

ETA: Here's another paper by Seidenfeld, whose title does rather suggest that it is going to argue against finite additivity, but whose closing words decline to resolve the matter.

Comment author: Lumifer 29 July 2015 06:38:50PM 1 point [-]

Two words: "opportunity costs".

Comment author: RichardKennaway 30 July 2015 01:10:46PM 0 points [-]

Two more words: "training montage".

Comment author: Gunnar_Zarncke 14 July 2015 02:26:00PM 3 points [-]

Gargantua's admonishment of Pantagruel to employ his youth to profit both in studies and in virtue:

I intend, and will have it so, that thou learn the languages perfectly; first of all the Greek, as Quintilian will have it; secondly, the Latin; and then the Hebrew, for the Holy Scripture sake; and then the Chaldee and Arabic likewise, and that thou frame thy style in Greek in imitation of Plato, and for the Latin after Cicero. Let there be no history which thou shalt not have ready in thy memory; unto the prosecuting of which design, books of cosmography will be very conducible and help thee much. Of the liberal arts of geometry, arithmetic, and music, I gave thee some taste when thou wert yet little, and not above five or six years old. Proceed further in them, and learn the remainder if thou canst. As for astronomy, study all the rules thereof. Let pass, nevertheless, the divining and judicial astrology, and the art of Lullius, as being nothing else but plain abuses and vanities. As for the civil law, of that I would have thee to know the texts by heart, and then to confer them with philosophy.

Now, in matter of the knowledge of the works of nature, I would have thee to study that exactly, and that so there be no sea, river, nor fountain, of which thou dost not know the fishes; all the fowls of the air; all the several kinds of shrubs and trees, whether in forests or orchards; all the sorts of herbs and flowers that grow upon the ground; all the various metals that are hid within the bowels of the earth; together with all the diversity of precious stones that are to be seen in the orient and south parts of the world. Let nothing of all these be hidden from thee. Then fail not most carefully to peruse the books of the Greek, Arabian, and Latin physicians, not despising the Talmudists and Cabalists; and by frequent anatomies get thee the perfect knowledge of the other world, called the microcosm, which is man. And at some hours of the day apply thy mind to the study of the Holy Scriptures; first in Greek, the New Testament, with the Epistles of the Apostles; and then the Old Testament in Hebrew. In brief, let me see thee an abyss and bottomless pit of knowledge; for from henceforward, as thou growest great and becomest a man, thou must part from this tranquillity and rest of study, thou must learn chivalry, warfare, and the exercises of the field, the better thereby to defend my house and our friends, and to succour and protect them at all their needs against the invasion and assaults of evildoers.

Furthermore, I will that very shortly thou try how much thou hast profited, which thou canst not better do than by maintaining publicly theses and conclusions in all arts against all persons whatsoever, and by haunting the company of learned men, both at Paris and otherwhere. But because, as the wise man Solomon saith, Wisdom entereth not into a malicious mind, and that knowledge without conscience is but the ruin of the soul [...]. Suspect the abuses of the world. Set not thy heart upon vanity, for this life is transitory, [...]. Be serviceable to all thy neighbours, and love them as thyself. Reverence thy preceptors: shun the conversation of those whom thou desirest not to resemble, and receive not in vain the graces which God hath bestowed upon thee. And, when thou shalt see that thou hast attained to all the knowledge that is to be acquired in that part, return unto me, that I may see thee and give thee my blessing before I die.

-- Chapter 2.VIII. in Project Gutenberg's Gargantua and Pantagruel, Complete, by Francois Rabelais written in 1532-1564, translated in 1894, see also Wikipedia on Gargantua and Pantagruel

Note that this is not advice for everyone but apparently for a very capable youth:

Pantagruel studied very hard, as you may well conceive, and profited accordingly; for he had an excellent understanding and notable wit, together with a capacity in memory equal to the measure of twelve oil budgets or butts of olives.

Comment author: RichardKennaway 30 July 2015 01:02:47PM *  1 point [-]

Here are the ellipses restored:

But because, as the wise man Solomon saith, Wisdom entereth not into a malicious mind, and that knowledge without conscience is but the ruin of the soul, it behoveth thee to serve, to love, to fear God, and on him to cast all thy thoughts and all thy hope, and by faith formed in charity to cleave unto him, so that thou mayst never be separated from him by thy sins. Suspect the abuses of the world. Set not thy heart upon vanity, for this life is transitory, but the Word of the Lord endureth for ever. Be serviceable to all thy neighbours...

