Originally posted by DoctorScribbles
You are miscalculating P(A). Recall that P(A) is a prior probability. You must do it from a position of ignorance about the truth of A itself.

Rethink your formulation of A and your calculation of P(A) for a second.
A is "The player comes forward."
Then when you calculate P(A), you assume that he did in fact come forward, when that's the very + .0001(1/1000)=.0001

This results in the prior not being perturbed by the "evidence."

I think you're muddling things because the two odds are the same.

There are, in fact, 3 possibilities for coming forward.

1) He would have cheated had he not won legitimately = 0.001*1/1000
2) He would not have cheated but won legitimately = 0.999*1/1000
3) He lost but he cheated = 0.001*999/1000

I just added 1 and 2 in my first term, but you're forgetting either 2 or 3 (I think that because numerically they are the same)

Edit - Ok, you edited a part out so part of my post doesn't make much sense. I'm not assuming that he comes forward, I'm calculating the probability that he does so I must assess all possibilities.

Edit 2 - I'm assuming that he must buy a ticket in order to fake it. Is that not so? If he doesn't need to buy, then the number of potential individuals that don't buy tickets needs to be precised.

Originally posted by Palynka
I think you're muddling things because the two odds are the same.

There are, in fact, 3 possibilities for coming forward.

1) He would have cheated had he not won legitimately = 0.001*1/1000
2) He would not have cheated but won legitimately = 0.999*1/1000
3) He lost but he cheated = 0.001*999/1000

I just added 1 and 2 in my first term, but you're f y, then the number of potential individuals that don't buy tickets needs to be precised.

Arithmetic is always my Achilles' Heel. Your numbers were correct from the start.

But in your model, how do you account for the actual winner not coming forward while the cheater always does, given that the problem stipulates only one person coming forward?

Originally posted by DoctorScribbles
Arithmetic is always my Achilles' Heel. Your numbers were correct from the start.

What time is it over there? Get some sleep man! 😉

Originally posted by Palynka
What time is it over there? Get some sleep man! 😉

1:41 am

By God, I think I will retire for the evening, after another fruitful day in Spirituality.

Originally posted by DoctorScribbles
In Bayesian analysis, all of that incriminating evidence is accounted for in the P(E) and P(E|I) terms, to be ultimately reflected in the revised P(I|E) term.

But you were not talking about Bayesian analysis, you were talking about the Justice system. So why should a Judge use P(I) as his starting point?

Originally posted by DoctorScribbles
But in your model, how do you account for the actual winner not coming forward while the cheater always does, given that the problem stipulates only one person coming forward?

Lotteries don't always have winners.

Originally posted by twhitehead
But you were not talking about Bayesian analysis, you were talking about the Justice system. So why should a Judge use P(I) as his starting point?

In the United States, the law requires him to presume that all defendants are innocent until evidence is presented. Are you asking what the merits of this system are, or are you asking if this is empirically a faulty input to the Bayesian model?

Originally posted by twhitehead
Lotteries don't always have winners.

I know, like in the Shirley Jackson story, for example.

But seriously, I guess we were using the term a bit differently. I presumed that exactly one ticket was a winner, since otherwise you can't draw any conclusions at all about how possessing a winning ticket affects the conditional probability of cheating until you specify how likely it is that any ticket is a legitimate winner.

Originally posted by DoctorScribbles
In the United States, the law requires him to presume that all defendants are innocent until evidence is presented. Are you asking what the merits of this system are, or are you asking if this is empirically a faulty input to the Bayesian model?

I was referring to you statement "This high P(I) is the Bayesian component corresponding to that doctrine." and your implication that the Bayesian model somehow justifies the Justice system. I do think that if the Justice system was about determining probability then yes it is empirically faulty. However I think that the Innocent until proven guilty law is based on the belief that an innocent man being convicted is worse than a guilty man being set free. Some dictator ships do not think that to be the case as there is a higher risk to the dictator when a guilty man is set free and little impact when an innocent man is convicted (the dictators conscience is hardened) so they would rather go with guilty until proven innocent. A similar situation arises when the accused is holding a gun. A policeman man may shoot to kill even when guilt has not in fact been established and effectively goes with a tentative 'guilty until proven innocent' when confronted with an armed man.

Originally posted by DoctorScribbles
I know, like in the Shirley Jackson story, for example.

But seriously, I guess we were using the term a bit differently. I presumed that exactly one ticket was a winner, since otherwise you can't draw any conclusions at all about how possessing a winning ticket affects the conditional probability of cheating until you specify how likely it is that any ticket is a legitimate winner.

In my experience (it may be different in the states), a lottery is a game where there is no guaranteed winner (and frequently is no winner) whereas a game where there is one and only one guaranteed winner is called a raffle.

I dont know who Shirley Jackson is I'll have to Google it.

Originally posted by twhitehead
In my experience (it may be different in the states), a lottery is a game where there is no guaranteed winner (and frequently is no winner) whereas a game where there is one and only one guaranteed winner is called a raffle.

I dont know who Shirley Jackson is I'll have to Google it.

Here you go. My favorite short story ever.

http://www.americanliterature.com/SS/SS16.HTML

Originally posted by twhitehead
I was referring to you statement "This high P(I) is the Bayesian component corresponding to that doctrine." and your implication that the Bayesian model somehow justifies the Justice system. I do think that if the Justice system was about determining probability then yes it is empirically faulty. However I think that the Innocent until proven guilty law i ...[text shortened]... vely goes with a tentative 'guilty until proven innocent' when confronted with an armed man.

This really is related to type I and type II errors, not to Bayesian computations. Do you know what these errors are? (Sorry, I don't know if you have a mathematical formation...)

Originally posted by Palynka
This really is related to type I and type II errors, not to Bayesian computations. Do you know what these errors are? (Sorry, I don't know if you have a mathematical formation...)

I have a degree in mathematics but never did much in probability and that was over 10 years ago, so no, I don't know what type I and type II errors are and am basically struggling to understand what everyone is talking about here.
But I do think that a presumption of innocence of the accused in the legal system cannot be justified via the claim that the probability of innocence of a random person is very low. Even before evidence is presented the probability of guilt is higher than for the average person. In fact due to the high costs there are many cases where the state will not even prosecute unless they already think they can get a guilty verdict so in those cases the likelihood of the accused guilt is very high indeed.

Originally posted by twhitehead
I have a degree in mathematics but never did much in probability and that was over 10 years ago, so no, I don't know what type I and type II errors are and am basically struggling to understand what everyone is talking about here.
But I do think that a presumption of innocence of the accused in the legal system cannot be justified via the claim that the ...[text shortened]... get a guilty verdict so in those cases the likelihood of the accused guilt is very high indeed.

I'm short on time but check this out if you're interested:
http://www.intuitor.com/statistics/T1T2Errors.html

Originally posted by DoctorScribbles
Here you go. My favorite short story ever.

http://www.americanliterature.com/SS/SS16.HTML

How could such a horrible commentary upon humankind be your favorite story?

Nemesio