Cont: Proof of Immortality VIII

[jsfisher]

- I've changed my wording since that expression to
3. If an event is unlikely – given a particular hypothesis (H) – but the event occurs, the occurrence will tend to have a negative effect upon the probability of H — but, it need not.

So the event either does or does not affect the probability of the hypothesis. How is that a useful statement?

 

[Jabba]

These are certainly important things you'll need, but there is something far more important you will need first.



You are making numbers up. That does not help at all. More to the point, though, is how can you come up with a valid estimate of P(H) for the prior probability of H before you have defined what you mean by H, a fair nickel?

So, what do you mean by a fair nickel? Would you take that to mean a nickel is fair if and only if P(Heads) = P(Tails) = 0.5? That's what you are thinking, right? If so, then the prior and the posterior probabilities of it being a fair nickel are both zero. A perfectly correct result, but not at all informative.
Are there better choices for the meaning of "a fair nickel"?

js,
- Yeah, that's what I mean -- but, the fact that P(Heads) = P(Tails) [two priors] = .05 doesn't say anything about the posterior probability of the nickle being fair.

 

[Mojo]

js,
- Yeah, that's what I mean -- but, the fact that P(Heads) = P(Tails) [two priors] = .05 doesn't say anything about the posterior probability of the nickle being fair.

Does it land on its edge 90% of the time or something?

 

[JayUtah]

Fatal flaw 1: You err in formulating a Bayesian inference.

Since you did not address the carefully laid-out reasons behind the rules for my assignment to you, I'll assume your disobedience of them -- again -- is both flagrant and deliberate.

Answer rejected.

 

[jsfisher]

js,
- Yeah, that's what I mean -- but, the fact that P(Heads) = P(Tails) [two priors] = .05 doesn't say anything about the posterior probability of the nickle being fair.

Those are not priors. Nonetheless, if by "fair nickel" you mean the probability of it landing heads is exactly 0.5, then the probability of the nickel being fair is exactly zero.

The prior probability of the coin being fair is zero.
The posterior probability of the coin being fair will be zero.

 

[Jabba]

Fatal flaw 1: You err in formulating a Bayesian inference.

Quote:
If something occurs that is unlikely to occur -- given a particular hypothesis -- the event is evidence against the hypothesis.

No. This is expressly what statistical inference is not. One applies a statistical inference to predict an as-yet unknown outcome so as to rationally inform decisions that must be made prior to knowing the outcome. The outcome, once known, is a fact. That it was previously deemed unlikely casts no doubt on the causality that produced it.


- I've changed my wording since that expression to 3. If an event is unlikely – given a particular hypothesis (H) – but the event occurs, the occurrence will tend to have a negative effect upon the probability of H — but, it need not.
- Also, I've pointed out the effect is indefinite as there are other variables in the formula.
- Also, probability is not an absolute value, it's an estimate based upon the info we have. If all we knew about the election was that the state elected a democrat and that only 10% of "red" states elected a democrat, our best guess would be that this is a "blue" state.
- And finally, Bayesian inference includes the probability of an event -- given a particular hypothesis -- and the event being considered may have already occurred.

So the event either does or does not affect the probability of the hypothesis. How is that a useful statement?

- I didn't say that the event either does or does not affect the probability of the hypothesis. I said, that it would tend to have a negative effect upon the probability of H — but, it need not.
- Also as noted, it's just one of the variables in the formula -- and if that were all the info we had, our best guess would be "blue state."

 

[The Sparrow]

I must be missing something here about stats and proof.
Jabba seems to be saying (incorrectly) that his current existence is "more likely" if his soul is recycled.

How does "more likely" = proof and impossible to be otherwise.

Rolling a die, it is more likely that 1-5 will come up than 6 will come up. Does that mean you cannot roll a 6 on a die?

 

[Mojo]

- I didn't say that the event either does or does not affect the probability of the hypothesis. I said, that it would tend to have a negative effect upon the probability of H — but, it need not.

Do you mean that the event could have a positive or negative effect on the probability of the hypothesis, but cannot have no effect on it?

 

[jsfisher]

- I didn't say that the event either does or does not affect the probability of the hypothesis. I said, that it would tend to have a negative effect upon the probability of H — but, it need not.

Your words do not mean what you think they do, but hyper-parse away if you so desire. Either way, though, you are presenting a tautology. "It would tend to..." (it may have an effect) "but, it need not" (or it may not).

 

[Belz...]

Fatal flaw 1: You err in formulating a Bayesian inference.

Quote:
If something occurs that is unlikely to occur -- given a particular hypothesis -- the event is evidence against the hypothesis.

No. This is expressly what statistical inference is not. One applies a statistical inference to predict an as-yet unknown outcome so as to rationally inform decisions that must be made prior to knowing the outcome. The outcome, once known, is a fact. That it was previously deemed unlikely casts no doubt on the causality that produced it.


- I've changed my wording since that expression to
3. If an event is unlikely – given a particular hypothesis (H) – but the event occurs, the occurrence will tend to have a negative effect upon the probability of H — but, it need not.

