[Merged] Immortality & Bayesian Statistics

Status
Not open for further replies.
Toontown said:
"At least one" implies all, many or a low probability. A low probability implies that you are unlikely to observe yourself, which is similar to the situation with finite uniqueness.
Click to expand...

Jabba said:
Jay, Toon and Lenny,

- Everyone else seems to disagree with my estimates:

- P(me|SM) either approaches zero, or is simply unimaginably small. (I think that it approaches zero.)
- For P(SM|k), I’m ALLOWING that given our existing knowledge, P equals 99%. (I don’t THINK that it’s nearly that much.)
- P(NSM|k) is simply what’s left after subtracting P(SM|k) – or, 1%.

- What do you guys think?
Click to expand...
- Does anyone agree with any of my estimates -- or, accept them as reasonable?
 
Pixel42 said:
Four is a number. Four is not an example of odds. "Four to one" is an example of odds.

"The odds are four to one" is an expression I immediately understand. "The odds to one are four" makes no sense to me unless I stop and think about what it might possibly be intended to mean.
Click to expand...


Although "the odds to one are four" makes no sense, it's because the phrase "odds to one" is unclear, not because odds isn't a number. The wikipedia page on "odds" is correct that the rigorous definition of the odds of an event A is odds(A) = P(A) / [1–P(A)], where P(A) is the probability of A. Clearly, then, odds is a number. If P(A) = .8, then odds(A) = 4. It's just that when communicating odds to a non-mathematical audience we usually state it explicitly as a ratio.


"Odds to one" is an expression I've never come across before and which threw me completely. I re-read the context and worked out what you meant by it, but I'd recommend not using it if you want to be generally understood.
Click to expand...


Also, I don't see how anyone would guess that the "odds to one" of an event is supposed to be the odds against the event.
 
Toontown said:
Hypothetically, because they read and understood this...

http://www.internationalskeptics.com/forums/showthread.php?postid=9616169#post9616169
Click to expand...


Which proves my point. Since the term "odds to one" is of your own invention, no one can understand it without you also stating your definition of it. Then, they can understand that for some bizarre reason you are referring to what everyone with an elementary understanding of probability calls "odds against" an event, and that you've given it the counterintuitive name "odds to one."
 
Pixel42 said:
Probability is confusing and counter-intuitive enough as it is
Click to expand...

Hi P42,

I think this may be the first time I disagree with you. :)

Perhaps intuitive probability should have its own thread on the education forum?

I agree, of course, that we should avoid creating new jargon whenever possible. But I'd also suggest odds need not (indeed usually in the world do not) correspond to probabilities. ... They usually do in maths departments of course.
 
Last edited:
Toontown said:
Yeah. Who would've thunk "odds" could mean something other than p/(1-p)?
Click to expand...

I would have, for one. That is why I wanted to stay with probabilities a page or so back, before my day job interviewed (sorry).

I agree using odds on and odds against is useful. regardless the the connection to probabilities does not hold in general.

Wasn't there a bookmaker on this thread:did your odds EVER correspond to probabilities?!?
 
jt512 said:
Which proves my point. Since the term "odds to one" is of your own invention, no one can understand it without you also stating your definition of it. Then, they can understand that for some bizarre reason you are referring to what everyone with an elementary understanding of probability calls "odds against" an event, and that you've given it the counterintuitive name "odds to one."
Click to expand...

Which proves nothing.

The "bizarre reason" was that lenny seemed confused by something I had posted earlier, and specifically asked for clarification. I wasn't sure lenny would automatically know what the 4 represented, so instead of leaving the 4 hanging, I added "to 1".

I see my mistake now. I should have left the 4 hanging, and if lenny or anyone else questioned it's meaning I could have snarked "Everyone with an elementary understanding of probability knows it's "odds against" an event."

OK, now I understand. This ain't no neverneverland. No more Mr Nice Guy. From here on out it's...

http://www.youtube.com/watch?v=6M9Q1QDhqAU
 
lenny said:
I would have, for one. That is why I wanted to stay with probabilities a page or so back, before my day job interviewed (sorry).

I agree using odds on and odds against is useful. regardless the the connection to probabilities does not hold in general.

Wasn't there a bookmaker on this thread:did your odds EVER correspond to probabilities?!?
Click to expand...

I chose odds against in lieu of division by infinity in a naive bid to avoid creating another bone of contention. Past experience suggested that doing so might deter division-by-infinity cops.

If you're a bookmaker, your odds had better correspond to probability in an attractive yet advantageous manner, or you're going broke.
 
