Rune comments on Two probabilities - Less Wrong

1 Post author: rwallace 15 February 2010 02:18PM

You are viewing a comment permalink. View the original post to see all comments and the full post content.

Article Navigation

Comments (43)

Comments (43)

Sort By: Best

You are viewing a single comment's thread.

Comment author: Rune 15 February 2010 05:20:12PM 7 points [-]

Why does the Bayesian say that the probability of there being life on Mars is 0.5?

Comment author: Eliezer_Yudkowsky 15 February 2010 06:21:25PM 7 points [-]

We don't. I'm not sure what's up with that, unless it was a deliberately bad example.

Comment author: Rune 25 February 2010 03:25:43AM 0 points [-]

I can't imagine anyone assigning the event probability 0.5 just because it's a Yes/No question. Does the probability drop to 1/3 if I added 1 more option to the question?

The person who assigns probability 1/k to all outcomes of any question with k options is NOT a Bayesian. That's someone who has misunderstood Bayes rule and should re-read all of Eliezer's posts.

Comment author: Kevin 16 February 2010 12:09:00AM 2 points [-]

"So roughly speaking, what are the chances the world is going to be destroyed? One in a million, one in a billion?"

"Well, the best we can say is about a 1 in 2 chance."

http://www.thedailyshow.com/watch/thu-april-30-2009/large-hadron-collider (video, region blocked)

Comment author: arundelo 16 February 2010 07:05:34AM 1 point [-]

I seem to remember seeing the idea that "all possibilities equally likely" is sort of a "default prior". In the case of life on Mars: Imagine getting all your information about life and Mars in little dribs and drabs, each one of which lets you update your probability of life on Mars. The place you start from (before you know stuff like what DNA is and whether Mars has an atmosphere) is 0.5.

Comment author: rwallace comment score below threshold [+] (23 children)

Comment author: Zack_M_Davis 16 February 2010 01:26:03AM 4 points [-]

We don't [...] even have data for an estimate, and ignorance translates to B = 0.5.

(Downvoted.) No, it doesn't: we know quite a bit about Mars and about life, surely enough to have some sort of prior probability before encountering specific data. More to the point, we're never that ignorant. If you literally had no information about a topic, then you wouldn't know enough to even phrase a question about it, or recognize an answer to such a question. By asking the question, you must have some notion in your mind of what you're asking about, and it is from that notion that we must draw our prior probabilities, rather than arbitrarily picking 0.5. "Whereof we cannot speak, we must pass over in silence."

Comment author: Jack 16 February 2010 01:41:58AM 1 point [-]

So priors matter if you and I have already updated our beliefs on really divergent sets of data. But if you're coming at a question from a place of total ignorance assigning even possibilities as your priors should work just fine. 0.5 sounds just fine to me. It doesn't really matter though because as soon as we have any significant amount of evidence to update on our beliefs will rapidly converge. My prior probability for life on Mars could be 99.99, as soon as my rover gets there and doesn't find any life that number drops dramatically. My prior could also be 0.01 but as soon as I learn about the geological indicators that suggest early Mars was much like early Earth that is going to go up somewhat (and come down again when I show up and don't see any life) either way the whole point is that it shouldn't matter much at all what your priors are.

At least that is how it was explained to me, I could be totally off base.

What doesn't make sense about rwallace's position is just that he doesn't seem to think we have any evidence to update on when it comes to life on Mars.

Comment author: rwallace 16 February 2010 02:05:36AM 0 points [-]

I'm not saying we have no data on Mars. I'm saying we have evidence one person reasonably believes is in favor of life on Mars, and evidence another person reasonably believes is against life on Mars; we even have knowledgeable scientists holding very strong opinions on either side of the issue. My conclusion is that when you add it all up, the net evidence doesn't justify a position very far from 0.5, and to take a position like 0.01 or 0.99 is really an expression of personal bias.

Comment author: Jack 16 February 2010 02:39:22AM 1 point [-]

My conclusion is that when you add it all up, the net evidence doesn't justify a position very far from 0.5, and to take a position like 0.01 or 0.99 is really an expression of personal bias.

Well thats an interesting conclusion and maybe someone has written something somewhere demonstrating that the right posterior probability given our science is around 0.5. But you can hardly expect your reader to have any idea where that number is coming from. 0.5 sounds much too high to me though what I know I basically know from general scientific knowledge and having done a science report on Mars in the 4th grade.

