[Merged] Immortality & Bayesian Statistics

[lenny]

- I'll see if I can find an official statement, but sure think we're expected to "speculate" in Bayesian statistics.

one is not encouraged to "speculate" in bayesian statistics so much as to make the background information you are using explicit.

in his book, Good Thinking: The Foundations of Probability and Its Applications, IJ Good has a paper in which he discusses the 46656 varieties of bayesian. there are more today. but none of them suggest one "speculate" in terms of "just make stuff up without a foundation".

the aim (as i read it) is to reach robust probability statements that would generally be agreed upon by all, and when that is not possible to agree that no robust statements can be made and to still find agreement on why this is the case.

 

[pakeha]

...
- As you know, based upon its statistical requirements, I think that the scientific theory that each of us has only one finite period of consciousness is extremely unlikely to be correct, and that my consciousness either exists continuously (in one form or another), or it returns periodically.
...

Are you referring to Sunday morning hangovers, Jabba?

Let's keep it going for the craic . ...

I had to Google the hilited word.
As usual, the Urban Dictionary came up trumps!
http://www.urbandictionary.com/define.php?term=craic

 

[lenny]

What a strange question to ask in a thread with "Bayesian" in the title.

agreed. yet the argument is not consistent from a frequentist point of view either. as noted (without response) here:

one would never ever "accept the null hypothesis as true". neither frequentist nor bayesian.

with a Bayesian hat on, to root confusion seems to be down to glymore's old evidence point.

i think it was suggested that the argument might fly better under a frequentist approach many, many pages ago. but if a coherent frequentist approach was suggested i missed it go by.








You keep using that word. I do not think it means what you think it means.[/QUOTE]

 

[lenny]

You keep making the mistake that highly unlikely is equivalent to impossible. It isn't.

Dave,
- Jut to make sure -- I assume that you do not consider a likelihood of one over infinity close enough to impossible to pretty much waive the difference. Is that correct?

dave's point is valid here.

a probability of 1 (and a prob of 0) are special. they reflect a certainty that is not present in any other assignment of probability, a certainty that is not present in any arbitrarily small non-zero probably. the bayesians even have a name for (not) mistaking a very small probability as a zero probability: Cromwell's Rule.

can we agree that Prob=0 is very different than prob = eps where eps is arbitrarily small?!? if not, there are examples to motivate agreement on this point...

 

[Jabba]

Lenny,
- No problem. I accept the difference. I was hoping that we could waive the difference in the case of one over infinity...

 

[lenny]

- No problem. I accept the difference. I was hoping that we could waive the difference in the case of one over infinity...

thanks for the reply and agreement jabba,

if by "one over infinity" you mean zero then there is no difference.

if by "one over infinity" you mean an extraordinarily small number greater than zero then we cannot waive the difference.

from your previous discussion, (it appears to me) your argument would benefit only from the second.

 

[Jabba]

one is not encouraged to "speculate" in bayesian statistics so much as to make the background information you are using explicit.

in his book, Good Thinking: The Foundations of Probability and Its Applications, IJ Good has a paper in which he discusses the 46656 varieties of bayesian. there are more today. but none of them suggest one "speculate" in terms of "just make stuff up without a foundation".

the aim (as i read it) is to reach robust probability statements that would generally be agreed upon by all, and when that is not possible to agree that no robust statements can be made and to still find agreement on why this is the case.

Lenny,
- I got the following from Google.

spec·u·late
ˈspekyəˌlāt/
verb
1.
form a theory or conjecture about a subject without firm evidence.
"my colleagues speculate about my private life"
synonyms: conjecture, theorize, hypothesize, guess, surmise;can be

- I think that the word "speculate" does apply here, though it is sort of ambiguous and can be confusing -- at least, for me.
- Whatever, by "speculate," I didn't mean to "just make stuff up without a foundation." The stuff should have a foundation, though the strength of the foundation isn't exactly firm.
- Otherwise, I think that I agree with everything you say above, and the speculations that I make regarding the different probabilities are such (it seems to me) that most everyone should be able to accept them.
- I provide my reasoning in post #1172.

 

[Jabba]

thanks for the reply and agreement jabba,

if by "one over infinity" you mean zero then there is no difference.

if by "one over infinity" you mean an extraordinarily small number greater than zero then we cannot waive the difference.

from your previous discussion, (it appears to me) your argument would benefit only from the second.

Lenny,
- I'm not sure how exactly to use the term, but "asymptote" is a word I would use. From Wikipedia:
In analytic geometry, an asymptote (/ˈæsɪmptoʊt/) of a curve is a line such that the distance between the curve and the line approaches zero as they tend to infinity. I'm not sure how that fits with your two alternatives.
- Also, I don't understand why my argument would benefit only from the second alternative.

 

[Toontown]

No.

If the U-brain assumption is true, then the target always existed. It was always the prerequisite to my existence. My U-brain did not become the supposed prerequisite brain after I discovered it was me. It already was the prerequisite brain, or there is no unique brain requirement.

That's what a target is. It defines a space which determines what is a hit and what is a miss. I did not define the target space. the U-brain assumption defines the target space.

The alternative to the U-brain assumption is that there is no defined target space. That gets the jungles lit up nicely.

It isn't just remotely true, it's standard probability, and it is how hypotheses are tested. You look at the existing observations, and you ask "given these observations, how likely is it that the hypothesis is true?" You can do that because the hypothesis gives certain expectations about the observations.

The expected frequency or likelihood is not considered a property of the observed system. It is considered a property of the hypothesis. You simply compare the observed frequency to the expected frequency as a test. There are statistical formulas which accurately convert the variance into a probability that the hypothesis is true, given the observations. I showed you one of them. Aside from complaining about the fact that I brought it up, you ignored it.

