[Merged] Immortality & Bayesian Statistics

[Toontown]

If p is the probability of an event A, that is, P(A) = p, then the odds of the event A, odds(A), is defined as odds(A) = p / (1–p), which is the reciprocal of your expression. That is, your expression is actually the odds of the complement of A.

Wrong.

That is not odds to 1 you are expressing there. What you are expressing there is something like the proportion of p to non-p.

p = 0.2

0.2/(1-0.2) = 0.25 , which is definitely not odds to 1, or anything useful.

If you want odds to 1, do it like this: 1/0.2-1 = 4 to 1

 

[jt512]

Wrong.

That is not odds to 1 you are expressing there. What you are expressing there is something like the proportion of p to non-p.

p = 0.2

0.2/(1-0.2) = 0.25 , which is definitely not odds to 1, or anything useful.

Sorry, but you don't know what you are talking about. The mathematical definition of odds is p / (1–p), the probability of the event of interest divided by the probability of the complementary event. You can verify that by just looking at the wikipedia article on "odds." If P(A) = .2, then indeed odds(A) = .2 / .8 = .25 or 1/4. In informal usage this is sometimes written as "1:4" or "1 to 4."

If you want odds to 1, do it like this: 1/0.2-1 = 4 to 1

I have never heard the phrase "odds to 1" or seen it in any textbook of probability. What you are calling "odds to 1" is the odds of the complement of the event whose probability is .2. That is if P(A) = .2, then P(~A) = .8, and odds(~A) = .8 / .2 = 4, which is the inverse of the odds of A itself: odds(A) = .25.

 

[Toontown]

I have never heard the phrase "odds to 1" or seen it in any textbook of probability. What you are calling "odds to 1" is the odds of the complement of the event whose probability is .2. That is if P(A) = .2, then P(~A) = .8, and odds(~A) = .8 / .2 = 4, which is the inverse of the odds of A itself: odds(A) = .25.

What I'm calling odds to 1 is, in fact, odds to 1. What I've been talking about is, in fact, odds to 1.

So it is, in fact, you who do not know what I am talking about, while I and millions of other people around the world know exactly what I'm talking about. It's called odds to 1.

http://en.wikipedia.org/wiki/Odds

I'll let you know when I have a use for your odds thingie. Offhand, no particular use is occurring to me at the present time. But I'll let you know.

 

[jt512]

What I'm calling odds to 1 is, in fact, odds to 1. What I've been talking about is, in fact, odds to 1.

So it is, in fact, you who do not know what I am talking about, while I and millions of other people around the world know exactly what I'm talking about. It's called odds to 1.

http://en.wikipedia.org/wiki/Odds

Since neither the phrase "odds to one" or "odds to 1" appears anywhere on the wikipedia "odds" page, it is difficult to understand why you would cite it as a reference. On the other hand, the article does say this: "In probability theory and statistics, where the variable p is the probability in favor of a binary event, and the probability against the event is therefore 1-p, "the odds" of the event are the quotient of the two, or p / (1–p)," which is precisely the definition that I gave.

I'll let you know when I have a use for your odds thingie. Offhand, no particular use is occurring to me at the present time. But I'll let you know.

Remind why I, a professional statistician, should care (or even be surprised) that you can't think of why odds is useful (while somehow simultaneously thinking that its reciprocal is).

To a statistician, odds is extremely useful. First of all, it is the relative probability of two events, a useful quantity in its own right. Secondly, it transforms a probability, whose range is [0, 1] to a quantity whose range is [0, +∞], which makes it an easier quantity to deal with in some mathematical models. Moreover, we can take the log of the odds to give us a quantity whose range is the entire real line, allowing us to model it by using relatively simple linear models.

In Bayesian inference, the ratio of the posterior odds of a hypothesis to the prior odds is the Bayes factor, the impact of the current evidence on the relative plausibility of the two hypotheses.

In epidemiology, the ratio of the odds of exposure among those with a disease divided by the odds of exposure of those not having the disease is the gives the odds ratio, which is the effect of the exposure on the likelihood of disease. The odds ratio is important because it, unlikely the relative risk, can be calculated in retrospective studies.

Besides, you say the "odds to one" of an event A with P(A)=.2 is 4 is a useful quantity, but it's reciprocal .25 is not. That is patently absurd, since it's just the reciprocal! And what about the "odds to one" on an event B with P(B)=.8? It's "odds to one" is .25. Is that useful, but it's reciprocal (its actual odds) 4 not useful? How so?