What might rationalist!Rabelais write in place of those passages?

Replacing "God" by "Reality" goes quite a long way.

Comment author: ike 29 July 2015 10:38:01PM 0 points [-]

And the point in the paper I linked has nothing to do with the prior, it's about the bayes factor, which is independent of the prior.

Let me put it differently. Yes, your chance of getting a bayes factor of >3 is 1.8 with data peeking, as opposed to 1% without; but your chance of getting a higher factor also goes down, because you stop as soon as you reach 3. Your expected bayes factor is necessarily 1 weighted over your prior; you expect to find evidence for neither side. Changing the exact distribution of your results won't change that.

Comment author: RichardKennaway 30 July 2015 12:55:27PM 1 point [-]

Your expected bayes factor is necessarily 1

Should that say, rather, that its expected log is zero? A factor of n being as likely as a factor of 1/n.

Comment author: g_pepper 29 July 2015 06:51:50PM 1 point [-]

The quoted section is fairly representative. Foucault's Pendulum is quite a good novel, IMO, and worth reading.

Comment author: RichardKennaway 29 July 2015 09:15:59PM 1 point [-]

Seconded.

Comment author: EHeller 29 July 2015 05:02:46PM *  3 points [-]

It is true that optional stopping won't change Bayes rule updates (which is easy enough to show). It's also true that optional stopping does affect frequentist tests (different sampling distributions). The broader question is "which behavior is better?"

p-hacking is when statisticians use optional stopping to make their results look more significant (by not reporting their stopping rule). As it turns out you in fact can "posterior hack" Bayesians - http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2374040

Edit: Also Debrah Mayo's Error Statistics book contains a demonstration that optional stopping can cause a Bayesian to construct confidence interval that never contain the true parameter value. Weirdly, those Bayesians can be posterior hacked even if you tell them about the stopping rule, because they don't think it matters.

Comment author: RichardKennaway 29 July 2015 08:20:36PM *  1 point [-]

p-hacking is when statisticians use optional stopping to make their results look more significant (by not reporting their stopping rule). As it turns out you in fact can "posterior hack" Bayesians - http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2374040

That is not my understanding of the term "optional stopping" (nor, more significantly, is it that of Jaynes). Optional stopping is the process of collecting data, computing your preferred measure of resultiness as you go, and stopping the moment it passes your criterion for reporting it, whether that is p<0.05, or a Bayes factor above 3, or anything else. (If it never passes the criterion, you just never report it.) That is but one of the large arsenal of tools available to the p-hacker: computing multiple statistics from the data in the hope of finding one that passes the criterion, thinking up more hypotheses to test, selective inclusion or omission of "outliers", fitting a range of different models, and so on. And of these, optional stopping is surely the least effective, for as Jaynes remarks in "Probability Theory as Logic", it is practically impossible to sample long enough to produce substantial support for a hypothesis deviating substantially from the truth.

All of those other methods of p-hacking involve concealing the real hypothesis, which is the collection of all the hypotheses that were measured against the data. It is like dealing a bridge hand and showing that it supports astoundingly well the hypothesis that that bridge hand would be dealt. In machine learning terms, the hypothesis is being covertly trained on the data, then tested on how well it fits the data. No measure of the latter, whether frequentist or Bayesian, is a measure of how well the hypothesis will fit new data.

Comment author: redding 28 July 2015 12:20:02PM 1 point [-]

There are different levels of impossible.

Imagine a universe with an infinite number of identical rooms, each of which contains a single human. Each room is numbered outside: 1, 2, 3, ...

The probability of you being in the first 100 rooms is 0 - if you ever have to make an expected utility calculation, you shouldn't even consider that chance. On the other hand, it is definitely possible in the sense that some people are in those first 100 rooms.

If you consider the probability of you being in room Q, this probability is also 0. However, it (intuitively) feels "more" impossible.

I don't really think this line of thought leads anywhere interesting, but it definitely violated my intuitions.

Comment author: RichardKennaway 29 July 2015 10:19:31AM *  3 points [-]

As others have pointed out, there is no uniform probability distribution on a countable set. There are various generalisations of probability that drop or weaken the axiom of countable additivity, which have their uses, but one statistician's conclusion is that you lose too many useful properties. On the other hand, writing a blog post to describe something as a lost cause suggests that it still has adherents. Googling /"finite additivity" probability/ turns up various attempts to drop countable additivity.

