[Merged] Immortality & Bayesian Statistics

[Humots]

What doesn't make sense to me in your argument is this:




By definition, the background information k is all the information that informs the prior probabilities, P(R) and P(NR). Remember that Jabba had included k in his original equation, but eventually agreed to omit it explicitly to simplify the notation. Nonetheless, k is implicit in Bayes' Theorem. Re-inserting k into the Jabba equation, gives us

[imgw=400]http://jt512.dyndns.org/images/bayes.full.png[/imgw]​

Since the term in the lhs of your equation appears in the rhs of Jabba's equation I'm confused about what you are trying to do.

Jay

I repeat: All I'm trying to do is show Jabba that I can come to a conclusion he will not accept by using his own reasoning.

I'm just playing with probability buzzwords, the way he is. I agree with everyone's objections to his "proof", and I have made my own (see posts 328 and 341).

For P(R|D), the only meaningful D entry is data that is relevant to the hypothesis R and that can be assigned a probability.

I'm trying to use Jabba's own reasoning against him as a form of http://en.wikipedia.org/wiki/Reductio_ad_absurdum. The only reason I referred to k was to copy Jabba's use of poorly-defined terms.

How about

For D = all data relevant to the validity of R and NR (such as Evolution, etc.)

P(NR|D) = P(D|NR)P(NR)/(P(D|NR)P(NR)+P(D|R)P(R))

P(R|D) = P(D|R)P(R)/(P(D|R)P(R)+P(D|NR)P(NR))

Where

1. P(D) is the probability that miracles will not replace Evolution.
2. P(D|NR) is the probability that Evolution, etc. is true given that the universe is not being run by some deity
3. P(D|R) is the probability of something like "God made the universe, and He created all the fossils to test our faith"
   P(NR) = 0.99 (re Jabba)
   P(R) = 0.01 (re Jabba)

I suspect that Jabba defined his values for P(NR) and P(R) (see http://messiahornot.com/Act2Scene2.php) to argue that even if we assign a low probability to R, the probability P(NR|me) is still vanishingly small.

 

[jt512]

I repeat: All I'm trying to do is show Jabba that I can come to a conclusion he will not accept by using his own reasoning.

I'm just playing with probability buzzwords, the way he is. I agree with everyone's objections to his "proof", and I have made my own (see posts 328 and 341).

For P(R|D), the only meaningful D entry is data that is relevant to the hypothesis R and that can be assigned a probability.

I'm trying to use Jabba's own reasoning against him as a form of http://en.wikipedia.org/wiki/Reductio_ad_absurdum. The only reason I referred to k was to copy Jabba's use of poorly-defined terms.

How about

For D = all data relevant to the validity of R and NR (such as Evolution, etc.)

P(NR|D) = P(D|NR)P(NR)/(P(D|NR)P(NR)+P(D|R)P(R))

OK, I think I understand what you're trying to do. You're assuming that all relevant information is incorporated into D. That is, there is no background information (what Jabba and I called 'k'), since, by definition, background information is information that was used to derive the prior probabilities.

I don't actually think that your argument is reductio ad absurdum. I think you've actually hit upon the major flaw in his argument, namely, that he has not considered all the data.

P(R|D) = P(D|R)P(R)/(P(D|R)P(R)+P(D|NR)P(NR))

Or simply P(R|D) = 1 – P(NR|D)

Where

1. P(D) is the probability that miracles will not replace Evolution.
2. P(D|NR) is the probability that Evolution, etc. is true given that the universe is not being run by some deity
3. P(D|R) is the probability of something like "God made the universe, and He created all the fossils to test our faith"

To do this right, it is probably unfair to the R hypothesis to treat "evolution" as data. Evolution is part of the NR hypothesis. The physical facts that suggest evolution (the fossil record, molecular biology, etc.) would be components of D and hence components of D|R and D|NR. Your P(D|R) should probably be stated something along the lines of "the probability of the fossil record, etc, given that the universe is not run by some deity"; and your P(D|NR) should be stated something like "the probability of the fossil record, etc, given that the universe is run by some deity."

P(NR) = 0.99 (re Jabba)
P(R) = 0.01 (re Jabba)

If you are including all relevant information in D, then that implies that there was no prior information, and therefore your P(NR) and P(R) should equal .5, since you have no information on which to base a preference for either hypothesis.

I suspect that Jabba defined his values for P(NR) and P(R) (see http://messiahornot.com/Act2Scene2.php) to argue that even if we assign a low probability to R, the probability P(NR|me) is still vanishingly small.

In practice, that is what one often does when it is difficult to specify a precise value for the prior probability of your hypothesis. That is, you specify a lower bound on it, thereby arguing a fortiori. That said, I don't think .01 is a reasonable lower bound on P(R), and I don't know what one would be. If I were to attempt to use Bayes' Theorem to estimate posterior probabilities for R or NR, I'd probably start with prior probabilities of .5, and then do what you are (I think) outlining, that is, try to incorporate all relevant information in D.