 

[Toontown]

Since neither the phrase "odds to one" or "odds to 1" appears anywhere on the wikipedia "odds" page, it is difficult to understand why you would cite it as a reference.

Why should it be difficult for you when the article gives actual examples? As a professional statistician, you are capable of reasoning, right? Here's a little exercise for you. From the page:

"The odds in favor of an event or a proposition is the ratio of the probability that the event will happen to the probability that the event will not happen. For example, the odds that a randomly chosen day of the week is a Sunday are one to six, which is sometimes written 1 : 6.;[1] see section 1.5 of Gelman et al. (2003).

'Odds' are an expression of relative probabilities. Often 'odds' are quoted as odds against, rather than as odds in favor. For example, the probability that a random day is a Sunday is one-seventh (1/7), hence the odds that a random day is a Sunday are 1 : 6. The odds against a random day being a Sunday are 6 : 1. The first figure represents the number of ways of failing to achieve the outcome and the second figure is the number of ways of achieving a favorable outcome."

Now, think really hard and read very carefully. What do you suppose the highlighted expression would be referring to, except odds to 1? See that 1 there? That means it's odds to 1. It is called "odds to 1" because it is expressed as odds to 1, or 6 "ways" against to 1 "way" for.

Perhaps this explains why you've never seen anything about odds to 1 in any book. It was right in front of your face, and you still didn't see it.

 

[jt512]

'Odds' are an expression of relative probabilities. Often 'odds' are quoted as odds against, rather than as odds in favor. For example, the probability that a random day is a Sunday is one-seventh (1/7), hence the odds that a random day is a Sunday are 1 : 6. The odds against a random day being a Sunday are 6 : 1. The first figure represents the number of ways of failing to achieve the outcome and the second figure is the number of ways of achieving a favorable outcome."

Sorry, but you've still made up your own term, "odds to one," or unwittingly acquired it from someone else who made it up.

Your made-up term "odds to one" of an event A is actually the reciprocal of the odds of A; that is, the odds against the event.

It is hilarious that you can simultaneously believe that that the odds of the event is useless, but the odds against the event is useful. That is absurd in its own right, but even more so when you consider that the odds against an event is simply the odds of another event (the complement of the event). Thus you contradict yourself when you say that one is useful but the other is not.

 

[Toontown]

Sorry, but you've still made up your own term, "odds to one," or unwittingly acquired it from someone else who made it up.

Wrong, and it is in fact an accurate descriptive term for the kind of odds being expressed, and expressed in such a way as not to be confused with your proportion. It is, in fact, odds to 1.

your made-up term "odds to one" of an event A is actually the reciprocal of the odds of A; that is, the odds against the event.

Expressed as ways against vs (1) way for. Hence, "odds to 1". Not to be confused with "odds".

Just out of curiosity: How much of your remaining ludicrously improbable sliver of sentience prior to the onset of eternal nothingness do you plan to devote to your little exercise in word-naziism? Because it's slipping away.

 

[jt512]

Just out of curiosity: How much of your remaining ludicrously improbable sliver of sentience prior to the onset of eternal nothingness do you plan to devote to your little exercise in word-naziism? Because it's slipping away.

Exactly as much as I intend to devote to anything you have to say in the future.

 

[Toontown]

Exactly as much as I intend to devote to anything you have to say in the future.

Does that mean you won't be clumsily attempting to pointlessly browbeat me any more?

See, it works like this. When I verbally express 6 : 1, I say "six to one".

 

[Toontown]

Who ARE these people? Goddamn, it takes forever to get permission to say "odds to 1"

Ist verboten!! Nevermind the fact that when you verbally express 6 : 1, you actually say "six to one".

 

[jt512]

It is simple to convert probability to odds, and odds to probability, and not even unusual. It's two ways of expressing the same proportion.

1/p-1 = odds to 1

1/(odds+1) = p

How funny that you don't realize that in your second equation you are using my definition of odds, the one you claim is unuseful.

 

[Toontown]

So, I suppose that in order to remain in the good graces of these bean counters, I would have to do this

0.2/(1-0.2) = 0.25

And then hit the reciprocal key, instead of doing this

1/0.2-1 = 4

If I want to calculate the verboten you-know-what, even though my way is simpler. Because the bean counters prefer that it be done their way.

But if I insist on doing it my way, and it suddenly becomes imperative that I obtain the statistician-beloved "odds", I will have to hit the reciprocal key. Oh, the bother. But I still eliminate the parentheses doing it my way. So I'm still a step ahead. But no matter.