If you don't think any of this has anything to do with immortality, then stop talking about it. Don't talk to me about it, I won't talk to you about it.

I never intended to go any further than explaining why I reject the U-brain assumption, and you don't even get that. So why would I try to interpret the alternative for you?

Misstating actuality does not make it true.

Or on topic.

Then state actuality and make it true and on topic.

You only need to answer one simple queston: is there a defined target space, or is there not a defined target space?

 

[dafydd]

Can the thread be split please? We have moved a long way from immortality.

 

[Slowvehicle]

"I think it's English, Jim, just not English as we know it".

Totally nommed...

 

[Slowvehicle]

Then state actuality and make it true and on topic.

You only need to answer one simple queston: is there a defined target space, or is there not a defined target space?

The way you are stating it, the "definition" you are applying to "target space" is only determined after your "target" has been "hit".

Classic TSF; nothing to do with immortality.

 

[dafydd]

The way you are stating it, the "definition" you are applying to "target space" is only determined after your "target" has been "hit".

There's a flaw there. I just threw a tennis ball into my garden and it hit a tree, and I decided that was the target. It's not science Jim, and we know it and bugger all to do with immortality.

 

[lenny]

"old Evidence"

what is the probability that an (american) college football team from a university starting with the letter A would pull ahead via a spectacular "bobbled ball" pass to win in the closing seconds of a game and then, the next week would win in the final second, a disputed one second that had to be put back up on the game clock after a lengthy review, by returning a failed field goal attempt the full 100 yards (endzone to endzone) on the last play of the game. Oh yes, and that against another team that was ranked first in the nation. And whose name also began with the letter A.

the odds against this are so high that, given the likely number of college football games ever to be played, it will never happen.

yet the probability of it happening is one.

it happened yesterday (when Auburn beat Alabama)

today, no bayesian will argue anything based upon that event having been "too unlikely to happen by chance". and no hypothesis that entails that event happening can take that event as evidence.

how exactly does this fail as a counterexample to those arguing that their existence (which has probability one) provides evidence for any hypothesis whatsoever?

 

[Toontown]

The way you are stating it, the "definition" you are applying to "target space" is only determined after your "target" has been "hit".

Classic TSF; nothing to do with immortality.

You brought up targets. I'm just continuing the analogy. I was just talking about the expected likelihood of an observation, implied by a particular hypothesis (which predates my birth), when you brought up the TSF, clearly unaware that the expected likelihood of a possibility is a property of the hypothesis, whether the possibility is realized by observation or not.

Stop accusing me of defining the target space after the fact and admit that the U-brain assumpion defines the target space, and you won't be trapped like a rat.

Continue to pretend that the U-brain assumption defines no target, when in fact it is the alternative that defines no target, and you will continue to be trapped like a rat.

Admitting the obvious doesn't mean you can't favor the U-brain assumption. It just means you have to acknowledge the immense odds you've beaten if it's true.

And of course, admitting the obvious means you have to allow me to probabalistically question the hypothesis without continuously accusing me of all manner of fallacies. And of course, if you do that, then I'll have no cause to keep 'off-topically' responding to your querulous fallacy accusations.

 

[Toontown]

Can the thread be split please? We have moved a long way from immortality.

Don't bother.

 

[dafydd]

Don't bother.

Yes, it's not worth the bother of asking you to stick to the topic of the thread. I did bother, and now it's up to the mods.

 

[Toontown]

what is the probability that an (american) college football team from a university starting with the letter A would pull ahead via a spectacular "bobbled ball" pass to win in the closing seconds of a game and then, the next week would win in the final second, a disputed one second that had to be put back up on the game clock after a lengthy review, by returning a failed field goal attempt the full 100 yards (endzone to endzone) on the last play of the game. Oh yes, and that against another team that was ranked first in the nation. And whose name also began with the letter A.

the odds against this are so high that, given the likely number of college football games ever to be played, it will never happen.

yet the probability of it happening is one.

it happened yesterday (when Auburn beat Alabama)

today, no bayesian will argue anything based upon that event having been "too unlikely to happen by chance". and no hypothesis that entails that event happening can take that event as evidence.

how exactly does this fail as a counterexample to those arguing that their existence (which has probability one) provides evidence for any hypothesis whatsoever?

1. Flawed counterexample. The game of football is completely understood and documented, therefore no resort to probability or hypothesis is indicated.

2. Biased biased counterexample. The football game was post-selected specifically because of it's perceived improbability.

3. All observations are probability 1. That's why we observe them. It is a red herring to invoke 'probability 1' to disqualify an observation from use in a test of a hypothesis.

4. Contrary to (2), one's existence should not be post-selected for the purpose of supporting or casting doubt upon any hypothesis, but simply observed, acknowledged, and when appropriate, may be used as a test of a hypothesis, like any other observation relative to any other hypothesis.

5. No chance event should ever be deemed "too unlikely to happen by chance". However, When testing a hypothesis, one does not assume that chance alone accounts for the variance between the observed and the expected, because one simply does not know what accounts for the variance, else one would not be doing the test. One simply determines the probability that the variance would occur by chance. This value is identical to the probability that the hypothesis is correct, unadjusted by any other known factors.

6. In a test between H₀ and the alternative H₁, one may favor H₁ in the degree to which the probability of chance rules against H₀.

That's it for now. The football game analogy is so wrong on so many levels that I may have missed a few levels.

 

[Toontown]

Yes, it's not worth the bother of asking you to stick to the topic of the thread. I did bother, and now it's up to the mods.

Well, there won't be anything added to the proposed thread by me.

 

[dafydd]

Well, there won't be anything added to the proposed thread by me.

That is good news.