Jay

 

[wollery]

OK, I think I understand what you're trying to do. You're assuming that all relevant information is incorporated into D. That is, there is no background information (what Jabba and I called 'k'), since, by definition, background information is information that was used to derive the prior probabilities.

I don't actually think that your argument is reductio ad absurdum. I think you've actually hit upon the major flaw in his argument, namely, that he has not considered all the data.

What data?

That's his main problem.

 

[Humots]

OK, I think I understand what you're trying to do. You're assuming that all relevant information is incorporated into D. That is, there is no background information (what Jabba and I called 'k'), since, by definition, background information is information that was used to derive the prior probabilities.

I don't actually think that your argument is reductio ad absurdum. I think you've actually hit upon the major flaw in his argument, namely, that he has not considered all the data.




Or simply P(R|D) = 1 – P(NR|D)




To do this right, it is probably unfair to the R hypothesis to treat "evolution" as data. Evolution is part of the NR hypothesis. The physical facts that suggest evolution (the fossil record, molecular biology, etc.) would be components of D and hence components of D|R and D|NR. Your P(D|R) should probably be stated something along the lines of "the probability of the fossil record, etc, given that the universe is not run by some deity"; and your P(D|NR) should be stated something like "the probability of the fossil record, etc, given that the universe is run by some deity."




If you are including all relevant information in D, then that implies that there was no prior information, and therefore your P(NR) and P(R) should equal .5, since you have no information on which to base a preference for either hypothesis.





In practice, that is what one often does when it is difficult to specify a precise value for the prior probability of your hypothesis. That is, you specify a lower bound on it, thereby arguing a fortiori. That said, I don't think .01 is a reasonable lower bound on P(R), and I don't know what one would be. If I were to attempt to use Bayes' Theorem to estimate posterior probabilities for R or NR, I'd probably start with prior probabilities of .5, and then do what you are (I think) outlining, that is, try to incorporate all relevant information in D.

Jay

Right on, well stated.

Just one thing. Shouldn't that be:

Your P(D|R) should probably be stated something along the lines of "the probability of the fossil record, etc, given that the universe is run by some deity"; and your P(D|NR) should be stated something like "the probability of the fossil record, etc, given that the universe is not run by some deity."

 

[shuttlt]

What data?

That's his main problem.

Can't he just use his intuition that he is special and inherently remarkably surprising given the assumption that we are not immortal to fill in approximate values?

 

[jt512]

Just one thing. Shouldn't that be:

Your P(D|R) should probably be stated something along the lines of "the probability of the fossil record, etc, given that the universe is run by some deity"; and your P(D|NR) should be stated something like "the probability of the fossil record, etc, given that the universe is not run by some deity."

Yeah. I wrote that backwards.

Jay

 

[Jabba]

JT & Humots,
- You guys are too fast for me.
- First, in P(NR|D) = P(D|NR)P(NR)/(P(D|NR)P(NR)+P(D|R)P(R)), you've substituted "D" for "me" -- I don't understand that...
--- Jabba

 

[Jabba]

- It might help to change a couple of my terms. I shouldn’t have used “Religious” and “Non-Religious.” I should have just used “current popular scientific model” and its complement – “S” and “NS.” The complement doesn’t have to be something “religious.”
- And, what I'm calling the current popular scientific model is that each of us has -- at most -- only one short life to live.
--- Jabba

 

[Jabba]

- I guess that you're just substituting "D" for "k"?
- I guess that you're saying that we could apply Bayes inference to "k" itself?
--- Jabba

 

[Nay_Sayer]

Day 24 of my immortality: To test out my powers I tried offing myself with explosive's, poison and electricity. Still here, Also ran into a young man named Duncan, I suspect he may be immortal as I am, I may have to kill him, There can only be one.

 

[Humots]

- I guess that you're just substituting "D" for "k"?
- I guess that you're saying that we could apply Bayes inference to "k" itself?
--- Jabba

Jay was critiquing my original argument in post 232. That's the one where I determine the probability of the NR and R hypotheses, using your approach to Bayes inference.

I am now using
D = the fossil record, molecular biology, that support evolution

P(D) = the probability of the fossil record, etc. being true
P(D|R) = the probability of the fossil record, etc. being true, given that the universe is run by some deity
P(D|NR) = the probability of the fossil record, etc. being true, given that the universe is not run by some deity

with
P(D|R) = 0.01 or less, since if the Religious hypothesis is true, most
if not all of D is false
P(D|NR) = 0.99 or more, since D fits a universe not run by a deity very well
P(NR) = 0.99 (your own argument)
P(R) = 0.01 (your own argument)

The probability of the NR hypothesis given D is now
P(NR|D) = P(D|NR)P(NR)/(P(D|NR)P(NR)+P(D|R)P(R))
= 0.99 * 0.99/0(.99 * 0.99 +0.01 * 0.01)
= 0.9801 / (0.9801 + .0001) = 0.9999

The probability of the R hypothesis given D is now
P(R|D) = P(D|R)P(R)/(P(D|R)P(R)+P(D|NR)P(NR))
= .01 * .01 / (.01 * .01 + .99 * .99) = .0001

Let me reiterate: this is not your argument as to the value of P(NR|me & k), this is my argument (as modified) from post 232, showing that by using your approach to Bayes inference and your probability values, we come to an interesting result.

