[Link] A Bayes' Theorem Visualization

15 hegemonicon 09 January 2012 04:44PM

A while ago when Bret Victor's amazing article Up and Down the Ladder of Abstraction was being discussed, someone mentioned that they'd like to see one made for Bayes' Theorem. I've just completed version 1.0 of my "Bayes' Theorem Ladder of Abstraction", and it can be found here: http://www.coarsegra.in/?p=111

(It uses the Canvas html5 element, so won't work with older versions of IE).

There's a few bugs in it, and it leaves out many things that I'd like to (eventually) include, but I'm reasonably satisfied with it as a first attempt. Any feedback for what works and what doesn't work, or what you think should be added, would be greatly appreciated.

Comment author: hegemonicon 05 January 2012 06:40:38PM 3 points [-]

From my buddy, a research psychologist:

"Oh yeah, those are a big issue. They're a big problem for medical shit and business shit. Less so for university stuff, for obvious reasons. Even the most basic recruitment agency knows about 'em. "

Comment author: Xachariah 01 December 2011 04:00:08AM *  4 points [-]

I don't see how this is a paradox at all.

Scenario (1) creates 100 years of utility, minus the death of one person. Scenario (2) creates 100 years of utility, plus the birth of one person, minus the death of two people. We can set them equal to each other and solve for the variables, you should prefer scenario (1) to scenario (2) iff the negative utility caused by a death is greater than the utility caused by a birth. Imagine that a child was born, and then immediately died ten minutes later. Is this a net positive or negative utility? I vote negative and I think most people agree; death outweighs birth.

(As an interesting sidenote, if we lived in a world where the value of Birth outweighed the value of Death, I think most of us would happily change our preference ordering. Eg, If we lived in the Children of Men world, we'd go with scenario (2) because a new birth is more important than a new death. Or if we lived in a universe where there really was a heaven, we'd go with scenario (2) as well because the value of death would be near zero.)

Things get less simple when we take into account the fact that all years and deaths don't generate equal (dis)utility. The disutility caused by Death(newborn) != Death(10 year old) != Death (20 year old) != Death (80 year old) != Death (200 year old). Similarly, the utility generated by a child's 3rd->4th year is nowhere near equivalent to the utility of someone's 18th->19th year. I would assume the external utility generated by someone 101st->200th year to far, far outweigh the external utility generated by the 1st->100th year (contributing to the world by being a valuable source of wisdom). By any reasonable calculations it seems that net utility in scenario (1) significantly outweighs the net utility of scenario (2).

Different people might have different expected values for the utility and disutility of years/deaths, and thus get differing results. But it seems if you had sufficiently accurate data with which to calculate expected utility, you could actually determine what those utilities are and they wouldn't come out equal. However, just because something is incredibly hard to calculate doesn't mean you throw your hands up and say that they must be equal. You do what you always do with insufficient information: approximate as best you can, double check your numbers, and hope you don't miss anything.

Comment author: hegemonicon 03 December 2011 02:01:35AM 2 points [-]

I'm not sure about the Children of Men example: a birth in that situation is only important in that it implies MORE possible births. If it doesn't, I still say that a death outweighs a birth.

But here's another extremely inconvenient possible world:

People aren't 'born' in the normal sense - instead they are 'fluctuated' into existence as full-grown adults. Instead of normal 'death', people simply dissolve painlessly after a given amount of time. Nobody is aware that at some point in the future they will 'die', and whenever someone does all currently existing people have their memories instantly modified to remove any trace of them.

I still prefer option (1) in this scenario, but I'm much less confident of it.

Comment author: Julia_Galef 30 November 2011 05:22:18PM 3 points [-]

I agree, and that's why my intuition pushes me towards Life Extension. But how does that fact fit into utilitarianism? And if you're diverging from utilitarianism, what are you replacing it with?

Comment author: hegemonicon 03 December 2011 01:49:25AM 3 points [-]

But how does that fact fit into utilitarianism?

That birth doesn't create any utility for the person being born (since it can't be said to satisfy their preferences), but death creates disutility for the person who dies. Birth can still create utility for people besides the one being born, but then the same applies to death and disutility. All else being equal, this makes death outweigh birth.