I agree that 99.99 or 00.01 seem much too extreme for estimations given our evidence- but they'd function perfectly fine as priors, was my point.

Comment author: pwno 18 February 2010 08:07:09PM 0 points [-]

More to the point, we're never that ignorant.

Sure we are. A priori, the probability that there's something instead of nothing is .5.

Comment author: JGWeissman 16 February 2010 12:15:27AM 1 point [-]

What probabilities do you assign to the following propositions?

There is life on the northern hemisphere of Mars.
There is life on the southern hemisphere of Mars.
There is life on Mars.

Comment author: rwallace 16 February 2010 12:25:34AM 0 points [-]

Good example. I assign B = 0.5 in all three cases, but I expect the (unknown) value of F to be very similar (and close to 0 or 1) for all three, unlike in the case of three coin flips.

Comment author: JGWeissman 16 February 2010 12:41:51AM * 0 points [-]

Now, without using probabilities of 0 or 1, can you coherently assign probabilities to

A. 1 and 2
B. 1 and not 2
C. not 1 and 2
D. not 1 and not 2

Comment author: rwallace 16 February 2010 01:13:17AM 0 points [-]

Sure. B(A) = B(D) = 0.5, B(B) = B(C) = epsilon. (The 0.5 is only good to one significant figure, and even that's a stretch.)

Comment author: JGWeissman 16 February 2010 01:33:54AM 1 point [-]

Just how small is this epsilon? I might want to propose a bet.

Comment author: rwallace 16 February 2010 01:58:18AM 0 points [-]

If I had a number, I would've given the number instead of saying "epsilon" :) What's your proposed bet?

Comment author: JGWeissman 16 February 2010 02:19:47AM 0 points [-]

I might bet on B or C against A or D at odds of epsilon to 1, to be settled when we have thoroughly explored Mars, assuming that if there is life, we will find it. This of course depends on the actual value of epsilon.

Comment author: Lightwave 16 February 2010 01:10:49PM 0 points [-]

So basically you're saying that the probability of there being life on only one of the hemispheres is arbitrarily small?

Comment author: rwallace 16 February 2010 03:27:10PM 0 points [-]

Mathematically nonzero, but small enough that we can treat it as zero for practical purposes, yes.

Comment author: Kevin 17 February 2010 08:46:22AM 0 points [-]

Can you link to some of the major chunks of data supporting life on Mars?

Comment author: RobinZ 16 February 2010 01:43:32AM 0 points [-]

Even if ignorance were total, some kind of Occam's-Razor prior would be applicable.

Comment author: rwallace 16 February 2010 03:25:57AM 0 points [-]

Put it this way: Of all the things that might have turned out to be controversial, I'm just surprised "we have no idea whether there is life on Mars" turned out to be the one; it still strikes me as fairly obviously reasonable. Oh well, surprises are part of the point of talking to people :-)

Comment author: Cyan 16 February 2010 04:53:35AM 0 points [-]

The problem may be that "we have no idea whether there is life on Mars" sounds a lot like "we have no evidence about the presence of life on Mars", which is simply not the case. (Of course, "we have no idea whether there is life on Mars" was operationalized as a probability assessment of 0.5, which does not imply zero evidence, so I can't be sure if my re-quotation is what you meant.)

Comment author: rwallace 16 February 2010 05:53:16AM 1 point [-]

Ah, indeed the paraphrased version would be incorrect, and wasn't what I meant; perhaps I phrased my version badly. I've added a clarification to my earlier comment, does that help?

Comment author: Cyan 16 February 2010 02:03:23PM 0 points [-]

Yup.

Comment author: wnoise 16 February 2010 12:05:40AM 0 points [-]

Surely we have some data.

Comment author: Jack 16 February 2010 12:21:22AM 1 point [-]

Right? I've seen lots of pictures of Mars and not identified any life in any of them!

Rune comments on Two probabilities - Less Wrong

Article Navigation

Comments (43)

Nearest Meetups

Virtual Study Room

Recent Comments

Recent Posts

Recent Rationality Quotes

Recent Wiki Edits

Top Contributors, 30 Days

Recent Karma Awards

Comments (43)

Top Contributors, 30 Days

You'll need to login or register to do that

(Don't worry, it only takes a few seconds)

Create

Login