- Also, I've pointed out the effect is indefinite as there are other variables in the formula.
- Also, probability is not an absolute value, it's an estimate based upon the info we have. If all we knew about the election was that the state elected a democrat and that only 10% of "red" states elected a democrat, our best guess would be that this is a "blue" state.
- And finally, Bayesian inference includes the probability of an event -- given a particular hypothesis -- and the event being considered may have already occurred.

First you say you can't do it, then you do, but with no respect towards the conditions of the request.

Why can't you do a single thing honestly, Jabba?

 

[Belz...]

- I didn't say that the event either does or does not affect the probability of the hypothesis. I said, that it would tend to have a negative effect upon the probability of H — but, it need not.

So it either does or does not affects the probability of the hypothesis negatively.

 

[Jabba]

js,
- Yeah, that's what I mean -- but, the fact that P(Heads) = P(Tails) [two priors] = .05 doesn't say anything about the posterior probability of the nickle being fair.

Those are not priors. Nonetheless, if by "fair nickel" you mean the probability of it landing heads is exactly 0.5, then the probability of the nickel being fair is exactly zero.

The prior probability of the coin being fair is zero.
The posterior probability of the coin being fair will be zero.

- I'm not getting any of this...
- If they're not priors, what are they?
- Why would the prior probability of the coin being fair be Zero?

 

[jsfisher]

- I'm not getting any of this...
- If they're not priors, what are they?

They are just probabilities. The only prior probability in the Bayesian inference would be P(H), and its posterior probability is P(H|E).

- Why would the prior probability of the coin being fair be Zero?

Your definition of fair requires the probability of heads on any given toss be exactly 0.5. Not 0.521, not 0.49999999, but exactly 0.5000000.... The probability of a coin meeting that criterion is 0.

Probabilities for continuous functions are like that.

 

[theprestige]

I think at this point we've given Jabba all the information he needs to craft posts perfectly designed to generate pages of frustration from his readers, without ever having to actually advance the debate.

I've started prepending

- I know this infuriates you,
- That's why I'm posting it​

To all of Jabba's posts. It's depressing how much sense they make that way.

 

[Belz...]

- I'm not getting any of this...

I don't believe you.

 

[Dave Rogers]

- I'm not getting any of this...
- If they're not priors, what are they?
- Why would the prior probability of the coin being fair be Zero?

Jabba,

Suppose you toss a coin ten times, and it comes up heads every time. However, you have previously examined the coin, tested it carefully, and determined unambiguously that it is completely unbiased. What is the probability, given that all ten tosses were heads, that the coin is fair?

Now, suppose you toss a coin that you know to be double-headed ten times, and it comes up heads every time. What now is the probability, given that all ten tosses were heads, that the coin is fair?

In the first case, the prior probability that the coin is fair is 1. In the second, the prior probability is zero. In the first case, therefore, the likelihood that the coin is fair is 1; it cannot be less. And in the second case, the likelihood is 0; it cannot be more.

Now, suppose you toss a third coin ten times, and it comes up heads every time. What is the probability, based on this knowledge alone, that the coin is fair? The only possible answer is that you cannot know that probability; you do not know a prior probability that the coin is fair, so you have insufficient data.

Dave

 

[Jabba]

...
Your definition of fair requires the probability of heads on any given toss be exactly 0.5. Not 0.521, not 0.49999999, but exactly 0.5000000.... The probability of a coin meeting that criterion is 0.

Probabilities for continuous functions are like that.

- I see what you mean.
- How About "fair" being a coin having the actual probability of between .501 and .499 of landing heads?



-

 

[Belz...]

- I see what you mean.
- How About "fair" being a coin having the actual probability of between .501 and .499 of landing heads?

How about you stop wasting time on things like that and do what Jay's been asking you to do for months now? It's hard to buy your excuse of not having time when you waste it on irrelevancies.

 

[jond]

- I see what you mean.
- How About "fair" being a coin having the actual probability of between .501 and .499 of landing heads?



-

- How about “fair” being that your body exists, and since we can alter your sense of self by altering your brain you need to account for your body’s existence in E, whether or not you have a soul.

 

[jsfisher]

- I see what you mean.
- How About "fair" being a coin having the actual probability of between .501 and .499 of landing heads?

jabba,
The interesting part of this little exercise is not that you have finally reached an operational definition for "fair", but the trouble you had reaching it. Do remember that this was a simple example that you put forward (because you thought you could relate to your immortality proof). It is a simple example, too, but you have stumbled at every step.

Now that you've settled on the interval, (0.499, 0.501), you'll need a probability distribution function and a bit of Calculus to come up with P(F), your prior probability for the fairness of your nickel. It is likely you have no idea what to make of the former and have no proficiency with the latter.

The only thing you have is an inference formula and a firm belief that if you plug in the right numbers you'll establish the "truth" of your immortality. You are way over your head. Your knowledge of statistics is minimal, and you simply do not know what you do not know.