Meta-reading recommendations

3 hegemonicon 28 November 2011 12:17AM

Despite a glut of reading recommendation engines, I still find that I rely on personal recommendations for 90% of the books that I read. Given that, I thought it might be useful to try to compile a list of prolific recommenders - people who provide a large number of reliable book recommendations.

I'll start off with the two obvious ones, Tyler Cowen and Cosma Shalizi. The LW/OB group of Eliezer, Robin Hanson, and Michael Vassar also provide useful recommendations (though much less frequently).

Who else can reliably recommend a good book?

Comment author: hegemonicon 05 October 2011 07:15:34PM *  1 point [-]

My estimate:

  • Lets say 40% of the people are going to do a naive estimate of 25 based on half of the average of random guesses between 1-100
  • Lets say 20% recurse one level and guess 12.5
  • Lets say 15% think they're clever and guess super low like 0/.5/1
  • Lets say 15% of people are going to be anchored to 40 and guess 20.
  • And lets say the remaining 10% just guess more or less randomly, the average being 50

This results in an 'average' guess of ~20.5, half of which is 10.25. I actually guessed 10.5 as I used slightly different estimates.

Of course, had I known this was posted on LW, I'd have used higher probabilities of low guesses.

Comment author: hegemonicon 23 September 2011 12:39:05PM 16 points [-]

From an actual physicist:

Chang Kee Jung, a neutrino physicist at Stony Brook University in New York, says he'd wager that the result is the product of a systematic error. "I wouldn't bet my wife and kids because they'd get mad," he says. "But I'd bet my house."

Comment author: calcsam 15 September 2011 06:39:07PM *  7 points [-]

Consider Le Corbusier, Robert Moses, etc. These men combined methods which claimed to be scientific. Corbusier tried to maximize population density; Moses, to maximize road construction.

But they were working in very intricate, complicated systems and ignored the effects that maximizing their favorite metric would have on everything else. They dictated everything from the center and ignored local knowledge.

This is what we call dangerous knowledge.

The failure of these methods -- "the projects" housing inspired by Corbusier, Moses's neighborhood destruction, helped trigger -- as far as I understand -- the current focus on aesthetics and intuition. It's a reaction to that, a "risk-averse" strategy to picking the wrong metrics and trying to maximize/minimize them.

A parallel example might be Robert McNamara and the whiz kids turning into the Best and the Brightest in Vietnam.

Comment author: hegemonicon 15 September 2011 08:51:17PM 2 points [-]

I don't really see a focus on aesthetics and intution as a "new" focus, or something that was turned to as a reaction to previous urban planning. I haven't read the previous works, but what seems to set Jacobs apart is that she didn't merely base her judgments on what was aesthetically pleasing - that she actually went out and did basic science, collecting observations and forming a hypothesis that explained them.

Comment author: Morendil 15 September 2011 06:51:12PM 4 points [-]

Many things that are obvious in retrospect are anything but at the time the important debates happen, and they become obvious in retrospect precisely because someone has come along who paid attention to what - in retrospect - really mattered.

See James Scott's Seeing Like a State (which puts Jacobs' work in that kind of broader perspective, largely in line with calcsam's comment) and Duncan Watt's Everything is Obvious (which lays out the research on why the social sciences are especially prone to that phenomenon).

Comment author: hegemonicon 15 September 2011 08:42:39PM *  3 points [-]

Right, inferential gaps always look smaller when they're behind you.

I'm not claiming that her insights were obvious, just that they weren't especially well constructed or well supported and that (critically) that doesn't seem to have improved with time.

Comment author: Unnamed 15 September 2011 04:41:01PM 2 points [-]

Rigor isn't the only thing that can make a book important and worth reading. When reading a book which is considered a "classic" in a field, which was written 50 years ago by a person who was not trained in that field, I would not expect a lot of rigor or use the book to assess the standard of research in that field. I'd focus more on the ideas, the implications of the ideas (e.g., where they conflict with existing practices), the style of thinking, and the value of the methods used. For instance, careful observation is an important technique in many fields for developing beliefs and models that are entangled with reality, though it is often more useful for generating hypotheses than for testing them.

Comment author: hegemonicon 15 September 2011 04:53:30PM *  1 point [-]

My issue isn't so much with the book (it's an impressive achievement considering Jacobs' wasn't even a college graduate, much less a trained urban planner) but the fact that the field doesn't seem to have advanced passed it - that even today it's still one of the very best books on the subject.

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