Last edited:
Jabba said:
Jay, Toon and Lenny,

- Everyone else seems to disagree with my estimates:

- P(me|SM) either approaches zero, or is simply unimaginably small. (I think that it approaches zero.)

- What do you guys think?
Click to expand...

First I think it is important to always note what you are conditioning on, the background information "I" which informs your probabilities, P(x |data, I).

Second, I think it is useful to evaluate the probability you expected to observe, under the assumption that I holds and your probability (forecast, in my case) is True.

Skill scores for probability forecast systems are useful both for seeing how good one system is relative to another, and (some of them) can be used to see how surprised you "should" be give a specific outcome. A poor score is surprising only if a good score was to be expected, given the probability forecast issued.

I cannot follow the whole of jabba's argument, but it seems suggest the observed value has too low a probability to happen by chance. It appears to me that the expected probability assigned to the outcome (that is, the value corresponding to an outcome determined by the true probability distribution) is vanishingly small. Thus it is no surprise that the probability of the observed outcome is vanishingly small.

If you are forecasting over a huge (finite) number of possible outcomes then, in the case some are high probability and others are very very low probability, it is surprising to observe a low probability outcome.

But if every possible outcome is carries a very very low probability, then you expect a low probability outcome, you just don't know which one.

I do not claim this is the first time this basic idea has been stated on this thread.
 
Last edited:
lenny said:
But if every possible outcome is carries a very very low probability, then you expect a low probability outcome, you just don't know which one.
Click to expand...

Jabba's angle is you don't expect a particular one. If a hypothesis says the realization of a very low probability is the only way you will be expecting anything at all, but you do find yourself expecting something, then you are justified to doubt the hypothesis with a certainty that is proportional to the unlikelihood of the specific observation.

Of couse this kind of test can only be valid if the hypothesis says the observation is impossible or extremely unlikely. For example, if a hypothesis says your existence is flat out impossible, you give that hypothesis the bum's rush. And you would also look upon the hypothesis with deep skepticism if it says your likelihood is 0.0000000.....1
 
Last edited:
Toontown said:
How do you say 4 : 1? I say "four to one". Hence, odds to one. How is that confusing?
Click to expand...

It's confusing because "to one" is already part of the odds. The odds are four to one. Not the [odds to one] are four. And certainly not the [odds to one] are [four to one].

"Odds to one" makes no sense whatsover. If the odds are four to one, then the odds to one must be four to one to one?

odds = [four to one] (identity)

odds to one = [four to one] to one (simple substitution)

Is English your first language?

I'll say it again, in case it's not clear. The odds are 4 : 1. Therefore, when you say "odds to one", it implies "4 : 1 to one". Which makes no sense whatsoever, either mathematically or in colloquial English.

Pixel went the other route, and assumed that you were parsing "the odds are four to one" as "[the odds are four] to one", implying that you were saying the odds were four. Hence, "the odds to one are four." But four isn't odds, and I think you managed to make it clear that's not what you intended.

I did, in fact, finally figure out what you meant, but it wasn't easy, and I shouldn't have had to work so hard to figure out what your bizarre phrasing was trying to convey. If you stick to normal English, people are much less likely to end up confused. Which should be a plus, unless your goal is to confuse.

And now that we've covered that, we can return to Jabba and his attempts to square the circle.
 
lenny said:
I would have, for one. That is why I wanted to stay with probabilities a page or so back, before my day job interviewed (sorry).

I agree using odds on and odds against is useful. regardless the the connection to probabilities does not hold in general.

Wasn't there a bookmaker on this thread:did your odds EVER correspond to probabilities?!?
Click to expand...

I used to be a bookmaker. There is no such thing as a dead cert.
 
http://messiahornot.com/ACT2Scene1.php
http://messiahornot.com/Act2Scene2.php

- In case you have wanted me to provide my whole argument at once, you can check out the links above.

- In regard to the need for Bayesian statistics, those of you doubting that need can go to the first page of the second “scene” above, where you will find, “1. The probability of drawing a particular sample (me) from a particular population (all potential “selves”) has mathematical implications re the probability that a particular sample was, in fact, drawn from that population... You might have to read that again...”
- The point being that I think I agree with you – at least, to some extent. The basic idea (stated above) underlying my claim is simple logic, and I probably could have left it there and avoided Bayes -- and perhaps, a lot of confusion. However, my best guess is that drawing on Bayes was useful…
 
Status
Not open for further replies.

Back
Top Bottom