Immortality & Bayesian Statistics

[victorxstc]

Thanks CB and Jabba for this nice discussion. I learned some basic notions regarding the Bayesian stats.

But the topic itself sounds to me irrefutable and completely out of the realm of science, and because of its irrefutable nature, impossible to debate. So bringing it on as a scientific / logical debate seems to me as the core flaw. Even if the probability of an existing self in the absence of any reincarnation turns convincingly to be zero, one might argue that there are infinite universes, giving existence to any impossible zero-probability event, and making such an impossible event happen for infinite times! So the zero chance Jabba mentioned in the fist post, doesn't seem to help at all. Such reasoning can go in cycles.

However, even if we could hypothetically gather evidence and make sure that there were not an infinite number of universes or planets etc, and also could make sure that the probability of a self without reincarnation is zero, the matter still remains irrefutable and completely out of reach.

 

[CB]

Thanks CB and Jabba for this nice discussion. I learned some basic notions regarding the Bayesian stats.

But the topic itself sounds to me irrefutable and completely out of the realm of science, and because of its irrefutable nature, impossible to debate.

Well yeah! There is not going to be a nice simple answer to the question posed, because it's unclear how we should specify any of the probabilities required for the application of Bayes' theorem. Usually we're sort of ok with the idea of subjective priors, but we want actual data for the likelihoods. In jabba's argument, all the probability values he is entering are purely subjectively determined, so this is a long way from the type of Bayesian analysis you'd see in an actual scientific study. But I'm happy to follow the discussion through as a learning opportunity to show what you can and can't do with Bayes' theorem. It's useful but not some kind of magical inference ticket.

 

[Jabba]

If you think anywhere near 1% of scientists believe in immortality or reincarnation, I'm afraid you are probably mistaken. However, the specification of priors in a Bayesian analysis is usually a subjective process anyway, so I'll leave this point for now and maybe come back to it later...

CB,
- I Googled "science and religion." The following were right at the beginning. These do not address my claim directly -- but surely, they support my claim. Don't they?

http://www.theguardian.com/science/...r/04/myth-scientists-religion-hating-atheists
http://www.huffingtonpost.com/2014/...ey-compatible-scientists-doubt_n_4953194.html
http://www.sacred-texts.com/aor/einstein/einsci.htm

- And again, There's the possibility that "now" (time) isn't what we think it is -- and, our conscious existence is like "Groundhog Day" (the movie), except that nothing changes as our movie keeps repeating. I.e., what I'm suggesting may not require what we normally think of as reincarnation or immortality.

 

[Jabba]

...But more importantly, you've made a more fundamental mistake later.



Point 146 is incorrect. There is no reason why L(me|WEBR) and L(me|~WEBR) need to add to the probability of P(~WEBR). I don't really follow why you would think that this is the case.

So you cannot calculate L(me|~WEBR) from the other values in the formula; you need to independently select and enter a plausible value here. And your result will differ drastically depending on what value you choose. So what is the probability of your existence, if reincarnation does exist?

CB,

145. And, L(me|~WEBR) is simply .01 minus (1/10100!) -- or, for all intents and purposes, .01.
146. (By setting P(~WEBR) as .01, and L(me|WEBR) as 1/10100!, L(me|WEBR) and L(me|~WEBR) must add up to .01.)

- I was hoping that you would just agree. I wasn’t sure that the claim was legitimate, but here’s why I figured it was.
- While the likelihood of my current existence is not part of the background knowledge in the prior probability of WEBR, my current existence is. Consequently, the fact that I currently exist means that L(me|WEBR) and L(me|~WEBR) — these being the only possibilities — has to add up to the overall likelihood that I would currently exist.
- If you still don’t agree, I have another way to figure L(me|WEBR) that would work (I think)…

- Thanks for your input. If I’m wrong about this stuff, now would be a good time to find out.