And then there is the stupid convention of calling a proportion "odds", and stubbornly insisting that everyone else do it too, and call the verboten you-know-what the "reciprocal of the odds". Even though the verboten is in fact the real odds against, and the other thing is in reality the reciprocal of the real odds against. Against 1, of course. But it's verboten to say it, for some weird terminological reason. Which, apparently, is a real word, since the spell-checker did not alert on it.

All this, when there was really no need to calculate anything at all, but I was called to task to explain myself for using odds terminology to express an idea, which cross-threaded a bean counter.

Because we are rigorous up in here, because Jabba said he was going to try to "prove" something. And we are rigorously testing the proper conventional usage of words and definitions, like never before. Rigorously, I tell you.

http://www.youtube.com/watch?v=WANNqr-vcx0

Rigorously.

 

[Toontown]

How funny that you don't realize that in your second equation you are using my definition of odds, the one you claim is unuseful.

How funny that you don't realize that you're wrong about that too.

1/(4+1) = 0.2 = p(A)

not 0.25, the vaunted reciprocal of the real odds against.

 

[Akhenaten]

Immortality?

Anyone?

 

[Pixel42]

I know. So who was the 5-year-old "you", who didn't have the same memories or even the same atoms as the current "you"?

There never was any standardized "you" in the first place

Exactly. That's the point I was trying to make - that the whole concept of personal identity, and hence what is meant by immortality and reincarnation etc, is a great deal more slippery than is being recognised by Jabba in his musings.

Death? Do the producers of this course know all about death? Not much to know about that, is there?

Shelly Kagan summarises the thoughts of generations of philosophers about the soul, the question of personal identity, the meaning of immortality and many other fascinating questions. I really can't recommend the course highly enough.

I'm sure the course is fascinating, but I have a ludicrously improbable sliver of sentience remaining prior to the onset of eternal nothingness, and a book to read.

If you've got time to converse with the likes of Jabba (and indeed with the rest of us) you've got time to watch at least a few of the lectures.

Incidentally I'm a graduate mathematician and I've never heard the phrase "odds to one" before either. Probability is confusing and counter-intuitive enough as it is, it's probably not wise to make up your own terms and expect other people to understand them.

 

[jt512]

How funny that you don't realize that you're wrong about that too.

1/(4+1) = 0.2 = p(A)

not 0.25, the vaunted reciprocal of the real odds against.

I stand corrected on that point. Your equations are consistent.

 

[Agatha]

Immortality?

Anyone?

Bueller? Bueller?

So far, I've got:

1. Some people find it scary to contemplate their own non-existence after their death.
2. Making up real numbers and assigning them to possibilities that may or may not be real is pointless.
3. Diversions into statistics and probability theory.
4. ????? (possibly "collect underpants").
5. Profit! Immortality!

Unless and until Jabba shows that there is, or could be, anything other than the "standard scientific model", assigning a probability of the SSM of less than 1 seems utterly futile to me.

 

[Jabba]

Toon,
- I have all sorts of questions. I'll start off with two:
1) What is your opinion concerning free will?

It it walks like a free duck, and quacks like a free duck, it's a free duck.

Don't look a free duck in the mouth.

Toon,
- I think you're saying that you believe that we do have free will. Is that correct?

 

[Akhenaten]

Toon,
- I think you're saying that you believe that we do have free will. Is that correct?

Jabba, you posted this a year ago:

- I think that I can essentially prove immortality using Bayesian statistics.

Why are you now wasting what you claim to be your precious time querying someone who only joined the thread three weeks ago about his beliefs in a completely unrelated topic?

 

[Jabba]

Immortality seems to be the only way I'll ever get Jabba to explain his numbers. If I had to live several lifetimes (I neither expect or want to live more than this one), I suspect in some future one I'd still be asking how Jabba calculated the probabilities he put into his Bayes' theorem.

Agatha,
- I'm not sure the following will answer your question. If it doesn't, please reword your question. Thanks.

- Below, “SM” is the current consensus “Scientific Model”; “NSM” is any possible explanatory model other than the “SM.” “k” is existing knowledge minus the implications I perceive in the fact of my own existence. Here’s the formula:
- P(SM|me) = P(me|SM)*P(SM|k)/P(me|SM)*P(SM|k)+P(me|NSM)*P(NSM|k)

- 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%.

- Consequently:
- P(SM|me) = (~.0000…1)*(.99)/(~.0000…1)(.99)+(.9)(.01)
- P(SM|me) = ~.0000…1/~.0000…1+.009
- P(SM|me) = ~.0000…1/~.009
- P(SM|me) = ~.0000…1 [/QUOTE]