Using

 

[Giordano]

I realize that we are currently only at the beginning of Jabba's proof, which focuses on the probability of such a unique individual as Jabba existing. Of course the approach is inherently invalid as explained to, but ignored by, Jabba. But I will be even more interested in Jabba's calculation as to how this relates to immortality. I presume the fact that no one has ever observed or experienced immortality is likely to weight the statistics rather strongly against the immortality hypothesis. I wonder how Jabba incorporates that data into his equations.

 

[tsig]

Day 24 of my immortality: To test out my powers I tried offing myself with explosive's, poison and electricity. Still here, Also ran into a young man named Duncan, I suspect he may be immortal as I am, I may have to kill him, There can only be one.

The more I read this thread the less will I have to even live out this life let alone want to be immortal.

 

[Jabba]

Jay was critiquing my original argument in post 232. That's the one where I determine the probability of the NR and R hypotheses, using your approach to Bayes inference.

I am now using
D = the fossil record, molecular biology, that support evolution

P(D) = the probability of the fossil record, etc. being true
P(D|R) = the probability of the fossil record, etc. being true, given that the universe is run by some deity
P(D|NR) = the probability of the fossil record, etc. being true, given that the universe is not run by some deity

with
P(D|R) = 0.01 or less, since if the Religious hypothesis is true, most
if not all of D is false
P(D|NR) = 0.99 or more, since D fits a universe not run by a deity very well
P(NR) = 0.99 (your own argument)
P(R) = 0.01 (your own argument)

The probability of the NR hypothesis given D is now
P(NR|D) = P(D|NR)P(NR)/(P(D|NR)P(NR)+P(D|R)P(R))
= 0.99 * 0.99/0(.99 * 0.99 +0.01 * 0.01)
= 0.9801 / (0.9801 + .0001) = 0.9999

The probability of the R hypothesis given D is now
P(R|D) = P(D|R)P(R)/(P(D|R)P(R)+P(D|NR)P(NR))
= .01 * .01 / (.01 * .01 + .99 * .99) = .0001

Let me reiterate: this is not your argument as to the value of P(NR|me & k), this is my argument (as modified) from post 232, showing that by using your approach to Bayes inference and your probability values, we come to an interesting result.

Using

Humots,
- I'm still struggling.
- So far, to me, D seems like just a major part of k, and P(R|k) is not appropriate as the left side of the Bayes Theorem. Am I wrong?
--- Jabba

 

[Humots]

Humots,
- I'm still struggling.
- So far, to me, D seems like just a major part of k, and P(R|k) is not appropriate as the left side of the Bayes Theorem. Am I wrong?
--- Jabba

By D I am referring to specific, well-defined data: the fossil record, molecular biology, DNA evidence, and so on, that are relevant to the argument of whether the universe is (R) or is not (NR) run by a deity.

k = "all knowledge" is poorly defined, too poorly to be included as data in Bayes inference. Neither is R as you originally defined it.

So P(R|k) is not appropriate as the left side of the Bayes Theorem, or on the right either.

NR = "current popular scientific model" = "each of us has -- at most -- only one short life to live" is also poorly defined.

The current scientific model says a great deal more than that, and is not simply a "popular" model, any more than "The Earth circles the sun" is a popular model.

So P(NR|k) is not appropriate either.

I say again, you are plugging vague notions into a mathematical model that requires precisely defined variables.

 

[Jabba]

Jay, do you agree with what Humots just said?
--- jabba

 

[jt512]

Jay, do you agree with what Humots just said?
--- jabba

I agree that your hypotheses need to be stated more specifically.

Jay

 

[Jabba]

I agree that your hypotheses need to be stated more specifically.

Jay

Jay,
- I'll try to be more specific, but I don't really understand why they are not specific enough already.
- I have two hypotheses -- one, the complement of the other. Could be that what I've called them confuses the issue -- "R" and "NR," for instance. I should probably just name them "A" and "Non-A," with A being simply "we each live only one, short, life at most."
- Would that help?
--- Jabba

 

[jt512]

Jay,
- I'll try to be more specific, but I don't really understand why they are not specific enough already.
- I have two hypotheses -- one, the complement of the other. Could be that what I've called them confuses the issue -- "R" and "NR," for instance. I should probably just name them "A" and "Non-A," with A being simply "we each live only one, short, life at most."
- Would that help?
--- Jabba

No, because you didn't do anything.

But, if that's your hypothesis, then there is no data at all to support the alternative.

Jay

 

[abaddon]

Jay,
- I'll try to be more specific, but I don't really understand why they are not specific enough already.
- I have two hypotheses -- one, the complement of the other. Could be that what I've called them confuses the issue -- "R" and "NR," for instance. I should probably just name them "A" and "Non-A," with A being simply "we each live only one, short, life at most."
- Would that help?
--- Jabba

Changing the labels makes no difference. At all. One might as well choose "banana" and "non-banana". They are just labels.