 

[spunky]

These do not address my claim directly -- but surely, they support my claim. Don't they? .

it has been a while since the last time i've pulled out my somewhat famous "sword in a field" scene from The Messanger movie (the story of Joan Of Arc).

http://www.talkstats.com/showthread...-me-how-this-is-statistically-possible-please


http://www.talkstats.com/showthread.php/53853-Probability-of-coincidence

this seems like the right place to put it now...
[YOUTUBE]w47UQxld7LM[/YOUTUBE]

 

[victorxstc]

Well yeah! There is not going to be a nice simple answer to the question posed, because it's unclear how we should specify any of the probabilities required for the application of Bayes' theorem. Usually we're sort of ok with the idea of subjective priors, but we want actual data for the likelihoods. In jabba's argument, all the probability values he is entering are purely subjectively determined, so this is a long way from the type of Bayesian analysis you'd see in an actual scientific study. But I'm happy to follow the discussion through as a learning opportunity to show what you can and can't do with Bayes' theorem. It's useful but not some kind of magical inference ticket.

Yeah that helps a lot in teaching rookies like me the very basics of Bayesian stats.

On another note, I was not referring only to this matter being completely subjective. There are complete subjective matters that can be translated with some error margins into an objective scale. For example, pain, happiness, etc. But there are other complete subjective matters that even cannot be translated into percentages or scales.

Again, there are subjective matters that can be refuted. We might use null hypothesis testing to invalidate them, and thus can suggest evidence for their opposite (alternative) hypotheses. So although such matters are completely subjective, we can still use scientific measures to find associations etc (like most of the completely subjective psychological concepts being tested everyday).

But there are subjective concepts that are naturally irrefutable (like god, soul, reincarnation etc). These are technically only and only believes and cannot be denied, nor can be proven be by any means. Thus they cannot be logically or mathematically discussed.

The only way of talking about these issues is "suggesting" this idea or suggesting that hypothesis against it, as an enjoyable philosophical talk.

So mixing them with scientific (logical) concepts is nothing by pseudoscience.

 

[CB]

- While the likelihood of my current existence is not part of the background knowledge in the prior probability of WEBR, my current existence is. Consequently, the fact that I currently exist means that L(me|WEBR) and L(me|~WEBR) — these being the only possibilities — has to add up to the overall likelihood that I would currently exist.

The overall (marginal) likelihood that you currently exist, L(me), is indeed the denominator that you would use in this application of Bayes theorem. That marginal likelihood is partially determined by the two conditional likelihoods, L(me|WEBR), and L(me|~WEBR). But it's not as simple as adding them up; you need to weight by the prior probability of WEBR. So L(me) = L(me|WEBR)*P(WEBR) + L(me|~WEBR)*P(~WEBR).

That expanded version of the denominator seems to be something you're aware of.

146. (By setting P(~WEBR) as .01, and L(me|WEBR) as 1/10100!, L(me|WEBR) and L(me|~WEBR) must add up to .01.)

Where you're getting confused especially is in thinking that the overall likelihood that you could currently exist, L(me), should be equivalent to the prior probability of WEBR, P(WEBR), which you've specified as 0.01. These are two independent quantities, and there is no need for them to be the same.

So yes, you need to find some other way to specify P(me|~WEBR) - again, you can't calculate this from the other probabilities you've specified.

 

[Jabba]

Where you're getting confused especially is in thinking that the overall likelihood that you could currently exist, L(me), should be equivalent to the prior probability of WEBR, P(WEBR), which you've specified as 0.01. These are two independent quantities, and there is no need for them to be the same.

So yes, you need to find some other way to specify P(me|~WEBR) - again, you can't calculate this from the other probabilities you've specified.

CB,

- Not to say that you're wrong that I'm wrong (you're probably right), but you haven't quite expressed what I'm actually suggesting.
- I'm suggesting that L(me|~WEBR) = P(~WEBR) - L(me|WEBR), because P(~WEBR) = L(me|~WEBR) + L(me|WEBR) because between WEBR and ~WEBR, we have all possibilities covered. And, because L(me|WEBR) is so small, we can round off L(me|~WEBR) to virtually 1.00. Whew!

- Unfortunately, you might notice that by trying to follow this reasoning more carefully, I've had to change my ultimate answer...