Another way of avoiding the axiom is to reject all infinities. There are then no countable sets to be countably additive over. This throws out almost all of current mathematics, and has attracted few believers.

In some computations involving probabilities, the axiom that the measure over the whole space is 1 plays no role. A notable example is the calculation of posterior probabilities from priors and data by Bayes' Theorem:

Posterior(H|D) = P(D|H) Prior(H) / Sum_H' ( P(D|H') Prior(H') )

(H, H' = hypothesis, D = data.)

The total measure of the prior cancels out of the numerator and denominator. This allows the use of "improper" priors that can have an infinite total measure, such as the one that assigns measure 1 to every integer and infinite measure to the set of all integers.

There can be a uniform probability distribution over an uncountable set, because there is no requirement for a probability distribution to be uncountably additive. Every sample drawn from the uniform distribution over the unit interval has a probability 0 of being drawn. This is just one of those things that one comes to understand by getting used to it, like square roots of -1, 0.999...=1, non-euclidean geometry, and so on.

Comment author: Jiro 28 July 2015 04:36:12PM 0 points [-]

I don't think that helps. For instance, if they alieve in an afterlife but their religion says that suicide and murder are mortal sins, they won't actually commit murder or suicide, but they would still not think it was sad that someone died in the way we think it's sad, would not insist that public policies should reduce deaths, etc.

You would also expect a lot of people to start thinking of religious prohibitions on murder and suicide like many people think of religious prohibitions on homosexuality--If God really wants that, he's being a jerk and hurting people for no obvious reason. And you'd expect believers to simply rationalize away religious prohibitions on murder and suicide and say that they don't apply just like religious believers already do to lots of other religious teachings (of which I'm sure you can name your own examples).

Comment author: RichardKennaway 28 July 2015 04:45:17PM 0 points [-]

If God really wants that, he's being a jerk and hurting people for no obvious reason.

Ask a Christian and they'll give you reasons. Ask a Jew and they'll give you reasons, except for those among the laws that are to be obeyed because God says so, despite there not being a reason known to Man. Ask a Buddhist, ask a Moslem.

There is no low-hanging fruit here, no instant knock-down arguments against any of these faiths that their educated practitioners do not know already and have answers to.

Comment author: Jiro 28 July 2015 02:39:43PM *  1 point [-]

-- Be happy that people have died and sad that they remain alive (same qualifiers as before: person is not suffering so much that even nothingness is preferable, etc.) and the reverse for people who they don't like

-- Want to kill people to benefit them (certainly, we could improve a lot of third world suffering by nuking places, if they have a bad life but a good afterlife. Note that the objection "their culture would die out" would not be true if there is an afterlife.)

-- In the case of people who oppose abortions because fetuses are people (which I expect overlaps highly with belief in life after death), be in favor of abortions if the fetus gets a good afterlife

-- Be less willing to kill their enemies the worse the enemy is

-- Do extensive scientific research trying to figure out what life after death is like.

-- Genuinely think that having their child die is no worse than having their child move away to a place where the child cannot contact them

-- Drastically reduce how bad they think death is when making public policy decisions; there would be still some effect because death is separation and things that cause death also cause suffering, but we act as though causing death makes some policy uniquely bad and preventing it uniquely good

-- Not oppose suicide

Edit: Support the death penalty as more humane than life imprisonment.

(Some of these might not apply if they believe in life after death but also in Hell, but that has its own bizarre consequences.)

Comment author: RichardKennaway 28 July 2015 04:32:43PM 2 points [-]

-- Be less willing to kill their enemies the worse the enemy is

Now might I do it pat. Now he is praying.
And now I’ll do ’t. And so he goes to heaven.
And so am I revenged.—That would be scanned.
A villain kills my father, and, for that,
I, his sole son, do this same villain send
To heaven.
Oh, this is hire and salary, not revenge.
He took my father grossly, full of bread,
With all his crimes broad blown, as flush as May.
And how his audit stands who knows save heaven?
But in our circumstance and course of thought
'Tis heavy with him. And am I then revenged
To take him in the purging of his soul
When he is fit and seasoned for his passage?
No.
Up, sword, and know thou a more horrid hent.
When he is drunk asleep, or in his rage,
Or in th' incestuous pleasure of his bed,
At game a-swearing, or about some act
That has no relish of salvation in ’t—
Then trip him, that his heels may kick at heaven,
And that his soul may be as damned and black
As hell, whereto it goes. My mother stays
This physic but prolongs thy sickly days.

-- Hamlet, Act 3, scene 3.

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