- Here (I think) is another way to express this reasoning.
1. Between WEBR and ~WEBR we have all the possible explanations covered.
2. While, for prior probabilities we haven't recognized how unlikely my existence is -- given WEBR, or ~WEBR -- we have recognized that I do exist.
3. Consequently, that I do exist needs to be accounted for (somehow) in the prior probabilities.
4. Doing that, we are forced to accept that the two likelihoods must add up to virtually 1.00.

- If you still disagree, I'll move on to a more obvious way to calculate L(me|~WEBR).

- Thanks, again.

 

[Dason]

P(~WEBR) = L(me|~WEBR) + L(me|WEBR)

That is wrong. How could it be right? IF that were true then you could make the same exact argument to claim that
P(WEBR) = L(me|WEBR) + L(me|~WEBR) = L(me|~WEBR) + L(me|WEBR) = P(~WEBR)

which would require P(WEBR) and P(~WEBR) to be .5 and since there is nothing special about WEBR you could make argument for any probability so ALL probabilities would be 0.5. Obviously this is wrong.

What IS true is

P(me) = P(me|~WEBR)P(~WEBR) + P(me|WEBR)P(WEBR)

 

[Jabba]

That is wrong. How could it be right? IF that were true then you could make the same exact argument to claim that
P(WEBR) = L(me|WEBR) + L(me|~WEBR) = L(me|~WEBR) + L(me|WEBR) = P(~WEBR)

which would require P(WEBR) and P(~WEBR) to be .5 and since there is nothing special about WEBR you could make argument for any probability so ALL probabilities would be 0.5. Obviously this is wrong.

What IS true is

P(me) = P(me|~WEBR) + P(me|WEBR)

Dason,
- Off the top of my head, I think that I misspoke. I should have said P(~WEBR) = L(me|~WEBR) minus L(me|WEBR). This stuff isn't easy. I'll be back.

 

[Dason]

Nope. Still wrong.

 

[Jabba]

- Try this.

- Since I do exist, the fact that I do has to be accounted for when determining likelihoods.
- And, since L(me|WEBR) and L(me|~WEBR) include all possible explanations for my existence:
- L(me|WEBR) + L(me|~WEBR) = 1.00.
- Or, L(me|~WEBR) = 1.00 - L(me|WEBR).
- And, if L(me|WEBR) is infinitesimally small (which seems to be the case), L(me|~WEBR) must be virtually 1.00.

- (I'm praying.)
- Any Amens?

 

[CB]

- Since I do exist, the fact that I do has to be accounted for when determining likelihoods.

No, it doesn't. I think you are a bit confused about what a likelihood is. Maybe some background reading would help: http://www.yudkowsky.net/rational/bayes

- And, since L(me|WEBR) and L(me|~WEBR) include all possible explanations for my existence:
- L(me|WEBR) + L(me|~WEBR) = 1.00.
- Or, L(me|~WEBR) = 1.00 - L(me|WEBR).
- And, if L(me|WEBR) is infinitesimally small (which seems to be the case), L(me|~WEBR) must be virtually 1.00.

You are confusing priors with likelihoods. L(me|~WEBR) is the probability of your existence if WEBR was false. L(me|~WEBR) is not an "explanation" for your existence. L(me|~WEBR) and L(me|WEBR) do not have to add to 1.

I've said this now several times: You cannot calculate L(me|~WEBR) from the other probability terms. You have to find some other way to determine this probability. In a "real" scientific study we would calculate the likelihoods using actual empirical data, but for the sake of argument you could find some other way to choose a number to insert.

 

[Jabba]

No, it doesn't. I think you are a bit confused about what a likelihood is. Maybe some background reading would help: http://www.yudkowsky.net/rational/bayes



You are confusing priors with likelihoods. L(me|~WEBR) is the probability of your existence if WEBR was false. L(me|~WEBR) is not an "explanation" for your existence. L(me|~WEBR) and L(me|WEBR) do not have to add to 1.

I've said this now several times: You cannot calculate L(me|~WEBR) from the other probability terms. You have to find some other way to determine this probability. In a "real" scientific study we would calculate the likelihoods using actual empirical data, but for the sake of argument you could find some other way to choose a number to insert.

CB,

- So far, I still disagree -- in the end.
- I agree that P(WEBR) + P(~WEBR) = 1.00
- But so far, it still seems to me that the fact of my current existence requires that L(me|WEBR) + L(me|~WEBR) =1.00 also.

- We have two possible hypotheses for "explaining" my current existence: WEBR and ~WEBR. I accept that "explain" isn't quite the right word to use -- but so far, I haven't been able to find the right word (or phrase)...
1) Theoretically, we have an excluded middle here -- which means that between WEBR and ~WEBR, we've covered all the possible bases ("explanations") for the fact that I currently exist -- and,
2) Since I do exist, and since my current existence is part of our background knowledge, I can logically conclude that L(me|WEBR) and L(me|~WEBR) must also add up to 1.00.

- #2 seems to be our hangup. Can you elaborate on why you disagree with me here?.

 

[CB]

CB,

- So far, I still disagree -- in the end.
- I agree that P(WEBR) + P(~WEBR) = 1.00
- But so far, it still seems to me that the fact of my current existence requires that L(me|WEBR) + L(me|~WEBR) =1.00 also.

- We have two possible hypotheses for "explaining" my current existence: WEBR and ~WEBR. I accept that "explain" isn't quite the right word to use -- but so far, I haven't been able to find the right word (or phrase)...
1) Theoretically, we have an excluded middle here -- which means that between WEBR and ~WEBR, we've covered all the possible bases ("explanations") for the fact that I currently exist -- and,
2) Since I do exist, and since my current existence is part of our background knowledge, I can logically conclude that L(me|WEBR) and L(me|~WEBR) must also add up to 1.00.

- #2 seems to be our hangup. Can you elaborate on why you disagree with me here?.

Let's take a simple counterexample to show why the likelihoods don't have to add to 1.

Imagine you are walking behind someone, and can't make out their gender very confidently. You have observed, however, that they are wearing pants. Let's assume the following probabilities:

50% of people are male, and 50% female; that is, P(Male) = 0.50
A large percentage, say 99%, of men wear pants; that is, L(Pants|Male) = 0.99
But quite a good number of women do too, say 55%; that is, L(Pants|Female) = 0.55

Now answer the following questions:
1. What is the posterior probability that the person is male?
2. Do the two likelihoods add to 1?
3. If not, is there any problem with that? Do the proportion of women who wear pants and the proportion of men who wear pants really have to sum to 1?

If that still doesn't make sense to you, I want you to forget about your immortality argument for a while and go do some actual reading to get a grasp of Bayes theorem. At the moment we are not being held up by a disagreement, but just by you not grasping the framework of Bayes theorem. Please have the humility to accept that.

Once you've done that, if you really want to apply Bayes theorem to your problem, you need to forget about this approach of trying to calculate L(me|~WEBR) from the other probability terms and instead try to find some other way of estimating this probability:

In a world with immortality or reincarnation, what would be the probability of your current existence?

Note: Even without a good grasp of Bayes theorem, it should be intuitively obvious to you that this should not be a very large probability! By your current assumption, L(me|~WEBR) is close to 1, but that's obviously not the case - for you to exist, even in a world with reincarnation or immortality, all kinds of unlikely things had to go "right".

Sorry to be harsh, but I'm not going to engage further in this discussion unless you show some actual effort at trying to grasp Bayes theorem - I have work to do.

 

[Dason]

At the moment we are not being held up by a disagreement, but just by you not grasping the framework of Bayes theorem. Please have the humility to accept that.

It's not even Bayes theorem that is causing the issue at the moment - it's just basic probability theory. I'm not trying to be condescending - just pointing out that we aren't even discussing the theorem of interest. These things are just simple properties of conditional probability.

 

[Jabba]

Let's take a simple counterexample to show why the likelihoods don't have to add to 1.

Imagine you are walking behind someone, and can't make out their gender very confidently. You have observed, however, that they are wearing pants. Let's assume the following probabilities:

50% of people are male, and 50% female; that is, P(Male) = 0.50
A large percentage, say 99%, of men wear pants; that is, L(Pants|Male) = 0.99
But quite a good number of women do too, say 55%; that is, L(Pants|Female) = 0.55

Now answer the following questions:
1. What is the posterior probability that the person is male?
2. Do the two likelihoods add to 1?
3. If not, is there any problem with that? Do the proportion of women who wear pants and the proportion of men who wear pants really have to sum to 1?

If that still doesn't make sense to you, I want you to forget about your immortality argument for a while and go do some actual reading to get a grasp of Bayes theorem. At the moment we are not being held up by a disagreement, but just by you not grasping the framework of Bayes theorem. Please have the humility to accept that.

Once you've done that, if you really want to apply Bayes theorem to your problem, you need to forget about this approach of trying to calculate L(me|~WEBR) from the other probability terms and instead try to find some other way of estimating this probability:

In a world with immortality or reincarnation, what would be the probability of your current existence?

Note: Even without a good grasp of Bayes theorem, it should be intuitively obvious to you that this should not be a very large probability! By your current assumption, L(me|~WEBR) is close to 1, but that's obviously not the case - for you to exist, even in a world with reincarnation or immortality, all kinds of unlikely things had to go "right".

Sorry to be harsh, but I'm not going to engage further in this discussion unless you show some actual effort at trying to grasp Bayes theorem - I have work to do.

It's not even Bayes theorem that is causing the issue at the moment - it's just basic probability theory. I'm not trying to be condescending - just pointing out that we aren't even discussing the theorem of interest. These things are just simple properties of conditional probability.

CB and Dason,

- I'm starting to think that you're both right...

- But, accepting for the moment that
1) ~WEBR is simply immortality (there's no "down time"), and
2) P(~WEBR) = .01, and
3) L(me|WEBR) is infinitesimal,
- Can't we then figure that
1) L(me|~WEBR)+L(me|WEBR) =.01, and
2) L(me|~WEBR) = .01(essentially)?

 

[CB]

- Can't we then figure that
1) L(me|~WEBR)+L(me|WEBR) =.01, and

No. There is no reason whatsoever that this should be the case. I have told you something like four times that you cannot calculate L(me|~WEBR) from the other probability values.

 

[Jabba]

It's not even Bayes theorem that is causing the issue at the moment - it's just basic probability theory. I'm not trying to be condescending - just pointing out that we aren't even discussing the theorem of interest. These things are just simple properties of conditional probability.

No. There is no reason whatsoever that this should be the case. I have told you something like four times that you cannot calculate L(me|~WEBR) from the other probability values.

17. For dummies:
a. The likelihood of a "red state" to elect Candidate X is 10%.
b. State A elects Candidate X.
c. State A is probably not a "red state."

CB,

- I accept that The above was misleading. P(BlueState|CandidateX) is not 90%.
- While the election of Candidate X does have mathematical implications re the likelihood of State A being blue, the implications are indefinite without further information. The likelihood of a "blue state" electing Candidate X could be zero %.
- I understand, and accept, that under "normal" Bayesian conditions, L(me|WEBR) + L(me|~WEBR) does not automatically equal 1.00, given that I do exist. Nor, does L(me|~WEBR) automatically equal virtually 100% if L(me|WEBR) is infinitesimal.
- My claim, at this point, is just that these are not normal Bayesian conditions...

- I'll see how well I can support that claim if you're "with me" so far.

 

[bryangoodrich]

My claim, at this point, is just that these are not normal Bayesian conditions...

Reinventing probability theory, are we? I don't think you understand, these aren't "conditions" or assumptions or anything about Bayes. This is simple conditional probability theory. The only thing you have control over are your assumed probabilities, to which anyone can say "I don't agree" because it's purely subjective. If you want objective probabilities, you'll need data.

http://courses.cs.washington.edu/courses/cse312/11wi/slides/04cprob.pdf

You should be able to understand all of these ideas as this is the basics. You showed in your work here that you don't understand the idea of total probability, that you don't understand the idea of conditional probability and how it relates (or doesn't) to the atomic probabilities. It appears you've taken an equation and wanted to fill in values so it might support your conclusions. However, that idea at its core (1) begs the question, and (2) doesn't have any substance. Logic alone doesn't say anything other than a conditional: if my antecedent hold, then the conclusion is justified. However, to make that fit reality means you have to fit reality into your antecedent, which is entirely unrealistic (all models are false at their core).